NETWORKING 2007, Ad Hoc and Sensor Networks, Wireless Networks, Next Generation Internet, 6 conf

Lecture Notes in Computer Science Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen

Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen University of Dortmund, Germany Madhu Sudan Massachusetts Institute of Technology, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Moshe Y. Vardi Rice University, Houston, TX, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany

4479

Ian F. Akyildiz Raghupathy Sivakumar Eylem Ekici Jaudelice Cavalcante de Oliveira Janise McNair (Eds.)

NETWORKING 2007 Ad Hoc and Sensor Networks, Wireless Networks, Next Generation Internet 6th International IFIP-TC6 Networking Conference Atlanta, GA, USA, May 14-18, 2007 Proceedings

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Volume Editors Ian F. Akyildiz Raghupathy Sivakumar Georgia Institute of Technology, School of Electrical and Computer Engineering Atlanta, GA 30332, USA E-mail: {ian, siva}@ece.gatech.edu Eylem Ekici The Ohio State University, Department of Electrical and Computer Engineering Columbus, OH 43210, USA E-mail: [email protected] Jaudelice Cavalcante de Oliveira Drexel University, ECE Department, Bossone 312 Philadelphia, PA 19104-2875, USA E-mail: [email protected] Janise McNair University of Florida, Department of Electrical and Computer Engineering Gainesville, FL 32611, USA E-mail: [email protected]

Library of Congress Control Number: 2007926314 CR Subject Classification (1998): C.2, C.4, H.4, D.2, J.2, J.1, K.6, K.4 LNCS Sublibrary: SL 5 – Computer Communication Networks and Telecommunications ISSN ISBN-10 ISBN-13

0302-9743 3-540-72605-5 Springer Berlin Heidelberg New York 978-3-540-72605-0 Springer Berlin Heidelberg New York

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © 2007 IFIP International Federation for Information Processing, Hofstraße 3, 2361 Laxenburg, Austria Printed in Germany Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper SPIN: 12066407 06/3180 543210

Preface

General Chairs’ Message It is our great pleasure to welcome you to the Sixth IFIP Networking conference held in Atlanta, May 14–18, 2007. This conference, the sixth of a planned series of annual meetings with a highly selective and a highly competitive technical program, has been established to serve as the premier forum to cover research on all aspects of networking and communication issues. The conference is intended to involve multiple networking paradigms such as wireless and wired networks, ad-hoc networks, sensor networks, mesh networks, and optical networks. An exciting and high-quality technical program was put together by Eylem Ekici, Jaudelice C. de Oliveira and Janise McNair with the help of an exceptional panel of experts who served on the Technical Program Committee. We were very fortunate to have Eylem, Jau and Janice as the Program Chairs to launch the IFIP Networking 2007 conference on a path of academic excellence and practical relevance; we express our sincere thanks to them. Together, they put together a high-quality program that educated attendees and at the same time inspired spirited discussions. A poster session and social events provided other opportunities for discussions, debates and exchange of information amongst conference participants. Chuanyi Ji, the Local Arrangements Chair, performed a good job overseeing all aspects of the meeting planning and organization. Our very special thanks go to Chuanyi for making sure it all happened just right. Faramarz Fekri, our Financial Chair, did an outstanding job to keep the books orderly. Our sincere and special thanks go to Faramarz for his exceptional handling of the finances, and going over and beyond his call of duty to take care of other aspects of the conference organization as well. Benny Bing did an excellent job in collecting the camera-ready papers from the authors and making sure to publish the conference proceedings on time. The co-operation and support of Springer in this matter is also greatly appreciated. We thank Cordai Farrar, who provided essential administrative and logistical assistance to Chuanyi and Faramarz in the planning and implementation of the conference. We also would like to acknowledge the efforts and contributions of Linda Jiang Xie and Ozgur B. Akan, who coordinated and implemented publicity for the conference as well as the management of the Web site. We express appreciation to Ed Knightly, Sherman (Xuemin) Shen and Josep Sole Pareta for raising sponsorship for the conference, to Mehmet Can Vuran and Vehbi Cagri Gungor, the Registration Chairs, to Giacomo Morabito, the Tutorials Chair, and to Giovanni Pau and George Kormentzas, the Workshop Chairs, for all their invaluable contributions. We also thank the members of the Steering Committee

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Preface

for providing much needed support and guidance during the organization of the conference. Finally, we thank all our industry sponsors who provided financial assistance toward the conference organization. We look forward to an exciting week of sharing technical ideas and visions with colleagues from around the world. We hope that you will find the conference to be very engaging and fruitful. We thank you for attending the conference and being a part of this very important event. May 2007

Ian F. Akyildiz Raghupathy Sivakumar IFIP Networking 2007 General Co-chairs

Technical Program Chairs’ Message

Welcome to Networking 2007! Networking 2007 was the sixth event in a series of International Conferences on Networking sponsored by the IFIP Technical Committee on Communication Systems (TC 6). Previous events were held in Paris (France) in 2000, Pisa (Italy) in 2002, Athens (Greece) in 2004, Waterloo (Canada) in 2005, and Coimbra (Portugal) in 2006. Networking 2007 brought together active and proficient members of the networking community, from both academia and industry, thus contributing to scientific, strategic, and practical advances in the broad and fast-evolving field of communications. The conference comprised highly technical sessions organized thematically, keynote talks, tutorials offered by experts, as well as workshops and panel discussions on topical themes. Plenary sessions with keynote speeches opened the daily sessions, covering the three main tracks of the conference. The Networking 2007 call for papers attracted 440 submissions from 40 different countries in Asia, Australia, Europe, North America, and South America. These were subject to thorough review by the Program Committee members and additional reviewers. A one-week discussion phase followed the regular review deadline where TPC leaders summarized comments made by the other reviewers and made a final recommendation. A high-quality selection of 96 full papers and 27 posters, organized into 24 regular sessions and 1 poster session, made up the Networking 2007 main technical program, which covered next-generation networks: content distribution, quality of service, topology design, routing, buffer management, optical networks, TCP, security, network measurement; ad hoc and sensor networks: connectivity and coverage, scheduling and resource allocation, mobility and location, routing, and key management; wireless networks: mesh networks, mobility, TCP, MAC performance, scheduling and resource allocation. The technical program was complemented by three keynote speeches: “Looking into the Future: Grand Challenges for Wireless Networks,” by Ness Shroff (Purdue University); “Key Technologies and Architectures for Next-Generation Networks,” by Krishan Sabnani (Bell Labs); and “Urban Mesh Networks: Coming Soon to a City Near You,” by Ed Knightly (Rice University). In addition to the main technical program, the day preceding the conference was dedicated to three excellent tutorials on “An Introduction to Network Coding,” by Muriel Medard (MIT), “Cognitive Radio Networks,” by Ian F. Akyildiz (Georgia Institute of Technology), and “WiMAX: Technology for Broadband Wireless Internet and QoS Driven Routing: Theoretical and Experimental Considerations,” by Shailender Timiri and Shantidev Mohanty (Intel Corporation).

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Preface

The final day of Networking 2007 was dedicated to two one-day workshops, on the following topics: “Security and Privacy in Mobile and Wireless Networking,” and “Challenges for Next-Generation Networks.” We would like to express our appreciation of the efforts of many people in making Networking 2007 a successful event: to the authors, we are most grateful to the hundreds of authors who spent countless hours preparing their submitted papers; to the Program Committee and to all associated reviewers: we thank you for your hard work, your promptness in submitting reviews, and your willingness and patience to accept extra assignments; to the other Executive Committee members: we thank you for your hard work and dedication to the organizational issues surrounding Networking 2007. Last, but by no means least, we thank our sponsors and supporting institutions, all the people that helped us at the Georgia Institute of Technology, and specially all the volunteers. March 2007

Eylem Ekici Janise McNair Jaudelice C. de Oliveira

Organization

Executive Committee General Co-chairs

Technical Program Co-chairs

Tutorial Chair Workshop Co-chairs

Publicity Co-chairs

Sponsor Co-chairs

Publication Chair Finance Chair Registration Co-chairs

Local Arrangements Chair

Ian F. Akyildiz (Georgia Institute of Technology, USA) Raghupathy Sivakumar (Georgia Institute of Technology, USA) Eylem Ekici (Ohio State University, USA) Janise McNair (University of Florida, USA) Jaudelice C. de Oliveira (Drexel University, USA) Giacomo Morabito (University of Catania, Italy) Giovanni Pau (University of California at Los Angeles, USA) George Kormentzas (University of Aegean, Greece) Ozgur Akan (Middle East Technical University, Turkey) Jiang (Linda) Xie (University of North Carolina-Charlotte, USA) Edward Knightly (Rice University, USA) Sherman Shen (University of Waterloo, Canada) Josep Sole Pareta (Universitat Polit`ecnica de Catalunya, Spain) Benny Bing (Georgia Institute of Technology, USA) Faramarz Fekri (Georgia Institute of Technology, USA) Mehmet Can Vuran (Georgia Institute of Technology, USA) Vehbi Cagri Gungor (Georgia Institute of Technology, USA) Chuanyi Ji (Georgia Institute of Technology, USA)

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Organization

Steering Committee Harry Perros (North Carolina State University, USA) Augusto Casaca (IST/INESC, Portugal) Guy Omidyar (TC6 WG6.8 Chair, USA) Guy Pujolle (University of Paris 6, France) Ioannis Stavrakakis (University of Athens, Greece) Otto Spaniol (RWTH-Aachen University, Germany)

Technical Program Committee Alhussein Abouzeid (Rensselaer Polytechnic Institute, USA) Nael Abu-Ghazaleh (State University of New York at Binghamton, USA) Rui Aguiar (Universidade de Aveiro, Portugal) Ozgur Akan (Middle East Technical University, Turkey) Kemal Akkaya (Southern Illinois University, USA) Fatih Alagoz (Bogazici University, Turkey) Kevin Almeroth (University of California at Santa Barbara, USA) Mostafa Ammar (Georgia Institute of Technology, USA) Tricha Anjali (Illinois Institute of Technology, USA) Regina Araujo (Federal University of So Carlos, Brazil) Lichun Bao (University of California at Irvine, USA) Stefano Basagni (Northeastern University, USA) Christian Bettstetter (University of Klagenfurt, Austria) Raheem Beyah (Georgia State University, USA) Andrea Bianco (Politecnico di Torino, Italy) Semih Bilgen (Middle East Technical University (ODTU), Turkey) Chris Blondia (University of Antwerp, Belgium) Fernando Boavida (Coimbra University, Portugal) Azzedine Boukerche (University of Ottawa, Canada) Torsten Braun (University of Bern, Switzerland) Milind Buddhikot (Bell Labs, Lucent Technologies, USA) Wojciech Burakowski (Warsaw University of Technology, Poland) Tracy Camp (Colorado School of Mines, USA) Guohong Cao (Pennsylvania State University, USA) Antonio Capone (Politecnico di Milano, Italy) Matteo Cesana (Politecnico di Milano, Italy) Chih-Yung Chang (Tamkang University, Taiwan) Han-Chieh Chao (National Ilan University, Taiwan) Edgar Chavez (Universidad Michoacana, Mexico) Ling-Jyh Chen (Academia Sinica, Taiwan) Yuh-Shyan Chen (National Taipei University, Taiwan) Sunghyun Choi (Seoul National University, Korea) Marco Conti (IIT-CNR, Italy) Jun-Hong Cui (University of Connecticut, USA) Jaudelice C. de Oliveira (Drexel University, USA)

Organization

Michel Diaz (LAAS, France) Constantinos Dovrolis (Georgia Institute of Technology, USA) Falko Dressler (University of Erlangen, Germany) Stephan Eidenbenz (Los Alamos National Laboratory, USA) Eylem Ekici (Ohio State University, USA) Hesham El-Rewini (Southern Methodist University, USA) Tamer ElBatt (San Diego Research Center, Inc., USA) Mourad Elhadef (University of Ottawa, Canada) Ehab Elmallah (University of Alberta, Canada) Ozgur Ercetin (Sabanci University, Turkey) Laura Feeney (Swedish Institute of Computer Science, Sweden) Wu-chi Feng (Portland State University, USA) Joe Finney (Lancaster University, UK) Eric Fleury (Insa de Lyon / INRIA, France) Mario Freire (University of Beira Interior, Portugal) Andrea Fumagalli (University of Texas at Dallas, USA) Laura Galluccio (University of Catania, Italy) Sabastia Galmes (Universitat de Ies Illes Balears, Spain) Javier Gomez (National University of Mexico, Mexico) Isabelle Guerin Lassous (INRIA, France) Ozgur Gurbuz (Sabanci University, Turkey) Eren Gurses (Norwegian University of Science and Technology, Norway) Guenter Haring (Universit˝ at Wien, Austria) Paul Havinga (University of Twente, The Netherlands) Ahmed Helmy (University of Southern California, USA) Raquel Hill (Indiana University, USA) Xiaoyan Hong (University of Alabama, USA) Hung-Yun Hsieh (National Taiwan University, Taiwan) Frank Huebner (AT&T Labs, USA) David Hutchison (Lancaster University, UK) Muhammad Jaseemuddin (Ryerson University, Canada) Vana Kalogeraki (University of California at Riverside, USA) Holger Karl (University of Paderborn, Germany) Can Emre Koksal (Ohio State University, USA) Kimon Kontovasilis (NCSR Demokritos, Greece) Turgay Korkmaz (University of Texas at San Antonio, USA) Sastri Kota (Harris Corporation, USA) Yevgeni Koucheryavy (Tampere University of Technology, Finland) Evangelos Kranakis (Carleton University, Canada) Bhaskar Krishnamachari (University of Southern California, USA) Srikanth Krishnamurthy (University of California at Riverside, USA) Santosh Kumar (University of Memphis, USA) Thomas Kunz (Carleton University, Canada) Miguel Labrador (University of South Florida, USA) Bu Sung Lee (Nanyang Technological University, Singapore)

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Organization

Chang-Gun Lee (Seoul National University, Korea) Sung-Ju Lee (HP Labs, USA) Kenji Leibnitz (Osaka University, Japan) Albert Levi (Sabanci University, Turkey) Baochun Li (University of Toronto, Canada) Jie Li (University of Tsukuba, Japan) Wei Li (University of Toledo, USA) Ben Liang (University of Toronto, Canada) Leszek Lilien (Western Michigan University, USA) Yung-Hsiang Lu (Purdue University, USA) Athina Markopoulou (University of California, Irvine, USA) Jose Marzo (Universitat de Girona, Spain) Xavier Masip-Bruin (Technical University of Catalonia (UPC), Spain) Mustafa Matalgah (University of Mississippi, USA) Ibrahim Matta (Boston University, USA) Ketan Mayer-Patel (University of North Carolina, USA) Janise McNair (University of Florida, USA) Sirisha Medidi (Washington State University, USA) Abdelhamid Mellouk (University Paris XII, France) Paulo Mendes (DoCoMo Eurolabs, Germany) Michael Menth (University of W¨ urzburg, Germany) Jelena Misic (University of Manitoba, Canada) Shantidev Mohanty (Intel Corporation, USA) Edmundo Monteiro (University of Coimbra, Portugal) Giacomo Morabito (University of Catania, Italy) Nidal Nasser (University of Guelph, Canada) Srihari Nelakuditi (University of South Carolina, USA) Ioanis Nikolaidis (University of Alberta, Canada) Stephan Olariu (Old Dominion University, USA) Joao Orvalho (IPC, Portugal) Giovanni Pau (University of California at Los Angeles, USA) Harry Perros (North Carolina State University, USA) Chiara Petrioli (University of Rome “La Sapienza,” Italy) Niki Pissinou (Florida International University, USA) Thomas Plagemann (University of Oslo, Norway) Radha Poovendran (University of Washington, USA) Konstantinos Psounis (University of Southern California, USA) Ramon Puigjaner (UIB, Spain) Guy Pujolle (University of Paris 6, France) Hazem Refai (Oklahoma University, USA) Reza Rejaie (University of Oregon, USA) George Rouskas (North Carolina State University, USA) Sergio S´ anchez-L´opez (Technical University of Catalonia, Spain) Paolo Santi (CNR, Italy) Caterina Scoglio (Kansas State University, USA) Subhabrata Sen (AT&T Labs - Research, USA)

Organization

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Harish Sethu (Drexel University, USA) Ness Shroff (Purdue University, USA) Jorge Silva (University of Coimbra, Portugal) Harry Skianis (National Centre for Scientific Research ‘Demokritos’, Greece) Josep Sole Pareta (UPC, Spain) Otto Spaniol (Aachen University of Technology, Germany) Burkhard Stiller (University of Z¨ urich and ETH Z¨ urich, Switzerland) Ivan Stojmenovic (University of Ottawa, Canada) Aaron Striegel (University of Notre Dame, USA) Tony Sun (University of California at Los Angeles, USA) Karthikeyan Sundaresan (Georgia Institute of Technology, USA) Violet Syrotiuk (Arizona State University, USA) Vassilis Tsaoussidis (Demokritos University, Greece) Tuna Tugcu (Bogazici University, Turkey) Damla Turgut (University of Central Florida, USA) Piet Van Mieghem (Delft University of Technology, The Netherlands) Ramanuja Vedantham (Georgia Institute of Technology, USA) Wenye Wang (NC State University, USA) Xudong Wang (Kiyon, Inc., USA) Steven Weber (Drexel University, USA) Cedric Westphal (Nokia, USA) Lars Wolf (Technical University of Braunschweig, IBR, Germany) Yang Xiao (University of Alabama, USA) Jiang (Linda) Xie (University of North Carolina at Charlotte, USA) Dong Xuan (The Ohio State University, USA) Guoliang Xue (Arizona State University, USA) Boon Sain Yeo (Wavex Technologies, Singapore) Mohamed Younis (University of Maryland Baltimore County, USA) Moustafa Youssef (University of Maryland, USA) Honghai Zhang (Lucent Technologies, USA) Lixia Zhang (University of California at Los Angeles, USA) Yongbing Zhang (University of Tsukuba, Japan) Rong Zheng (University of Houston, USA) Fang Zhu (Verizon, USA) Hao Zhu (Florida International University, USA) Taieb Znati (University of Pittsburgh, USA)

Additional Reviewers Ibrahim Abualhaol Helmut Adam Rui Aguiar Markus Anwander Jesus Arango Baris Atakan

Jeroen Avonts Abdel Aziz Leonardo Badia Seung Baek Mario Barbera Pere Barlet-Ros

Sujoy Basu V´eronique Baudin Osama Bazan Luca Becchetti Alper Bereketli Johan Bergs

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Organization

Antoni Bibiloni Ali Bicak Steven Borbash Bart Braem Tiago Camilo Luca Campelli Davide Careglio Maxweel Carmo Eduardo Cerqueira Coskun Cetinkaya Sriram Chellappan Chao Chen Kuan-Ta Chen Yuh-Shyan Chen Maggie Cheng Roman Chertov Harshal Chhaya Philip Chimento Girish Chiruvolu Youngkyu Choi Cherita Corbett Vedat Coskun Paul Coulton S´ergio Cris´ostomo Sukrit Dasgupta Peter De Cleyn Isabel Dietrich Stylianos Dimitriou Lun Dong Yu Dong Khalil Drira Roman Dunaytsev Christopher Edwards Hesham Elsayed Thierry Ernst Amir Esmailpour Ramon Fabregat Silvia Farraposo Wissam Fawaz Xin Fei Anja Feldmann Pep-Lluis Ferrer Stefano Ferretti Ilario Filippini Rosario Firrincieli

Pedro M. F. M. Ferreira Alexandre Fonte James Gadze Wilfried Gansterer Mar´ıa L. Garc´ıa-Osma Ghayathri Garudapuram Damianos Gavalas Samik Ghosh Paolo Giaccone Silvia Giordano Oscar Gonzalez de Dios Jorge Granjal Vehbi Cagri Gungor Vaibhav Gupta Burak Gurdag Michael Gyarmati Thomas Hacker Omar Hammouri Seon Yeong Han Yuning He Mohamed Hefeeda Helmut Hlavacs Philipp Hofmann Carl Hu Cunqing Hua Pai-Han Huang Mehmet Isik Mikel Izal Mandana Jafarian Gentian Jakllari Jakub Jakubiak Jiwoong Jeong Yusheng Ji Tao Jiang Yingxin Jiang Changhee Joo Teodor Jov’ Carlos Juiz Eleni Kamateri Arzad Kherani Anna Kim Seongkwan Kim Vinay Kolar Jiejun Kong Ibrahim Korpeoglu

Li Lao Anis Laouiti Lap Kong Law Gabriela Leao Mauro Leoncini Nicolas Letor Chengzhi Li Hyuk Lim Ching-Ju Lin Yuan Lin Anders Lindgren Changlei Liu David Liu Jun Liu Jun Liu Ke Liu Yunhuai Liu Mahdi Lotfinezhad Ngok-Wah Ma Dhia Mahjoub Lefteris Mamatas Devu Manikantan Shila Cesar Marcondes Gustavo Marfia Eva Marin/Tordera Ruediger Martin Saverio Mascolo Marco Mellia Michela Meo Lyudmila Mihaylova Fabio Milan Dragan Milic Ingrid Moerman Dmitri Moltchanov Edmundo Monteiro Paolo Monti Xenia Mountrouidou Bala Natarajan Konstantinos Oikonomou Sema Oktug Evgeny Osipov Philippe Owezarski Claudio Palazzi Alessandro Panconesi

Organization

Michael Pascoe Stefan Penz Fabio Picconi Jonathan Pitts Ioannis Psaras Chunming Qiao Sundaram Rajagopalan Thierry Rakotoarivelo Rabie Ramadan Ulrich Reimers Mauricio Resende Jorge Rodriguez Sanchez Utz Roedig Sylwia Romaszko Kevin Ross Dario Rossi Emilia Rosti Nararat Ruangchaijatupon Christos Samaras Kamil Sarac Lambros Sarakis Emre Sayin Matthias Scheidegger Udo Schilcher Francesco Scoto Karim Seddik Alexandro Sentinelli Bartomeu Serra Ghalib Shah Manolis Sifalakis Paulo Simoes

Paul Smith Aaron So Rute Sofia Fernando Solano Donado Christoph Sommer Hanhee Song Hui Song Kathleen Spaey Vladimir Stankovic Thomas Staub Daniel Stutzbach Weilian Su Kyoungwon Suh Oguz Sunay Violet Syrotiuk Lei Tang Saurabh Tewari George Theodorakopoulos Masoomeh Torabzadeh Laurent Toutain Ageliki Tsioliaridou Tuna Tugcu Li-Ping Tung Alexander Tyrrell Suleyman Uludag Anna Urra Nicolas Van Wambeke Giacomo Verticale Michael Voorhaen Serdar Vural Mehmet Vuran

Markus Waelchli Gerald Wagenknecht Jiong Wang Lan Wang Alicia Washington Song Wei Wei Wei Michael Welzl Ralf Wienzek Damon Wischik Rita Wouhaybi Kai Wu Yan Wu Ariton Xhafa Yufeng Xin Kaiqi Xiong Lisong Xu Guang Yang Sichao Yang Yi Yang Marcelo Yannuzzi Sakir Yucel Ahmed Zahran Qian Zhang Wensheng Zhang Jing Zhao Qunwei Zheng Shengli Zhou Yuanyuan Zhou Zhong Zhou Andre Zimmermann Michele Zorzi

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Table of Contents

Ad Hoc and Sensor Networks AHS - Connectivity and Coverage On the Resilient Overlay Topology Formation in Multi-hop Wireless Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fei Xing and Wenye Wang

1

Placing and Maintaining a Core Node in Wireless Ad Hoc Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Amit Dvir and Michael Segal

13

Flooding Speed in Wireless Multihop Networks with Randomized Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vasil Mizorov, J¨ org Widmer, Robert Vilzmann, and Petri M¨ ah¨ onen

25

AHS - Scheduling and Resource Allocation Power Amplifier Characteristic-Aware Energy-Efficient Transmission Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kwanghun Han, Youngkyu Choi, Sunghyun Choi, and Youngwoo Kwon

37

Energy Efficient Throughput Optimization in Multi-hop Wireless Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dan Xu and Xin Liu

49

Election Based Hybrid Channel Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xin Wang and J.J. Garcia-Luna-Aceves

61

Asynchronous Data Aggregation for Real-Time Monitoring in Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jie Feng, Derek L. Eager, and Dwight Makaroff

73

AHS - Mobility and Location Awareness A Novel Agent-Based User-Network Communication Model in Wireless Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sang-Sik Kim and Ae-Soon Park

85

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Table of Contents

Realistic Mobility and Propagation Framework for MANET Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mesut G¨ une¸s, Martin Wenig, and Alexander Zimmermann

97

Localization for Large-Scale Underwater Sensor Networks . . . . . . . . . . . . . Zhong Zhou, Jun-Hong Cui, and Shengli Zhou

108

Location-Unaware Sensing Range Assignment in Sensor Networks . . . . . . Ossama Younis, Srinivasan Ramasubramanian, and Marwan Krunz

120

AHS - Routing I A Distributed Energy-Efficient Topology Control Routing for Mobile Wireless Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yan Ren, Bo Wang, Sidong Zhang, and Hongke Zhang

132

Integrated Clustering and Routing Strategies for Large Scale Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ataul Bari, Arunita Jaekel, and Subir Bandyopadhyay

143

On-Demand Routing in Disrupted Environments . . . . . . . . . . . . . . . . . . . . . Jay Boice, J.J. Garcia-Luna-Aceves, and Katia Obraczka

155

Delivery Guarantees in Predictable Disruption Tolerant Networks . . . . . . Jean-Marc Fran¸cois and Guy Leduc

167

AHS - Routing II PWave: A Multi-source Multi-sink Anycast Routing Framework for Wireless Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Haiyang Liu, Zhi-Li Zhang, Jaideep Srivastava, and Victor Firoiu

179

Simple Models for the Performance Evaluation of a Class of Two-Hop Relay Protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ahmad Al Hanbali, Arzad A. Kherani, and Philippe Nain

191

Maximum Energy Welfare Routing in Wireless Sensor Networks . . . . . . . Changsoo Ok, Prasenjit Mitra, Seokcheon Lee, and Soundar Kumara

203

Analysis of Location Privacy/Energy Efficiency Tradeoffs in Wireless Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sergio Armenia, Giacomo Morabito, and Sergio Palazzo

215

Efficient Error Recovery Using Network Coding in Underwater Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zheng Guo, Bing Wang, and Jun-Hong Cui

227

Table of Contents

XIX

AHS - Key Management Key Predistribution Schemes for Sensor Networks for Continuous Deployment Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ¨ u, Onsel ¨ Abd¨ ulhakim Unl¨ Arma˘gan, Albert Levi, Erkay Sava¸s, and ¨ ur Er¸cetin Ozg¨

239

Using Auxiliary Sensors for Pairwise Key Establishment in WSN . . . . . . . Qi Dong and Donggang Liu

251

Privacy-Aware Multi-Context RFID Infrastructure Using Public Key Cryptography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ¨ ur Er¸cetin Selim Kaya, Erkay Sava¸s, Albert Levi, and Ozg¨

263

Wireless Networks WiNet - Mesh Networks Minimum Cost Configuration of Relay and Channel Infrastructure in Heterogeneous Wireless Mesh Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aaron So and Ben Liang Optimization Models for the Radio Planning of Wireless Mesh Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Edoardo Amaldi, Antonio Capone, Matteo Cesana, and Federico Malucelli

275

287

Interference-Aware Multicasting in Wireless Mesh Networks . . . . . . . . . . . Sudheendra Murthy, Abhishek Goswami, and Arunabha Sen

299

Characterizing the Capacity Gain of Stream Control Scheduling in MIMO Wireless Mesh Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yue Wang, Dah Ming Chiu, and John C.S. Lui

311

WiNet - Mobility AP and MN-Centric Mobility Prediction: A Comparative Study Based on Wireless Traces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jean-Marc Fran¸cois and Guy Leduc

322

A Flexible and Distributed Home Agent Architecture for Mobile IPv6-Based Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Albert Cabellos-Aparicio and Jordi Domingo-Pascual

333

Using PANA for Mobile IPv6 Bootstrapping . . . . . . . . . . . . . . . . . . . . . . . . . Julien Bournelle, Jean-Michel Combes, Maryline Laurent-Maknavicius, and Sondes Larafa

345

XX

Table of Contents

Detecting 802.11 Wireless Hosts from Remote Passive Observations . . . . Valeria Baiamonte, Konstantina Papagiannaki, and Gianluca Iannaccone

356

WiNet - TCP A Scheme for Enhancing TCP Fairness and Throughput in IEEE 802.11 WLANs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eun-Jong Lee, Hyung-Taig Lim, Seung-Joon Seok, and Chul-Hee Kang

368

TCP NJ+: Packet Loss Differentiated Transmission Mechanism Robust to High BER Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jungrae Kim, Jahwan Koo, and Hyunseung Choo

380

TCP WestwoodVT: A Novel Technique for Discriminating the Cause of Packet Loss in Wireless Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jahwan Koo, Sung-Gon Mun, and Hyunseung Choo

391

Modeling TCP in a Multi-rate Multi-user CDMA System . . . . . . . . . . . . . Majid Ghaderi, Ashwin Sridharan, Hui Zang, Don Towsley, and Rene Cruz

403

WiNet - MAC Performance IEEE 802.11b Cooperative Protocols: A Performance Study . . . . . . . . . . . Niraj Agarwal, Divya ChanneGowda, Lakshmi Narasimhan Kannan, Marco Tacca, and Andrea Fumagalli It Is Better to Give Than to Receive – Implications of Cooperation in a Real Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thanasis Korakis, Zhifeng Tao, Salik Makda, Boris Gitelman, and Shivendra Panwar

415

427

Modeling Approximations for an IEEE 802.11 WLAN Under Poisson MAC-Level Arrivals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ioannis Koukoutsidis and Vasilios A. Siris

439

Performance and Equilibrium Analysis of Heterogeneous IEEE 802.11 Based WLANs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hao Zhu

450

Exploring a New Approach to Collision Avoidance in Wireless Ad Hoc Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jun Peng and Liang Cheng

462

Table of Contents

XXI

WiNet - Scheduling and Resource Allocation Video Rate Adaptation and Scheduling in Multi-rate Wireless Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sourav Pal, Sumantra R. Kundu, Amin R. Mazloom, and Sajal K. Das

475

On Scheduling and Interference Coordination Policies for Multicell OFDMA Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G´ abor Fodor

488

Distributed Uplink Scheduling in CDMA Networks . . . . . . . . . . . . . . . . . . . Ashwin Sridharan, Ramesh Subbaraman, and Roch Gu´erin

500

Resource Allocation in DVB-RCS Satellite Systems . . . . . . . . . . . . . . . . . . Andr´e-Luc Beylot, Riadh Dhaou, and C´edric Baudoin

511

WiNet - Miscellaneous Enhanced Downlink Capacity in UMTS Supported by Direct Mobile-to-Mobile Data Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Larissa Popova, Thomas Herpel, and Wolfgang Koch

522

Impact of Technology Overlap in Next-Generation Wireless Heterogeneous Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ahmed Zahran, Ben Liang, and Aladdin Saleh

535

An On-Line Measurement-Based Admission Control for VBR Video Traffic in Wireless Multimedia Home Networks . . . . . . . . . . . . . . . . . . . . . . Yi-Hsien Tseng, Eric Hsiao-Kuang Wu, and Gen-Huey Chen

546

On Event Signal Reconstruction in Wireless Sensor Networks . . . . . . . . . . ¨ ur B. Akan Barı¸s Atakan and Ozg¨

558

Next Generation Internet NGI -Content Distribution Peer-Assisted On-Demand Streaming of Stored Media Using BitTorrent-Like Protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Niklas Carlsson and Derek L. Eager

570

Multiple Identities in BitTorrent Networks . . . . . . . . . . . . . . . . . . . . . . . . . . Jin Sun, Anirban Banerjee, and Michalis Faloutsos

582

Graph Based Modeling of P2P Streaming Systems . . . . . . . . . . . . . . . . . . . Damiano Carra, Renato Lo Cigno, and Ernst W. Biersack

594

XXII

Table of Contents

Modeling Seed Scheduling Strategies in BitTorrent . . . . . . . . . . . . . . . . . . . Pietro Michiardi, Krishna Ramachandran, and Biplab Sikdar

606

NGI -QoS I Streaming Performance in Multiple-Tree-Based Overlays . . . . . . . . . . . . . . Gy¨ orgy D´ an, Vikt´ oria Fodor, and Ilias Chatzidrossos

617

Path Selection Using Available Bandwidth Estimation in Overlay-Based Video Streaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Manish Jain and Constantine Dovrolis

628

Fundamental Tradeoffs in Distributed Algorithms for Rate Adaptive Multimedia Streams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vilas Veeraraghavan and Steven Weber

640

Optimal Policies for Playing Buffered Media Streams . . . . . . . . . . . . . . . . . Steven Weber

652

NGI - Qos II Non-parametric and Self-tuning Measurement-Based Admission Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thomas Michael Bohnert, Edmundo Monteiro, Yevgeni Koucheryavy, and Dmitri Moltchanov

664

Optimal Rate Allocation in Overlay Content Distribution . . . . . . . . . . . . . Chuan Wu and Baochun Li

678

SLA Adaptation for Service Overlay Networks . . . . . . . . . . . . . . . . . . . . . . . Con Tran, Zbigniew Dziong, and Michal Pi´ oro

691

NGI - Topology Design Virtual Private Network to Spanning Tree Mapping . . . . . . . . . . . . . . . . . . Yannick Brehon, Daniel Kofman, and Augusto Casaca

703

Optimal Topology Design for Overlay Networks . . . . . . . . . . . . . . . . . . . . . . Mina Kamel, Caterina Scoglio, and Todd Easton

714

Construction of a Proxy-Based Overlay Skeleton Tree for Large-Scale Real-Time Group Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jun Guo and Sanjay Jha

726

Increasing the Coverage of a Cooperative Internet Topology Discovery Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Benoit Donnet, Bradley Huffaker, Timur Friedman, and K.C. Claffy

738

Table of Contents

XXIII

NGI - Routing I Robust IP Link Costs for Multilayer Resilience . . . . . . . . . . . . . . . . . . . . . . Michael Menth, Matthias Hartmann, and R¨ udiger Martin

749

Integer SPM: Intelligent Path Selection for Resilient Networks . . . . . . . . . R¨ udiger Martin, Michael Menth, and Ulrich Sp¨ orlein

762

Beyond Centrality - Classifying Topological Significance Using Backup Efficiency and Alternative Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yuval Shavitt and Yaron Singer

774

Incorporating Protection Mechanisms in the Dynamic Multi-layer Routing Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anna Urra, Eusebi Calle Ortega, Jose L. Marzo, and Pere Vila

786

NGI - Routing II Accelerated Packet Placement Architecture for Parallel Shared Memory Routers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Brad Matthews, Itamar Elhanany, and Vahid Tabatabaee

797

RSVP-TE Extensions to Provide Guarantee of Service to MPLS . . . . . . . Francisco J. Rodr´ıguez-P´erez, Jos´e Luis Gonz´ alez-S´ anchez, and Alfonso Gazo-Cervero

808

An Adaptive Management Approach to Resolving Policy Conflicts . . . . . Selma Yilmaz and Ibrahim Matta

820

Reinforcement Learning-Based Load Shared Sequential Routing . . . . . . . . Fariba Heidari, Shie Mannor, and Lorne G. Mason

832

NGI - Buffer Management An Adaptive Neuron AQM for a Stable Internet . . . . . . . . . . . . . . . . . . . . . Jinsheng Sun and Moshe Zukerman Light-Weight Control of Non-responsive Traffic with Low Buffer Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Venkatesh Ramaswamy, Leticia Cu´ellar, Stephan Eidenbenz, Nicolas Hengartner, Christoph Amb¨ uhl, and Birgitta Weber

844

855

The Effects of Fairness in Buffer Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mei Wang and Yashar Ganjali

867

Time to Buffer Overflow in an MMPP Queue . . . . . . . . . . . . . . . . . . . . . . . . Andrzej Chydzinski

879

XXIV

Table of Contents

NGI - Miscellaneous Fundamental Effects of Clustering on the Euclidean Embedding of Internet Hosts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sanghwan Lee, Zhi-Li Zhang, Sambit Sahu, Debanjan Saha, and Mukund Srinivasan

890

A Multihoming Based IPv4/IPv6 Transition Approach . . . . . . . . . . . . . . . Lizhong Xie, Jun Bi, and Jianping Wu

902

Offline and Online Network Traffic Characterization . . . . . . . . . . . . . . . . . . Su Zhang, Mary K. Vernon

912

Catching IP Traffic Burstiness with a Lightweight Generator . . . . . . . . . . Chlo´e Rolland, Julien Ridoux, and Bruno Baynat

924

NGI - Optical Networks Importance of the Maturity of Photonic Component Industry on the Business Prospects of Optical Access Networks: A Techno-Economic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dimitris Varoutas, Thomas Kamalakis, Dimitris Katsianis, Thomas Sphicopoulos, and Thomas Monath

935

The Token Based Switch: Per-Packet Access Authorisation to Optical Shortcuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mihai-Lucian Cristea, Leon Gommans, Li Xu, and Herbert Bos

945

Online Multicasting in WDM Networks with Shared Light Splitter Bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yuzhen Liu and Weifa Liang

958

Evaluation of Optical Burst-Switching as a Multiservice Environment . . . Pablo Jes´ us Argibay-Losada, Andres Su´ arez-Gonz´ alez, Manuel Fern´ andez-Veiga, Ra´ ul Rodr´ıguez-Rubio, and C´ andido L´ opez-Garc´ıa

970

NGI -TCP The TCP Minimum RTO Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ioannis Psaras and Vassilis Tsaoussidis

981

Improving XCP to Achieve Max-Min Fair Bandwidth Allocation . . . . . . . Lei Zan and Xiaowei Yang

992

TCP Libra: Exploring RTT-Fairness for TCP . . . . . . . . . . . . . . . . . . . . . . . . 1005 Gustavo Marfia, Claudio Palazzi, Giovanni Pau, Mario Gerla, M.Y. Sanadidi, and Marco Roccetti

Table of Contents

XXV

Interactions of Intelligent Route Control with TCP Congestion Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014 Ruomei Gao, Dana Blair, Constantine Dovrolis, Monique Morrow, and Ellen Zegura

NGI - Security Fast and Scalable Classification of Structured Data in the Network . . . . 1026 Sumantra R. Kundu, Sourav Pal, Christoph L. Schuba, and Sajal K. Das An Efficient and Secure Event Signature (EASES) Protocol for Peer-to-PeerMassively Multiplayer Online Games . . . . . . . . . . . . . . . . . . . . 1037 Mo-Che Chan, Shun-Yun Hu, and Jehn-Ruey Jiang Unified Defense Against DDoS Attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047 M. Muthuprasanna, G. Manimaran, and Z. Wang Integrity-Aware Bandwidth Guarding Approach in P2P Networks . . . . . . 1060 Wen-Hui Chiang, Ling-Jyh Chen, and Cheng-Fu Chou

NGI - Network Measurement Measuring Bandwidth Signatures of Network Paths . . . . . . . . . . . . . . . . . . . 1072 Mradula Neginhal, Khaled Harfoush, and Harry Perros A Non-cooperative Active Measurement Technique for Estimating the Average and Variance of the One-Way Delay . . . . . . . . . . . . . . . . . . . . . . . . 1084 Antonio A. de A. Rocha, Rosa M.M. Le˜ ao, and Edmundo de Souza e Silva The P2P War: Someone Is Monitoring Your Activities! . . . . . . . . . . . . . . . 1096 Anirban Banerjee, Michalis Faloutsos, and Laxmi Bhuyan On-Line Predictive Load Shedding for Network Monitoring . . . . . . . . . . . . 1108 Pere Barlet-Ros, Diego Amores-L´ opez, Gianluca Iannaccone, Josep Sanju` as-Cuxart, and Josep Sol´e-Pareta On the Schedulability of Measurement Conflict in Overlay Networks . . . . 1120 Mohammad Fraiwan and G. Manimaran

Poster Session SEA-LABS: A Wireless Sensor Network for Sustained Monitoring of Coral Reefs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1132 Matt Bromage, Katia Obraczka, and Donald Potts

XXVI

Table of Contents

Capacity-Fairness Performance of an Ad Hoc IEEE 802.11 WLAN with Noncooperative Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136 Jerzy Konorski Multi-rate Support for Network-Wide Broadcasting in MANETs . . . . . . . 1140 Tolga Numanoglu, Wendi Heinzelman, and Bulent Tavli BRD: Bilateral Route Discovery in Mobile Ad Hoc Networks . . . . . . . . . . 1145 Rendong Bai and Mukesh Singhal Correction, Generalisation and Validation of the “Max-Min d-Cluster Formation Heuristic” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1149 Alexandre Delye de Clauzade de Mazieux, Michel Marot, and Monique Becker Analytical Performance Evaluation of Distributed Multicast Algorithms for Directional Communications in WANETs . . . . . . . . . . . . . . . . . . . . . . . . 1153 Song Guo, Oliver Yang, and Victor Leung Beyond Proportional Fair: Designing Robust Wireless Schedulers . . . . . . . 1157 Soshant Bali, Sridhar Machiraju, and Hui Zang A Voluntary Relaying MAC Protocol for Multi-rate Wireless Local Area Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1161 Jaeeun Na, Yeonkwon Jeong, and Joongsoo Ma Throughput Analysis Considering Capture Effect in IEEE 802.11 Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1165 Ge Xiaohu, Yan Dong, Zhu Yaoting Performance Improvement of IEEE 802.15.4 Beacon-Enabled WPAN with Superframe Adaptation Via Traffic Indication . . . . . . . . . . . . . . . . . . . 1169 Zeeshan Hameed Mir, Changsu Suh, and Young-Bae Ko Analysis of WLAN Traffic in the Wild . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1173 Caleb Phillips and Suresh Singh Enhanced Rate Adaptation Schemes with Collision Awareness . . . . . . . . . 1179 Seongkwan Kim, Sunghyun Choi, Daji Qiao, and Jongseok Kim A Study of Performance Improvement in EAP . . . . . . . . . . . . . . . . . . . . . . . 1183 Eun-Chul Cha and Hyoung-Kee Choi Characterization of Ultra Wideband Channel in Data Centers . . . . . . . . . 1187 N. Udar, K. Kant, R. Viswanathan, and D. Cheung Evaluating Internal BGP Networks from the Data Plane . . . . . . . . . . . . . . 1192 Feng Zhao, Xicheng Lu, Baosheng Wang, and Peidong Zhu

Table of Contents XXVII

Performance of a Partially Shared Buffer with Correlated Arrivals . . . . . . 1196 Dieter Fiems, Bart Steyaert, and Herwig Bruneel Filter-Based RFD: Can We Stabilize Network Without Sacrificing Reachability Too Much? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1200 Ke Zhang and S. Felix Wu Network Access in a Diversified Internet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1204 Michael Wilson, Fred Kuhns, and Jonathan Turner Outburst: Efficient Overlay Content Distribution with Rateless Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1208 Chuan Wu and Baochun Li Adaptive Window-Tuning Algorithm for Efficient Bandwidth Allocation on EPON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1217 Sangho Lee, Tae-Jin Lee, Min Young Chung, and Hyunseung Choo Optical Burst Control Algorithm for Reducing the Effect of Congestion Reaction Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1221 Myungsik Yoo and Junho Hwang Incremental Provision of QoS Discarding Non-feasible End-to-End Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1225 Alfonso Gazo-Cervero, Jos´e Luis Gonz´ alez-S´ anchez, and Francisco J. Rodr´ıguez-P´erez Enhancing Guaranteed Delays with Network Coding . . . . . . . . . . . . . . . . . 1229 Ali Mahmino, J´erˆ ome Lacan, and Christian Fraboul LPD Based Route Optimization in Nested Mobile Network . . . . . . . . . . . . 1233 Jungwook Song, Heemin Kim, Sunyoung Han, and Bokgyu Joo PIBUS: A Network Memory-Based Peer-to-Peer IO Buffering Service . . . 1237 Yiming Zhang, Dongsheng Li, Rui Chu, Nong Xiao, and Xicheng Lu A Subgradient Optimization Approach to Inter-domain Routing in IP/MPLS Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1241 Artur Tomaszewski, Michal Pi´ oro, Mateusz Dzida, Mariusz Mycek, and Michal Zago˙zd˙zon Cost-Based Approach to Access Selection and Vertical Handover Decision in Multi-access Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1245 Fanchun Jin, Hyeong-Ah Choi, Jae-Hoon Kim, Se-Hyun Oh, Jong-Tae Ihm, JungKyo Sohn, and Hyeong In Choi Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1249

On the Resilient Overlay Topology Formation in Multi-hop Wireless Networks Fei Xing and Wenye Wang Department of Electrical and Computer Engineering North Carolina State University, Raleigh, NC 27695, USA [email protected], [email protected]

Abstract. In this paper, we study the problem of how to design overlay topologies in multi-hop wireless networks such that the overlays achieve perfect resilience, in terms of all cooperative nodes included but misbehaving nodes excluded, and preserve the k-connectivity with high probability. To address this problem, we propose a new distributed topology control protocol called PROACtive. By using PROACtive, every node pro-actively selects its cooperative adjacent nodes as neighbors by mutually exchanging neighbor request and reply messages. As a result, the union of all neighbor sets forms a resilient overlay for a given network. Our analysis finds that the PROACtive protocol is light-weighted with the message complexity of only O(m), where m is the number of links in the original network. Our simulation results validate the effectiveness of PROACtive and show that the overlays generated by our protocol preserve the k-connectivity with high probability (> 90%) and low false positive ratio (< 5%).

1

Introduction

Multi-hop wireless networks, especially mobile ad hoc networks, are more vulnerable to failures compared with wired networks due to nodal mobility and errorprone wireless channels. In addition, node misbehaviors, such as selfishness by refusing to forward packets of other nodes and maliciousness by launching Denial of Service (DoS) attacks, can also cause failures. For example, two DoS attacks, Jellyfish and Blackhole, were shown in [1] to have the network partitioning effect which degrades the network performance severely. In [2], a stochastic analysis on node isolation problem also shown that misbehaving nodes may damage the connectivity of mobile ad hoc networks substantially. Since misbehaving nodes may not provide connectivity to other adjacent nodes, existing routing protocols cannot cope with the failures caused by misbehaving nodes, which leaves the design of resilient multi-hop wireless networks an open and challenging problem in the presence of misbehaving nodes. To enhance the resilience to misbehaving nodes, some efforts were made by using different approaches. Two techniques called watchdog and pathrater were proposed in [3] to identify misbehaving nodes and avoid them in routes. A creditbased system called Sprite was proposed in [4] to stimulate cooperation among I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 1–12, 2007. c IFIP International Federation for Information Processing 2007 

2

F. Xing and W. Wang

selfish nodes. In [5], a secure ad hoc routing protocol called Ariadne was presented to prevent attacks from tampering routing control messages by using symmetric cryptographic primitives. Multi-path routing scheme in [6] introduced redundancy to avoid single path failure caused by node failures or node misbehaviors. Nevertheless, the previous schemes are “passive” to misbehaving nodes since even a misbehaving node can be detected, it is very difficult to prevent it from being selected as intermediate relays for all paths. In this paper, we study the problem of how to design overlay topologies in multi-hop wireless networks such that the overlays achieve perfect resilience, in terms of all cooperative nodes included but misbehaving nodes excluded, and preserve the k-connectivity with high probability (w.h.p.). Through the formation of resilient overlays, routing and data transferring can be performed upon cooperative platforms. Our contributions are mainly on two aspects. 1. A new distributed and localized protocol called PROACtive is proposed to generate a resilient overlay for a given network. By using PROACtive, every node pro-actively selects only cooperative adjacent nodes as its neighbors, which results in the exclusion of misbehaving nodes from the overlay. 2. The PROACtive protocol is shown to be light-weighted with the message complexity of only O(m), where m is the number of links in the original network, and the overlays preserve k-connectivity w.h.p. (> 90%) and low false positive ratio (< 5%). Note that our objective distinguishes itself from the existing topology control works [7,8,9], which usually focused on minimizing the energy consumption as well as keeping networks connected. For example, in [7], the K-Neigh protocol, based on distance estimation, was proposed to preserve the connectivity of static multihop networks, with efficient power consumption, by selecting K closest neighbors for each node. Nevertheless, our approach differs from the existing resilience-enhancing works in that we employ the topology control technique in the PROACtive protocol to connect cooperative nodes dynamically by mutual neighbor selections. The remainder of this paper is organized as follows. In Section 2, we formulate the problem. In Section 3, we describe the details of the PROACtive protocol. In Section 4, we validate our approach by simulations, followed by conclusions in Section 5.

2

Problem Statement

In this section, we describe the system model and formulate the perfect resilient overlay generation (PROG) problem. 2.1

System and Threat Model

In this paper, we denote multi-hop wireless networks by M(N ), where N is the set of nodes. All nodes are assumed to be distributed independently and

On the Resilient Overlay Topology Formation

3

uniformly on a two-dimensional plane, and they use omni-directional antennas with the same transmission radius r. For a pair of node u and v, they are called adjacent if the distance between them, denoted by d(u, v), is no greater than r. When d(u, v) > r, u and v may communicate via multiple intermediate hops. It is known that the geometric random graph (GRG) [10], denoted by G(N, r), is a graph in which N vertices are independently and uniformly distributed in a metric space with edges existing between any pair of vertices u and v if and only if d(u, v) ≤ r. Thus, we use the GRG to model the underlying topologies of multi-hop wireless networks. In order to identify the type of misbehaviors our work has targeted, we loosely classify the different types of misbehaviors in a multi-hop wireless network below, though the classification is not intended to be comprehensive. (I) Nodes participate in routing but not in data forwarding, like Jellyfish and Blackhole; (II) Nodes do not cooperate in forwarding control or data packets for others, like selfish nodes; (III) Compromised nodes, though appearing to be legitimate, malfunction maliciously; (IV) Malicious attacker nodes generate DoS traffic or signals, impersonate legitimate nodes, or tamper with routing messages. Our research focuses on misbehavior (I); while our approach can also be applicable to address misbehavior (II) and (III). Our approach, however, does not address misbehavior (IV), which requires suitable authentication and privacy mechanisms. Further, colluding attacks are out of the scope of this work. 2.2

Problem Formulation

The objective of this work is to enhance the resilience of multi-hop wireless networks against node misbehaviors. As mentioned in Section 1, misbehaving nodes may undermine network connectivity and network performance. Here we take an example to look at the effect of misbehaving nodes on path reliability. For a path with h relay hops, let the probability of any relay node being failed (due to node mobility or energy depletion) be Pf , then the path reliability, denoted by RP , can be presented by RP = (1 − Pf )h . While, if any relay node may also misbehave to disrupt communications, the representation of RP becomes RP = (1 − Pf − Pm )h , where Pm is the probability of any node misbehaving. Then we can easily show that RP can be significantly decreased by the route disruption effect resulting from misbehaving relays, and the negative impact is more exaggerative when the number of hops h increases. Therefore, it has been an important issue in the design of resilient networks to “exclude” misbehaving nodes. For a multi-hop wireless network in the presence of misbehaving nodes, we call a connected subnet consisting its all and only cooperative nodes as a perfect resilient overlay (PRO). If the routing and data transfer operations are conducted only on the induced PRO, then the communication between cooperative nodes is guaranteed to be resilient to misbehaving nodes. Here we formulate our problem as the perfect resilient overlay generation (PROG) problem, as follows:

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Definition 1. PROG Problem: Given a connected multi-hop wireless network M and a connectivity requirement k, generate a perfect resilient overlay M− such that M− is k-connected with high probability. To solve the PROG problem, we propose a distributed and localized protocol called PROACtive, by which every node can pro-actively select cooperative adjacent nodes as its neighbors, which will be described in detail right next.

3

PROACtive Protocol Design

In this section, we propose the PROACtive protocol as the solution to the PROG problem. 3.1

Basic Idea

In the PROACtive protocol, each node is assumed to be able to know whether its adjacent nodes forward packets for other nodes. For example, if wireless cards operate in promiscuous mode, a node can use the Watchdog method [3] to tell if its next-hop node drops packets instead of forwarding. By this way, a node u should quantitatively measure the cooperativity (borrowed from Biochemistry) of its adjacent nodes, which indicates the likelihood that a node performs normal network operations. Based on the obtained cooperativities, a node u can select neighbors by sending the soliciting messages called Neighbor Request (Ngbr-Rqst) to its adjacent nodes with high cooperativities. Once receiving an acknowledge message called Neighbor Reply (Ngbr-Rqst) from one of its adjacent nodes, say node v, then u knows that v has agreed to accept u as v’s neighbor, so u can add v into its neighbor set. By this mutual neighbor selection process, a cooperative node can have a cooperative neighborhood easily; while a misbehaving node can hardly have any neighbors. As a result, the union of cooperative neighbor sets generates a perfect resilient overlay which excludes misbehaving nodes. To satisfy the constraint of the k-connectivity, we refer to some results shown in a few recent literatures, which reveal the probabilistic relations between the connectivity κ(G) and the minimum degree δ(G) of the graph G. It was proved in [10] (Theorem 1.1) that if N is sufficiently large, the GRG G(N, r), obtained by adding links between nodes in the order of increasing length, becomes k-connected at the instant when it achieves a minimum degree of k, w.h.p.. In [11] (Theorem 3 ), it was shown that for a GRG G(N, r) P r(κ(G) = k) ≈ P r(δ(G) ≥ k)

(1)

holds if N  1 and P r(δ(G) ≥ k) ≈ 1. The result was further verified by extensive simulations in [11], [12], and [13]. Moreover, it was shown in [2] that to achieve the k-connectivity in a multi-hop wireless network where misbehaving nodes present, a necessary condition is that each node should have at least k cooperative neighbors. This result implies that for a network M, if let θ(M) denote the minimum number of cooperative neighbors of M, then P r(κ(M) = k) ≈ P r(θ(M) ≥ k)

(2)

On the Resilient Overlay Topology Formation

5

holds for the sufficiently large system size N . Therefore, in our protocol, each (cooperative) node should maintain at least k cooperative neighbors such that the k-connectivity is achievable in the overlay w.h.p.. In the next section, we describe the details of our approach. 3.2

PROACtive Protocol Details

As described briefly in Section 3.1, the essential idea of the PROACtive protocol is to build up cooperative neighbor sets, which is done by the mutual neighbor selections via Ngbr-Rqst and Ngbr-Rply message exchanges. In this section, we provide the detailed procedures of building up cooperative neighbor sets. For clarity of the description, we denote the adjacent nodes and cooperative neighbors of a node u by Adj(u) and N gbr(u), respectively, and denote the cooperativity of a node u by c(u). We will first discuss the procedure of querying potential neighbors as follows. Once a node u knows the cooperativities of its adjacent nodes, u selects a node v of the highest cooperativity from set Adj(u) as a potential neighbor, if v is not in set N gbr(u). Then u sends a Ngbr-Rqst message to v, indicating that u intends to add v to its neighbor set. If u receives a Ngbr-Rply message from v within a timeout, then u can add v into set N gbr(u); otherwise, u queries another adjacent node of the next highest cooperativity. Node u will continue the inquiries until k Ngbr-Rply messages from different adjacent nodes are received, which guarantees u with at least k neighbors. This procedure is summarized by Algorithm 1 as follows. Algorithm 1. Procedure of querying potential neighbors Input: k, node u, and Adj(u) 1: Initiate N gbr(u) := ∅, create a temporary set T emp(u) := ∅, create a counter numRplyRcvd := 0 2: ∀v ∈ Adj(u), Measure c(v) 3: while (numRplyRcvd < k AND T emp(u) = Adj(u)) do 4: Select v if c(v) = max{c(w) : ∀w ∈ Adj(u) − T emp(u)} 5: Send Ngbr-Rqst to v 6: T emp(u) := T emp(u) + v 7: if (Receive Ngbr-Rply from v) then N gbr(u) := N gbr(u) + v 8: 9: numRplyRcvd := numRplyRcvd + 1 10: end if 11: end while

Next we discuss how a node processes the incoming neighbor requests. In our approach, each node, say u, can calculate its own threshold, based on the information available from its local environment, to decide if it should accept a querying node as its neighbor. We call this threshold as the neighbor cooperativity threshold and denote a node u’s threshold by c∗ (u). For a node u, since u can

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measure the behaviors of its adjacent nodes quantitatively, u’s threshold can be defined as the average cooperativity of its adjacent nodes, i.e., c∗ (u) =

1 d



c(v), for d = |Adj(u)|.

(3)

∀v∈Adj(u)

Hence, when u receives a Ngbr-Rqst message from one of its adjacent nodes v, it compares c(v) to its threshold c∗ (u). If c(v) ≥ c∗ (u), u replies v with a Ngbr-Rply message and adds v into u’s neighbor set; Otherwise, u discards this neighbor request and replies nothing. Algorithm 2 summaries the procedure of processing neighbor requests. Algorithm 2. Procedure of processing neighbor requests Input: node u, and Adj(u) 1: ∀v ∈ Adj(u), Measure c(v) 2: Calculate c∗ (u) by Equation (3) 3: if (Receive Ngbr-Rqst from v ∈ Adj(u)) then / N gbr(u)) then 4: if (c(v) ≥ c∗ (u) AND v ∈ 5: Send Ngbr-Rply to v 6: N gbr(u) := N gbr(u) + v 7: else 8: Discard Ngbr-Rqst 9: end if 10: end if

By this mutual neighbor selection, a node with high cooperativity, in contrast to the nodes with low cooperativities, may receive multiple requests and immediate replies from adjacent nodes. Consequently, a resilient overlay topology can be constructed from the neighbor sets. We use Algorithm 3 to summarize the perfect resilient overlay generation. Algorithm 3. Generate a perfect resilient overlay M− Input: k, and a multi-hop wireless network M 1: Let N − be the node set of M− , N − := ∅ 2: for each u ∈ M do 3: Build up N gbr(u) by using Algorithms (1) and (2) 4: N − := N − ∩ N gbr(u) 5: end for 6: return M− induced from N −

3.3

Cooperativity Measurement Scheme

To measure the cooperativity of a generic node, we investigate the characteristics of misbehaving nodes on the network layer. A selfish node, for selfish reasons such as saving energy, usually refuses to forward data packets for other nodes.

On the Resilient Overlay Topology Formation

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A malicious node can do anything such as dropping partial data packets at a random or periodic manner, or pretending to be adjacent to a node actually far-away from it, thus trapping all packets destinated to that node afterwards. Thus, dropping “transient” packets is one of the most common characteristic of most misbehaviors, especially the Type-I misbehavior mentioned in Section 2.1. This observation implies that for a node u, we can use u’s packet drop ratio, denoted by qdrp , to measure u’s cooperativity c(u). Let nf wd (u) and ndrp (u) denote the numbers of packets should be forwarded and dropped, then we have, c(v) = 1 − qdrp (v) = 1 −

ndrp . nf wd

(4)

We use an example in Fig. 1(a) to illustrate this method. In Fig. 1(a), every time node u asks node w to forward a packet to v, u increases a counter nf wd (w) by 1. If u cannot overhear w’s forwarding after a timeout (e.g., round-trip delay), u increases another counter ndrp (w) by 1. Moreover, when one of u’s adjacent nodes, x, requires w to forward packets to v, u can record w’s behavior as well. Based on the measurements from both “own experience” and ”indirect observation”, u can calculate w’s cooperativity c(w) by (4). 00 11

00 x11 00 11

u

w w

v

u

(a)

v ACK

1 0 0 1 0 1

x

(b)

Fig. 1. Measuring cooperativity (a) by promiscuous mode (b) by ACKs

Notice that in our PROACtive protocol, the cooperativity measurement scheme is not limited to the technique that employs promiscuous mode only; it can also use other techniques such as close-loop feedbacks. For example, in Fig. 1(b), when u sends a data packet to w, it can piggyback an ACK request. Based on whether u can receive an ACK from one of w’s downstream nodes, say x, u may tell if w has forwarded the packet successfully. 3.4

Features of PROACtive Protocol

In this section, we discuss some unique features of our approach. First, the “individual” threshold defined in (3) allows each node to reach a trade-off between system resilience and individual connectivity, compared to a global threshold. This is due to the fact that a node surrounded by nodes with relatively low cooperativities can hardly find enough neighbors although a relatively high global threshold can achieve a resilient overlay of only cooperative nodes. On the contrary, by using the individual threshold, for a node u with adjacent nodes of relatively low cooperativities, its neighbor cooperativity threshold can decrease accordingly. Thus u may still have enough “neighbors”. Nevertheless, a global threshold can be also applicable for our protocol and more flexible decision policies in neighbor can be designed by combining the global threshold and individual thresholds.

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Second, regarding the issue of neighbor set updating, our PROACtive protocol is able to deal with the dynamic topology changes due to node mobility. For instance, a mobile node can refresh its neighbor set when it detects a disconnection with its neighbor(s). If the topology is highly dynamic (e.g., mobility is high), then mobile nodes can keep the records of its neighbors to avoid frequent neighbor set updates. Further, the PROACtive protocol is able to deal with the dynamic changes of node behaviors as well due to the flexibility provided by our threshold design. For instance, the updating overhead can be also reduced by deleting a neighbor only if its cooperativity is below the minimum requirement for a specific application. Third, our approach does not involve new security vulnerabilities and can avoid the false accusation problem. For instance, the cooperativity information measured by one node are not shared with others in our protocol, and the neighbor selection is only dependent on each node’s own knowledge to its neighborhood. By this way, one node’s cooperativity cannot be falsely rated to a low or high value by several other (might be malicious) nodes, which prevents any node from the false accusation. No information sharing also helps to avoid the complexity of deciding the actual cooperativity of one node when multiple different measurements are received. Nevertheless, the integrity of Ngbr-Rqst and Ngbr-Rply messages can be protected by traditional cryptographic techniques. Finally, the PROACtive protocol is completely distributed and localized, which makes our approach more feasible to be implemented in a real scenario. Additionally, our protocol can be run locally, in an on-demand manner, whenever a mobile node detects a significant cooperativity change among its neighborhood. Further, our protocol is light-weighted in terms of the overhead of message exchanges. For example, given a wireless multi-hop network, in the worst case, every node should send either a Ngbr-Rqst or Ngbr-Rply message to each of its adjacent nodes in order to build up a neighbor set. This implies that to generate a resilient overlay, the total number of messages needed is no more than the number of links, denoted by m, in the original network. Therefore, the message complexity of our protocol is only O(m). Until now, the PROG problem, how to generate a perfect resilient overlay, has been solved by applying the PROACtive algorithm on given networks. We will evaluate the effectiveness of our solution by simulations in the next section.

4

Simulation Evaluations

To evaluate our PROACtive protocol, we performed a considerable body of experiments by using NS2 v2.28 and MATLAB v7sp3 tools. In our simulations, nodes are distributed randomly and uniformly in an area. Distinct node pairs randomly establish constant bit rate (CBR) connections, with packet size of 512 bytes and rate of 5 packets/sec, such that nodes can measure their adjacent nodes’ coopertivities by the method described in Section 3.3. The AODV routing protocol is used. The connectivity requirement k is 3 for all simulations.

On the Resilient Overlay Topology Formation

(a)

(b)

9

(c)

Fig. 2. The topologies of the underlying network and overlays generated: (a) no topology control, (b) applied with PROACtive, (c) K-Neigh with K = 9 (Phase I)

We show how the PROACtive protocol generates overlays first, then show the effectiveness of our protocol with regard to the k-connectivity preservation and the false positive (negative) rate. 4.1

Topology Generated by PROACtive Protocol

In this simulation, 500 nodes are distributed on a 1500 m×1500 m area at random with the same transmission radius of 150 m. Among 500 nodes, 150 misbehaving nodes drop packets to be forwarded or report false routes. Fig. 2(a) illustrates the network without applying any topology control, in which a pair of nodes are connected by a link as long as their distance is no larger than 150 m. Fig. 2(b) shows the network structure after applying our PROACtive protocol, in which cooperative and misbehaving nodes are represented by solid and hollow dots, respectively. From the figure, we can see that the overlay topology generated by PROACtive excludes most of misbehaving nodes, while containing almost all cooperative nodes. Though some links are removed in the overlay due to the mutual neighbor selection, the generated overlay is still connected. To highlight the feature of our protocol, the topology generated by the K-Neigh protocol (Phase 1 only, with K = 9) [7] is shown in Fig. 2(c), where we can see that all misbehaving nodes are included in the topology. This is because the neighbor selection in K-Neigh is only based on the distance between nodes, that is each node selects K nearest adjacent nodes as its neighbors. 4.2

Preservation of k-Connectivity

One of the major tasks in our simulations is to verify that the k-connectivity should be preserved, w.h.p., for the overlays generated by PROACtive, when the original network is k-connected. To test whether the network is k-connected, we use breadth first search (BFS) to compute how many disjoint paths connecting two distinct nodes. In this simulation, the nodes are placed uniformly at random in a bounded region of 2000 m × 2000 m. The transmission radius is set to 100 m. The number of nodes N ranges from 500 to 5000 with an interval of 100,

F. Xing and W. Wang

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Probability of k−connectivity, k=3

Probability of k−connectivity, k=3

10

0.8 0.6 0.4 0.2 0 2000

2500

The original M, Pm=0.1 Overlay M−, Pm=0.1 The original M, Pm=0.3 Overlay M−, Pm=0.3 3000 3500 4000 System size N

1 0.8 0.6 0.4 0.2 0 0

Analysis for M, N=3000 Simulation for M−, N=3000 Analysis for M, N=4000 Simualtion for M−, N=4000 0.1 0.2 0.3 0.4 0.5 0.6 Ratio of misbehaving nodes in original net (Pm)

(a)

0.7

(b)

Fig. 3. The k-connectivity probabilities of the overlays generated, compared to those of the original networks: (a) against N , (b)against PM

FPR, Pm=0.1 FNR, Pm=0.1 FPR, Pm=0.3 FNR, Pm=0.3 FPR, Pm=0.5 FNR, Pm=0.5

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N=1000 N=2000 N=3000 N=4000

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0 500 1000

2000 3000 System size N

4000

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0 0

(a)

0.1 0.3 0.5 0.7 0.9 Ratio of misbehaving nodes in original net (PM)

(b)

Fig. 4. The false positive and negative ratios produced by PROACtive (a) against N , (b) against PM (FNR only)

which makes the network placements representative for both sparse and dense networks. For every value of N , a certain number of nodes are misbehaving, whose ratio to the total, denoted by PM , is ranging from about 1% up to 90% with a interval of 10%. The simulation results are shown in Fig. 3(a) and 3(b). For clarity, only the results for 2000 < N < 4000 are shown, and we omit the part for PM > 0.7 by the similar reason. From the two figures, we can see that the overlays generated preserve the k-connectivity with probability greater than 90%, when the original network is k-connected. 4.3

False Positive and Negative Ratio

As we described in Section 3.4, though the individual threshold helps nodes to reach a trade-off between system resilience and individual connectivity, it is possible that a cooperative node u cannot build up its neighbor set if c(u) < c∗ (v) ∀v ∈ Adj(u). In this case, we say u is a false positive. On the contrary, a misbehaving node u may have the chance to be added to another node v’s neighbor set if v cannot have enough neighbors without adding u. In this case, we say u is a false negative. Since the perfect resilient overlay (PRO) is an overlay

On the Resilient Overlay Topology Formation

11

that contains all and only cooperative nodes of the original network, we can use two metrics, false positive rate (FPR) and false negative rate (FNR), to evaluate the effectiveness of the PROACtive protocol in generating PROs. If let NC and NM denote the number of cooperative and misbehaving nodes in the original network, then the FPR and FNR can be calculated by F P R = NCm /NC and c c F N R = NM /NM , respectively, with NCm and NM denoting the number of false positives and false negatives. Our simulation results are reported in Fig. 4(a) and 4(b). In Fig. 4(a), the FPRs are very low (< 5%) for all networks of different system size N as well as different PM ; however, the FNRs are more significant for small N than for large N . This indicates that relatively more misbehaving nodes are added into the overlay to keep it connected when the network is sparse. Another observation is that the FNRs increase significantly when PM increases, which is further illustrated in Fig. 4(b), where the FNR for N = 4000 raises even up to 50% when PM = 0.9. This is due to the fact that more false negatives are produced to keep enough neighbors for every node when many misbehaving nodes present. These observations show that the PROACtive protocol is more “conservative” in satisfying the k-connectivity constraint.

5

Conclusion and Future Work

In this paper, we proposed a distributed and localized protocol, PROACtive, to generate perfect resilient overlays which contain all and only cooperative nodes of the original wireless multi-hop networks. The PROACtive protocol has a light-weighted message complexity, O(m), and the overlays generated achieve k-connectivity with high probability and low false positive ratio. The main advantage of applying our PROACtive protocol is that the resilient overlays generated essentially provide cooperative platforms for multi-hop routing and data transmission when misbehaving nodes are present. Based on the resilient overlays, new routing strategies and data aggregation schemes can be designed, which will be our next works. Further, more advanced cooperativity measurement schemes are also needed to be explored.

References 1. Aad, I., Hubaux, J.P., Knightly, E.W.: Denial of Service Resilience in Ad Hoc Networks. In: Proc. of ACM MobiCom ’04. (2004) 202–215 2. Xing, F., Wang, W.: Modeling and Analysis of Connectivity in Mobile Ad Hoc Networks with Misbehaving Nodes. In: Proc. of IEEE conference on communication (ICC) ’06. (2006) 1879 – 1884 3. Marti, S., Giuli, T.J., Lai, K., Baker, M.: Mitigating Routing Misbehavior in Mobile Ad hoc Networks. In: Proc. of ACM MobiCom ’00. (2000) 255–265 4. Zhong, S., Chen, J., Yang, Y.R.: Sprite: A Simple, Cheat-Proof, Credit-based System for Mobile Ad-Hoc Networks. In: Proc. of IEEE INFOCOM ’03. (Mar. 2003) 1987–1997

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5. Hu, Y., Perrig, A., Johnson, D.B.: Ariadne: A Secure OnDemand Routing Protocol for Ad Hoc Networks. In: Proc. of ACM MobiCom ’02, Atlanta, USA (Sep. 2002) 6. Ganesan, D., Govindan, R., Shenker, S., Estrin, D.: Highly-Resilient, EnergyEfficient Multipath Routing in Wireless Sensor Networks. Mobile Computing and Communications Review (MC2R) 5(4) (2001) 1–13 7. Blough, D.M., Leoncini, M.: The K-Neigh Protocol for Symmetric Topology Control in Ad Hoc Networks. In: Proc. of ACM MobiHoc ’03, ACM Press (2003) 141–152 8. Shen, C.C., Srisathapornphat, C., Liu, R., Huang, Z., Jaikaeo, C., Lloyd, E.L.: CLTC: A Cluster-Based Topology Control Framework for Ad Hoc Networks. IEEE Transactions on Mobile Computing 3(1) (2004) 18–32 9. Cardei, M., Wu, J., Yang, S.: Topology Control in Ad Hoc Wireless Networks Using Cooperative Communication. IEEE Transactions on Mobile Computing 5(6) (Jun. 2006) 711–724 10. Penrose, M.D.: On k-connectivity for a Geometric Random Graph. Random Struct. Algorithms 15(2) (1999) 145–164 11. Bettstetter, C.: On the Minimum Node Degree and Connectivity of a Wireless Multihop Network. In: Proc. of ACM MobiHoc ’02, ACM Press (Jun. 2002) 80–91 12. Li, X.Y., Wan, P.J., Wang, Y., Yi, C.W.: Fault Tolerant Deployment and Topology Control in Wireless Networks. In: Proc. of ACM MobiHoc ’03. (Jan. 2003) 117–128 13. Bettstetter, C.: On the Connectivity of Ad Hoc Networks. The Computer Journal, Special Issue on Mobile and Pervasive Computing 47(4) (2004) 432–447

Placing and Maintaining a Core Node in Wireless Ad Hoc Sensor Networks Amit Dvir and Michael Segal Department of Communication Systems Engineering Ben Gurion University of the Negev Israel azdvir, [email protected]

Abstract. Wireless Ad hoc sensor networks are characterized by several constraints, such as bandwidth, delay, power, etc. These networks are examined by constructing a tree network. A core node usually chosen to be the median or center of the multicast tree network with a tend to minimize a performance metric, such as delay or bandwidth. In this paper, we present new efficient strategy for constructing and maintaining a core node in multicast tree for wireless ad hoc sensor networks that undergo dynamic changes based on local information. The new core (centdian) function is defined by convex combination that signifies total bandwidth and delay constraints. We provide two bounds of O(d) and O(d + l) time for maintaining the centdian using local updates, where l is the hop count between the new center and the new centdian and d is the diameter. We also show a O(n log n) time solution for finding centdian in the Euclidian complete network using interesting observations. Finally a simulation is presented.1 Keywords: Sensor networks, Wireless Ad hoc Networks, Multicast tree, Core Node.

1 Introduction Wireless Ad hoc sensor networks is a network architecture that can be rapidly deployed without relying on pre-existing fixed network infrastructure . Wireless communication is used to deliver information between nodes, which may be mobile and rapidly change the network topology. The wireless connections between the nodes (which later will be referred as links or edges) may suffer from frequent failures and recoveries due to the motion of the nodes and due to additional problems related to the propagation channels (e.g. obstructions, noise) or power limitations. A wireless ad hoc sensor network consists of a number of sensors spread across a geographical area. Each sensor has wireless communication capability and some level of intelligence for signal processing and networking of the data. Recently, wireless sensor networks have been attracting a great deal of commercial and research interest [13,27,29]. In particular, practical emergence of wireless ad hoc networks is widely considered revolutionary both in terms of paradigm shift as well as enabler of new applications. 1

This research has been partially supported by INTEL and REMON consortium.

I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 13–24, 2007. c IFIP International Federation for Information Processing 2007 

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Group communication is the basis for numerous applications in which a single source delivers concurrently identical information to multiple destinations. This is usually obtained with efficient management of the network topology in the form of tree having specific properties. For example, multicast routing refers to the construction of a spanning tree rooted at the source and spanning all destinations [3,11,25,30,36]. Delivering the information only through edges that belong to the tree generates an efficient form of group communication which uses the smallest possible amount of network resources. In contrast, with unicast routing from the source to each destination, one needs to find a path from the source to each destination and generates an inefficient form of group communication where the same information is carried multiple times on the same network edges and the communication load on the intermediate nodes may significantly increase. We notice that wireless ad hoc sensor networks pose the reliable and efficient communication services necessary for distributed computing [6, 31], while objective functions considered are the most classical that involve the minimization of the average or the maximum distance to service facilities. Generally, there are two well-known basic approaches to construct multicast trees: the minimal Steiner tree (SMT) and the shortest path tree (SPT). Steiner tree (or groupshared tree) tends to minimize the total cost of a tree spanning all group nodes with possibly additional non group member nodes. The optimal construction of the SMT is known to be a NP-hard problem [14,22]. Some heuristics that offer efficient solutions to this problem are given in [21, 37]. The best up today solution has been derived by [38] and proved factor of 1.55. In contrary, SPT tends to minimize the cost of each path from the root source to each destination. This can be achieved in polynomial time by using the well-known algorithm by Dossey et al. [12]. The goal of a SPT is to preserve the minimal distances from the root to the nodes without any attempt to minimize the total cost of the tree. Gupta and Srimani [16] present distributed core selection and migration protocols for multicast tree in MANET with dynamically changing network topology. The proposed core location method is based on the notion of median node of the current multicast tree instead of the median node of the entire network. The adaptive distributed core selection and migration method uses the fact that the median of a tree is equivalent to the centroid of that tree. Gupta and al. [17] present efficient core migration protocol for MANET that migrates the core until the multicast tree branches reflect the desired QoS requirements of the multicast application where the proposed core location method is based on the notion of center node of the current multicast tree. Bing-Hong and al. [9] gave heuristic to the minimum non-leaf multicast tree problem that reduce the number of non-leaves nodes in the multicast tree and their experimental results show that the multicast tree after the execution of their method has smaller number of non-leaves than others in the geometrically distributed network model. The bandwidth of a tree is defined as the total distance of packet transmissions required to deliver packet from core node v to all others nodes. The maximum delay of the tree is the maximum distance to traversed by any packet in traveling from core node v to other node. The transport of a node is defined as the total distance of the node to all others nodes in the tree. The corresponding solution concepts have been considered in literature as median and center [26, 28, 39]. Since the median approach is based on

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averaging, it often provides a solution in which remote and low-population density areas are discriminated against in terms of accessibility to public facilities, as compared with centrally situated and high-population density areas. For this reason, an alternative approach, involving the maximum distance between any customer and closest facility can be applied. This approach is referred to as the center solution concept [4]. The minmax objective primarily addresses geographical equity issues, which are of particular importance in spatial organization of emergency service systems. On the other hand, locating a facility at the center may cause a large increase in the total distance, thus generating a substantial loss in spatial efficiency. The problems of using only center or median as a core lead to search for a compromised solution concept called centdian, where centdian function presents some kind of trade-off between the center and the median functions ( [19]). The centdian function for node v in the network is defined by Dv = λ · sum(v) + (1 − λ) · dist(v), 0 ≤ λ ≤ 1 where dist(v) is the maximum distance from node v to other nodes in the network, sum(v) is the sum of distances from node v to all other nodes in the networks. Halpern [18] introduced the centdian model and studied the properties of the centdian in a tree. In a subsequent work, Carrizosa et al. [10] presented an axiomatic approach justifying the use of the centdian criterion. Tamir et al. [41] present the first polynomial time algorithm for the p-centdian problem on a tree with O(pn6 ) complexity where p is the number of facilities. For more results about centdian problem, see [2,7,20,32,33,40]. Other related notion of ordered median of a tree ( [5, 23, 34, 35]) generalizes the most common criteria mentioned above, e.g., median, center and centdian. If there are n demand points in a tree T , this function is characterized by a sequence of reals, κ = (κ1 , . . . , κn ), satisfying κ1 ≥ κ2 . . . ≥ κn ≥ 0. For a given subtree S ∈ T , let X(S) = {x1 , . . . , xn } be the set of weighted distances of the n points to S. The value of the ordered median objective at S is obtained as follows: Sort the n elements in X(S) in non-increasing order, then compute the scalar product of the sorted list with the sequence κ. It is easy to see that when κi = 1, i = 1, . . . , n, we get the median objective and when κ1 = 1 and κi = 0, i = 2, . . . , n, we obtain the center objective. For the case κ1 = 1 and κi = λ, i = 2, . . . , n we get the centdian objective. Unfortunately, constructing and maintaining cores by use of ordered median technique is not suitable for wireless ad hoc sensor networks, since this technique requires keeping some global information about nodes of network which is completely inconceivable in the case of wireless ad hoc sensor networks. Most protocols for constructing core node are not suitable for wireless ad hoc sensor networks, since these algorithms are not based on local updates. In this paper, we present new efficient strategy for constructing and maintaining a core node under centdian criteria in multicast tree for wireless ad hoc sensor networks with dynamic changes in the network topology. The new core node is defined by convex combination of the sum of the weighted distance paths (sum of the weighted edges in the path) of all the nodes in the tree network to the core node and the maximum weighted distance from the core node to the farthest node in the tree network satisfied center and median core functions. We also provide two bounds of O(d) and O(d + l) time for maintaining the centdian after a change (add/remove edge/node) in the topology of the tree network, where l is the hop count between the new center and the new centdian of the multicast

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tree and d is the diameter of the tree. We show an O(n log n) time algorithm for finding a centdian node in the Euclidian complete network bases on observation in [8]. Finally, we present a simulation that compare our new core solution with well known cores’ strategies to exhibit the advantages and the efficiency of our algorithms. This paper is organized as follows: Section 2 presents a new algorithm that finds and maintains a centdian core in a multicast tree. In Section 2.2 we show a solution for a static Euclidian network. Next we show our simulation results and finally, we conclude with several ideas for future work.

2 Algorithm to Find Centdian of Multicast Tree in Wireless Ad Hoc Sensor Networks We model the topology of wireless ad hoc sensor networks by weighted undirected graph G(V, E, We ), where V is the set of nodes, E is the set of edges between neighboring nodes and We is an edge weight function, e.g. squared distance between the endpoints of edges. Note that the edges represent logical connectivity between nodes, i.e., there is an edge between two nodes u and v if they can hear each other’s local broadcast. Since the nodes are mobile, the network topology graph stochastically changes. Let us define by T(V’, E’) a weighted multicast tree of G. For a node v ∈ T we define by Kv the number of nodes in the connected component containing v (created by removing e(v, x)); by Wv the total sum of weighted distances from the nodes in the connected component containing v (created by removing e(v, x)) to node v. Center of a tree T is a node c1 ∈ T such that the maximal distance from c1 to any other node in T is minimized, i.e. dist(c1 , T ) = minv∈T dist(v, T ). In order to find a center of tree T we can use the distributed algorithm described in [26] that requires r(I)+(d(T )/2) time, where r(I) is the the maximal weighted distance from the initiator node I to any other node in T and d(T ) is the weighted diameter of the tree. This algorithm finds the center node by starting form an arbitrary node I and goes from the internal nodes towards the leaves and back to the new center using the information from the leaves about the weighted distance path and the knowledge that the center of the tree lies on the diameter of the tree. Median of a tree T is a node c2 ∈ T such that the sum of the weighted distances from c2 to any other node in T is minimized, i.e. sum(c2 , T ) = minv∈T sum(v, T ). In order to find a median of a tree T we can use the distributed algorithm in [26] that requires maxx∈T (r(I) + d(x, c2 )) time, where d(x, c2 ) is the weighted distance between node x and the new median. This algorithm finds the median node by starting form an arbitrary node I and goes from the internal nodes towards the leaves. Each leave propagates the weight of its edge and each internal node propagates the sum of values obtain from its descendants plus the weight of the edge connecting him to its predecessor in the tree. Next, we show a simple algorithm to find the number of nodes in each one of node v branches. We define by Kvi , i = 1 . . . b, to be the number of nodes in the ith branch of node v, with b standing for the number of branches of node v. By convergecast process from the leaves towards the center of the tree we can find the total number of nodes in the tree. By knowing this number, we start a new process from the leaves to find for each node v its values Kvi . Each leaf sends to its father w in a rooted tree T a num(1)

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message. Each internal node w gets from his sons their num messages and sums all the values in the messages. The process converges towards c1 . It is a well-known fact that a centdian is located on the path connecting center c1 and median c2 ( [18]). The following lemma presents an efficient way of calculating centdian in a multicast tree based on knowledge about location of the center and median. Lemma 1. Dv > Dx iff λ((Kx − Kv ) + 1) < 1. Proof: A centdian node x must minimize expression Dx = λ · sum(x, T  ) + (1 − λ) · dist(x, T  ) . Denote by Dv = λ · sum(v, T  ) + (1 − λ) · dist(v, T  ) the cost of node v who is the neighbor of current centdian x with the minimum value of D from x neighbors. We should move the centdian towards v only if Dx > Dv . Notice T ) . We conclude that sum(x, T  ) = Wx + (Kv + that dist(x, T  ) = Dx −λsum(x, (1−λ) 1) · d(x, v) + Wv and sum(v, T  ) = Wv + (Kx + 1) · d(x, v) + Wx . Therefore, Dv = λ( Wv + (Kx + 1) · d(x, v) + Wx ) + (1 − λ)dist(v, T  ). It easy to see that there are 5 different cases (out of 9) that we should deal when Dx > Dv , 1) sum(v, T  ) < sum(x, T  ) and dist(v, T  ) < dist(x, T  ). 2) sum(v, T  ) > sum(x, T  ) and dist(v, T  ) < dist(x, T  ). 3) sum(v, T  ) = sum(x, T  ) and dist(v, T  ) < dist(x, T  ) . 4) sum(v, T  ) < sum(x, T  ) and dist(v, T  ) = dist(x, T  ). 5) sum(v, T  ) < sum(x, T  ) and dist(v, T  ) > dist(x, T  ). We present an analysis only for cases 1-3 that are relevant (case 4 is trivial (sum(v, T  ) = sum(x, T  ))) and case 5 is equivalent to cases 1-3. In cases 1-3 |dist(x, T  ) − dist(v, T  )| ≤ d(x, v), therefore Dv = λ( Wv + (Kx + 1) · d(x, v) + Wx ) + (1 − λ)dist(v, T  ) = λ( Wv + + (Kx + 1) · d(x, v) + Wx ) + (1 − λ)(dist(x, T  ) − dist(x, v)) = λ( Wv + T ) + (Kx + 1) · d(x, v) + Wx ) + (1 − λ)( Dx −λsum(x, − dist(x, v)) = (1−λ) = λ( Wv + (Kx + 1) · d(x, v) + Wx ) + Dx − λsum(x, T  ) − dist(x, v)(1 − λ) = = λWv + λ (Kx + 1) · d(x, v) + λWx + Dx − λsum(x, T  ) − dist(x, v)(1 − λ) = = λWv + λ (Kx + 1) · d(x, v) + λWx + Dx − λ(Wx + (Kv + 1) · d(x, v) + Wv )− −dist(x, v)(1 − λ) = λWv + λ (Kx + 1) · d(x, v) + λWx + Dx − λWx − λ(Kv + 1)· ·d(x, v) − λWv − dist(x, v)(1 − λ) = Dx + λd(x, v)(Kx − Kv ) − dist(x, v)(1 − λ).

As we stated above, we move the centdian node only if D1 > D2 . This happens when Dx − (Dx + λd(x, v)(Kx − Kv ) − dist(x, v)(1 − λ)) > 0 or in other words λ(Kx − Kv + 1) < 1. In case 4 dist(x, T  ) = dist(v, T  ), thus Dv = λ( Wv + (Kx + 1) · d(x, v) + Wx ) + (1 − λ)dist(x, T  ). Analysis similar to the previous one shows that Dx > Dv only if λd(x, v)(Kx − Kv ) < 0. In case 5 we get that Dx > Dv only if λ((Kv − Kx ) − 1) < −1. It follows that the inequality Dx > Dv holds when λ(Kx − Kv + 1) < 1  

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Based on this lemma, we can locate the centdian in the multicast tree, starting either at center or the median of the multicast tree and going over the path between them, locally improving from one neighboring node to another. Thus, the centdian in the tree can be found in O(l) time when the location of the center and the median are known, with l standing for the number of nodes in the path connecting center and median. 2.1 Maintaining a Centdian in a Multicast Tree When we have some change in the multicast tree, each node needs to update the number of nodes in each of its branches. By using Kx values of the centdian node, our maintaining algorithms running on the subtree with the highest number of the multicast group members. In what follows we show two different approaches to maintain centdian in a multicast tree. Both approaches use the fact that the centdian function is convex and therefore has only one minimum point. The first approach is to maintain the center of the tree in O(d) time using the algorithm in [24]. The new centdian lies on the path between the center and the median of the updated tree. Therefore, starting from the new center and finding the node that locally improves the centdian function value, point us the direction towards the new centdian of the tree. The centdian, thus, can be maintained in worst-case O(d + l) time, where l is the hop count between the new center and the new centdian of the multicast tree and d is the diameter of the tree. The second approach uses the fact that the neighbor of the old centdian x that the most improves the centdian function value lies on the path between the old centdian and the new centdian. Therefore, the centdian can be maintained in worst-case O(d) time. Since we want only multicast group members to be assigned the responsibility of core node, the second approach needs to be modified. If the new centdian node is a multicast member it becomes the actual new centdian of the tree. If not, we seek the path towards the old centdian in order to find a node that belongs to multicast group and declare this node to be the new actual centdian of the multicast tree. 2.2 Algorithm to Find Centdian in Euclidean Plane We model the topology of planar network as explained above by having the edge weight function defined as the squared distance between the nodes. The motivation to choose this function is the common method that power transmitting behaves quadratically to the distance between transmitting and receiving node. Using the observation in Bespamyatnikh et al. [8] we are able to solve the centdian problem in Euclidean plane in O(n log n) time. The farthest point Voronoi diagram of a collection of points S in the plane is a partition of plane into cells, each of which consists of the points further to one particular points than to any others. This diagram can be constructed in O(n log n) time supporting a query requests in O(log n) time. For a given point p, a query asks about the farthest neighbor of p in S. Thus, in O(n log n) time we can find, for each point, its farthest neighbor performing total n queries. In other words, for every node v in the network, we find dist(v) in total O(n log n) time. Bespamyatnikh et al. [8] observed that “squared” Euclidean metric is separable, i.e. the distance between two points is the sum of their squared x and y-coordinates’ differences. We follow the notations from [8]. We sort our points according to their x and

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y-coordinates. Let {p1 , . . . , pn } be the sorted points. For every point pi ∈ S we can compute the sum Σix of the x-distances from pi to the rest of the points in S. This is performed efficiently as follows. For the point p1 we compute Σ1x by computing and summing up each of the n − 1 distances. For 1 < i ≤ n we define Σix recursively: asx sume the x-distance between pi−1 and pi is δ, then Σix = Σi−1 +δ·(i−1)−δ·(n−i+1). x The sums Σi (for i  = 1, . . . n) can be computed in linear time when n the points are y sorted. The value of i is computed similarly. Next, let sumxi = j=1 (xj − xi )2 . The recursion formula for  computing all the squared x-distances is easily computed to be sumxi = sumxi−1 − 2δ xi−1 −nδ 2 , where the x-distance between pi−1 and pi is δ. Assume the point p ∈ S is ith in the x order and j th in the y order. The sum of squared Euclidean distances from p to the points in S is sum(p) = sumxi + sumyj . It remains to compute, for every node v the value of centdian function based on values of computed already sum(v) and dist(v) values. This is done in linear time. Thus, we can conclude, Theorem 1. Given a set S of n nodes in Euclidean complete graph with a cost of every edge that equals the squared Euclidean distance between nodes, we can find the centdian node in this graph in O(n log n) time.

3 Simulation This section describes the medium-scale experiment in details. The objectives of the experiment were to test whether the suggested maintaining algorithm actually works, and to compare its results to the performance of other core algorithms. For this simulation we choose to implement the second approach. As we performed our simulation we made an interesting observation about the runtime bound of the first approach of maintaining the centdian node. 3.1 Environment The following assumptions have been made: – For each node, the transmission and reception range are equal; however different nodes can have different ranges. The radius value refers to the transmission range. – All the nodes are equal in their functionalities and abilities. – The movement of each node is based on mobility model of random walk based on random directions and speeds ([15]).2 – There is no dependence between the nodes and the boundary of the network is predefined. In our simulation we used 5 different types of cores: center, median, continuous median, centdian and continuous centdian (with different values of λ). The difference between continuous and non continuous core is that non continuous core can “jump” from one node to another while continuous core keep continuous track of the path of previous core towards the newly computed core. 2

In this model each node moves from its current location to a new location by randomly choosing speed and direction in which to travel.

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3.2 Results The main goal of our simulation is to examine the influence of the multicast group on the cores’ behavior. One of the parameters we wish to exam is the period of time that cores are co-located at the same node (defined by collision). From the obtained results we can learn that the behavior of the cores in the multicast tree is sometimes similar to the behavior of the cores in regular network tree, for example: – When λ = 1 the collision between the centdian core and center core is 100%. – When λ ≤ 0.5 the collision between the centdian core and median core is 100% as has been proved in [18]. In some cases, the collision value between the median/center core and centdian core should be 1, but in our simulation the collision value in those cases are less then 1. The reason for that is the well known fact that in a tree two centers/medians may possibly exist. In the simulation we choose them in arbitrarily fashion. We simulate ad hoc sensor network with 100 nodes and 50 multicast nodes with a variety range of radius and λ values in network boundary of 600x600 meters. Figures 1–7 show the influence of the radius on the constraints’ values of the network. In particular, Figures 1–2 show the transport and delay values of the tree network as an unimodal linear function with a break point being a maximal value. The reason for that is as long as the radius is growing the network becomes more connected and more nodes are participating in the network. Starting at some point of time the network becomes to be connected and the pathes from nodes to the core contain small amount of hops. Figure 3 shows the connection between the radius and the life span of the cores, with life span being the period of time/rounds that the core does not change its location. It easy to see that as we increase the radius the life span also grows up. The collision between the cores with various values of λ and radius is depicted in Figures 4–7. In Figure 4 we focus on the collision between the centdian and median, while in Figures 5–6 we have examined the collision between the continuous centdian and the well known cores. Figure 7 shows the collision between the new centdian and the new center. From Figure 8 we can learn that for most radius’ values, the value l (number of hops between center and centdian) is small. The continuous centdian core

Fig. 1. Total transport of the cores with variety Fig. 2. Total delay of the cores with variety values of radius values of radius

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Fig. 3. Cores life span with variety values of ra- Fig. 4. The collision between the Centdian and Median with variety values of radius and λ dius

Fig. 5. The collision between the Centdian and Fig. 6. The collision between the Continuous Continuous Centdian with variety values of ra- Centdian and Continuous Median with variety dius and λ values of radius and λ

Fig. 7. The collision between the Centdian and Fig. 8. The Average Hop Count between CentCenter with variety values of radius and λ dian and Center with variety values of radius and λ

achieves improved convergence to delay performance than median core and better transportation performance than center core. The continuous centdian core achieves these properties in a well connected networks, as well as in sparse networks too.

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4 Conclusion and Future Work We have developed a new distributed algorithm for finding and maintaining centdian core in ad hoc sensor network that is based on processing local information of the network. Analytic analysis to bound value l seems to be very interesting. One interesting future direction is by adapting self-stabilizing algorithm to core selection problem in ad hoc sensor network when it gets partitioned and partitions get connected. The analysis of the model where one assumes some distribution for the velocities of the nodes seems also attractive.

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Flooding Speed in Wireless Multihop Networks with Randomized Beamforming Vasil Mizorov1 , J¨ org Widmer2 , Robert Vilzmann3 , and Petri M¨ ah¨ onen4 1

Siemens AG, Corporate Technology, D-81730 Munich, Germany 2 DoCoMo Euro-Labs, D-80687 Munich, Germany 3 Technische Universit¨ at M¨ unchen, D-80290 Munich, Germany 4 RWTH Aachen University, D-52072 Aachen, Germany

Abstract. This paper analyzes aspects of message propagation in multihop wireless networks with beamforming antennas. In particular, we focus our intention on the message propagation in the time domain. Our work uses a simulation based implementation of the 802.11 MAC protocol and a simplified version of a previously proposed MAC protocol, called BeamMAC [1]. Both protocols are compared under different network scenarios with several antenna array implementations (including an omnidirectional antenna). Our conclusions confirm the advantages beamforming antennas have over omnidirectional antennas in wireless multihop networks. Reduced hop distances and reduced time for information dissemination speed up flooding of messages. Moreover, we observe the impact network topology parameters have on the overall performance of the message propagation. Keywords: Ad Hoc Networks, antenna arrays, randomized beamforming, flooding speed.

1

Introduction

The concept of wireless ad hoc networking has been until recently considered only with omnidirectional antennas. Their advantage is that they are small, compact, spatial and radiate power omnidirectionally, i.e. equally in all spatial directions. However, they cause higher interference and block transmissions of other network nodes, significantly reducing the capacity and the throughput of the network. Seeking a way to increase the network capacity and throughput, directional (i.e. beamforming) antennas have been addressed. Their most important feature, to focus the energy into specific spatial directions, has proven to be appealing for providing higher network capacity and greater spatial reuse. There are some downsides in implementing beamforming antennas for wireless ad hoc networking. Firstly, an antenna array means increased hardware size as opposed to the small size of the wireless gadgets. However, the latest technology allows antenna arrays to be smaller in size, making their implementation easier. Secondly, beamforming antennas must “know” the direction of the intended recipient. Otherwise, they might “miss” and radiate in a nonoptimal I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 25–36, 2007. c IFIP International Federation for Information Processing 2007 

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direction. Therefore, additional signal processing algorithms, like Direction-ofArrival (DoA) or Angle-of-Arrival (AoA) algorithms, are necessary for achieving optimal performance. Despite these facts, some research papers report achieving significantly larger gains in terms of network throughput when deploying beamforming antennas. However, they are based on knowing the neighbors’ locations so each node can properly position its antenna beam ([2], [4], [3]). The location information can be obtained by means of Global Positioning System (GPS) [6] or AoA or DoA estimation algorithms ([4], [5]). Bearing in mind battery life consumption, complexity and sometimes processing capabilities of the mobile devices, we believe that these algorithms will overburden the devices and reduce their usage time. Therefore, to reduce the implementation complexity and to simplify the communication, we use randomized beamforming [7]. Nodes choose the direction of radiation randomly and avoid signal processing complexity. Thus, it turns out to be a practical approach when no a priori information is available about location of the nodes. With respect to network topology properties, authors in [7] show that the randomized beamforming improves the connectivity in the network. Due to the longer links beamforming antennas provide, it is possible to ”build a bridge” among previously isolated subnetworks [7]. In addition, [9] discusses the hop distances when randomized beamforming is implemented. It shows that the network diameter, as well as the random node pair hop distance are significantly reduced in the case of randomized beamforming. These findings are very interesting considering that the randomized beamforming introduces zigzag paths, which may increase the hop distances and lead to slower message dissemination. However, authors in [7] and [9] do not consider the effects that a Medium Access Control (MAC) layer introduces to the process of message propagation. The work presented in this paper aims to further investigate the communication features in wireless ad hoc networks with randomized beamforming. In particular, we focus our intention on the time domain of the message propagation in these networks. As this type of study was missing in the scope of the related papers [9] and [7], our work represents the first step towards more realistic approach in the investigation of the time-related features in the message propagation in networks implementing randomized beamforming. For comparison purposes, we simulate the IEEE 802.11 MAC protocol with both, omnidirectional and beamforming antennas. We use flooding speed as main performance metric. In addition, we analyze the route discovery process and discuss its impact on the message propagation. The remainder of this paper is organized as follows. Section 2 describes the proposed BeamMAC protocol. Section 3 explains the antenna and link model, as well as the scenarios used in our simulations. In section 4 we present the time aspects of the message propagation. In addition, we discuss the route discovery process and the impacts beamforming antennas have on it. Finally, Section 5 concludes the work.

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Protocol Model

Work done in the field of implementing beamforming antennas for ad hoc networking resulted in various modifications of the IEEE 802.11 MAC protocol. Some propose extending the Network Allocation Vector (NAV) into directional NAV (D–NAV) by keeping directionality related information [3]. Other proposals implement directional and omnidirectional transmission of Request-To-Send (RTS) and Clear-To-Send (CTS) messages [2]. However, as the 802.11 protocol was designed for omnidirectional transmissions, network performance can deteriorate due to issues specific to directional antennas [8]. Therefore, in order to investigate the time aspects of message propagation in wireless multihop networks, we evaluate a simplified version of the BeamMAC [1] protocol. It gains access to the wireless transmission channel using the following control packets: – Announcement (ANN) – Ready-To-Receive (RTR) – Objection. (OBJ) A node willing to initiate a data transmission, must announce it beforehand. For this purpose, it sends an ANN to inform the transmitter’s surrounding of the forthcoming transmission. In other words, each desired transmission is ”simulated” before being carried out. If the intended destination of the communication, for which the ANN packet is meant, is idle (i.e. not transmitting or receiving), it transmits an RTR packet back to the transmitter. The idea here is to inform the transmitter that the desired addressee is available. Upon reception of an ANN, each neighbor currently engaged in a parallel communication as a receiver, determines the interference that would be caused by the forthcoming transmission.

ANN

Source

Destination Other Receiving Stations

DATA

RTR

ACK

OBJ Estimation

Fig. 1. BeamMAC Channel Access

If the interference is so high to degrade the ongoing communication, the receiver sends an OBJ back to the sender of the ANN. In case the level of the interference maintains an acceptable level, the receiver does not send an OBJ back. In case an OBJ is received, the node enters a backoff state. Details of how an ANN packet is assessed by a receiving node are not discussed in this paper. Instead, we refer the interested reader to [1]. When the transmission is successfully “simulated” (ANN and RTR are sent, and no OBJ is received), the actual data packet can be sent. Upon error-free reception of the data packet, the receiving node transmits an acknowledgment (ACK) back.

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3

Network Model

3.1

Antenna Model

Antenna arrays, used in Multiple Input Multiple Output (MIMO) systems to increase the user data rate, can have different shapes; most prominently, linear or circular. Antennas with linear geometry are referred to as linear antenna array, whereas antennas with circular geometry are known as circular antenna arrays. Circular antenna arrays offer higher diversity and improved link capacity ([17], [18]. Thus, the antenna model used in our simulations is Uniform Circular Array (UCA) [7]. An UCA array comprises m identical isotropic radiators placed uniformly on a closed circumference. Each antenna element transmits with the same power pt /m at a wavelength λ = fc , with c = 3 · 108 m/s and carrier frequency f . By implementing a phase shift between the array elements, the resulting antenna beam pattern can be controlled. The shape of the resulting beam depends on the target direction Θb , known as boresight direction, and the number of antenna elements. Examples of antenna patterns for UCA antenna with m = 4 elements are shown in Figure 2. Directivity of a 4−element UCA

Directivity of a 4−element UCA 90

Directivity of a 4−element UCA

90

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5

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0

210

330

240

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◦

(a) Θb = 0

300 270

◦

(b) Θb = 30

◦

(c) Θb = 70

Fig. 2. Gain patterns of UCA with m = 4 elements

In general, an antenna pattern consists of a main lobe and side lobes. The main lobe represents the radiation in the desired direction, whereas the side lobes refer to the radiation in all other directions. It can be noted from antenna theory [10] that with an increase in the number of elements in the antenna array the radiated power in the direction of the main lobe increases. Note that due to antenna reciprocity, the gain characteristic is valid for both, transmission and reception. 3.2

Wireless Link Model

The wireless link model is based on a line-of-sight communication between two nodes, given their transmission parameters and their distance. Figure 3 depicts the implemented link model.

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Transmitter d

pt gt

gr

Receiver

pr

Fig. 3. Wireless link model

One node transmits the signal with power pt , which is received by the other node with power pr . The gain of the antenna at the transmitting node is gt . The gain of the receiver’s antenna in the corresponding direction toward the transmitter is gr . Thus, we can write  −α d pr = gt gr , (1) pt 1m where α represents the pathloss exponent of the propagation environment. The value of α is environment-dependent and is approximately α = 2 for a free space scenario and α = 3...5 for urban areas [10]. The link establishment between two nodes assumes that the received power pr is above the receiver sensitivity pr0 , that is (2) pr ≥ pro . In the following, we assume that all nodes have the same transmission power pt and reception sensitivity pro . Thus, considering the fact that antenna pattern reciprocity holds (same antenna pattern for transmission and reception), all links in the network can be considered as bidirectional (or undirected) links. That is, if a node A can communicate with node B, then node B can communicate with node A, as well. One should note that our simulation model does not implement propagation phenomena like fading. 3.3

Randomized Beamforming

As mentioned in Section 1, in order to avoid implementing complex signal processing algorithms, we use a communication paradigm referred to as randomized beamforming [7]. Its implementation is based on nodes choosing a random direction where to point their antenna beams. With choosing both, the boresight direction and the antenna array direction, uniformly distributed in the interval [0, 2π] the shape of the resulting pattern is fully described. In addition, all nodes keep their beam direction constant the whole time, i.e. once chosen it does not change. 3.4

Network Topology and Scenarios

The network topology in our simulations comprise n nodes distributed uniformly at random on a square area with side length l. For obtaining the node coordinates

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(x, y) we use the Mersenne Twister pseudo-random number generator [11]. Nodes in the network are static. We use a simple flooding mechanism to disseminate messages into the network. One node sends a packet and all other nodes forward the packet until received by every node. To more closely model reality, we borrow parameters from the IEEE 802.11 standard [12]. Namely, parameters used in our simulations are: frequency f = 2 GHz, pathloss exponent α = 3 (urban area), maximum transmission power pt = 0.1 W , communication threshold Pr0 = −111 dB, sensitivity threshold (for 802.11) Ps0 = −121 dB and transmission range for omnidirectional antenna Tx -Range = 121 m. In addition, we simulate the 802.11 protocol only with omnidirectional antennas, whereas the BeamMAC protocol with both, omnidirectional and UCA antennas (particularly UCA with m = 4 or UCA4 and m = 10 or UCA10). Table 1. Network scenarios Network size Small Medium Large

n

l (m) Area (km2 )

100 577 500 1290 2000 2580

0.33 1.66 6.65

We conduct our simulations with node density n/l2 = 300 km−2 . In order to obtain at least 95% connectivity in the network, we use calculations taken from [13] and calculate the area for a certain number of nodes so to guarantee the required connectivity. In fact, the connectivity in the network is above 99%. In order to perform a thorough analysis of the message dissemination process, we regard three scenarios in our simulations [15]. Namely, we use different network sizes, i.e. small, medium and large, as we want to clearly investigate any connection between the size of the network and the performance of the both protocols. The number of nodes for each network scenario is 100, 500 and 2000 nodes, respectively. In addition, the network area is 0.33 km2 , 1.66 km2 and 6.65 km2 , respectively. The simulated scenarios (number of nodes, length, network area) are given in Table 1.

4

Simulation Analysis

For the purpose of conducting the analysis we apply a protocol driven ad hoc network simulation tool (PANTS). It is an event-based simulator developed in C++ language, incorporating realistic models for beamforming antenna patterns, calculated using accurate formulas provided by antenna theory [10] and moreover, implementing the two investigated protocols, IEEE 802.11 and BeamMAC. For visualization purposes of the network topology and the distribution of the nodes in it, our simulation tool uses the Library of Efficient Data Types and Algorithms (LEDA) [14].

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With respect to the simulated parameters, we were interested in the flooding speed, flooding time and route reply time. The first one describes the speed with which a message propagates in the network, in terms of how many nodes have received the message until a certain time instant. The second parameter tells us how long it takes to flood a message in the network. Finally, the third parameter helps us better understand the route reply in networks implementing randomized beamforming. To be compliant with the protocol specifications, for 802.11 we implement broadcasting as defined in the IEEE 802.11 standard [12] (without RTS/CTS control handshake) and we omit the ACK packet in BeamMAC implementation. In addition, in the route reply process we make use of the 802.11 DCF function (RTS/CTS scheme) and all of the BeamMAC protocol functions. For accuracy purposes, we run a large number of simulations for every scenario. In particular, for the small and medium network we use 200 runs and for the large network we use 100 runs (due to large memory consumption). In addition, in our graphs we give a confidence interval of one sigma (σ being standard deviation) which equals to a confidence level of 68.27%. 4.1

Flooding Speed

We define the flooding speed as a curve that gives the percentage of flooded nodes depending on the time. We calculate the number of flooded nodes on every packet transmission and the result (nodes, time) is represented as a point of the flooding speed curve. Figures 4–6 depict the results we obtained from the considered scenarios given in Table 1. Flooding speed Nodes=100, Node density=300 (nodes/km2)

Percentage flooded nodes

100

80

60

40 802.11 BeamMAC-OMNI BeamMAC-UCA4 BeamMAC-UCA10

20

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Time (s)

Fig. 4. Flooding speed for 802.11 and BeamMAC protocol, small network

Figure 4 gives the results for the small network scenario (n = 100). It compares several different combinations of antenna and MAC protocol, namely the 802.11 protocol (implemented with OMNI antenna) and the BeamMAC protocol implemented with directional antenna (UCA4 and UCA10) and OMNI antenna. The obtained flooding speed curves are close to one another, which means that the advantages of the beamforming antennas are hardly noticeable.

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There is a minor difference in the Percentage of Flooded Nodes (PFN) between the BeamMAC and the 802.11 for a fixed value of the time, which is about 1%–5% for BeamMAC-UCA4 and BeamMAC-UCA10, respectively. However, the BeamMAC-UCA10 scheme has the highest flooding speed. The poor performance observed in the small network scenario is due to the impact of the border effects on the message propagation. Namely, caused by the random beamforming and the fact that the network area is relatively small, many nodes transmit outside the area. This is more visible in the beamforming case, as their transmission range is up to several times bigger than the one of the omnidirectional antennas. Flooding speed 2 Nodes=500, Node density=300 (nodes/km )

Percentage flooded nodes

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20

0 0

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 Time (s)

Fig. 5. Flooding speed for 802.11 and BeamMAC protocol, medium network Flooding speed Nodes=2000, Node density=300 (nodes/km2)

Percentage flooded nodes

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20

0.1

0.2

0.3

0.4

0.5

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0.7

0.8

Time (s)

Fig. 6. Flooding speed for 802.11 and BeamMAC protocol, large network

The medium network scenario shown on Figure 5 as well as the large network scenario on Figure 6 show an improvement in the message propagation for beamforming antennas. In particular, the larger the network size is, the better the flooding speed of the beamforming antennas. In the latter network, the difference between the BeamMAC-UCA4 and the 802.11 is more than 20%, which makes the UCA4 antenna a more sensible and more practical solution. The impact that border effects have on the message propagation is minor, as a larger portion of the nodes radiate inside the network area and less transmissions are void.

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It can be noted from Figures 4–6 that the performance of the combination of the BeamMAC protocol and omnidirectional antenna (BeamMAC-OMNI) experiences the poorest performance. The main reason for this inferior behavior is protocol related. Namely, the BeamMAC protocol takes longer to access the wireless channel (ANN and RTR) compared with the 802.11 protocol (only DIFS - Distributed Inter Frame Space). Consequently, this has proven to be reason for the slower flooding speed of the BeamMAC-OMNI implementation. 4.2

Flooding Time

The flooding time parameter is defined as time it takes to flood the whole network. It can be derived from the flooding speed curves, as the time instance when the percentage of flooded nodes is 100 (i.e. whole network is flooded). We show the obtained values from our simulations in Figure 7. The parameter flooding time can be understood as a follow-up to the flooding speed analysis. In the small network scenario there is scarcely a difference between the omnidirectional and directional antenna implementation. However, increasing the network size the difference in the flooding time between the directional and omnidirectional antenna implementation is continuously reducing, meaning that beamforming antennas have the dominance in larger network areas. The reduction of the flooding time is about 20%–30% (large network scenario) for the BeamMAC-UCA4 and for the BeamMAC-UCA10, respectively. Flooding time Node density=300 (nodes/km2) 0.7 0.6

Time (s)

0.5 0.4 0.3 802.11 BeamMAC-OMNI BeamMAC-UCA4 BeamMAC-UCA10

0.2 0.1 0

500

1000

1500

2000

Number of nodes

Fig. 7. Flooding time for 802.11 and BeamMAC protocol

4.3

Route Reply (RREP) Time

In addition to the flooding mechanism analyzed in Section 4.1, we implemented and analyzed a route reply mechanism, as well. We believe that this parameter will give us more understanding about the time it takes two nodes to establish a path. The initiator of the route discovery (i.e. the source) broadcasts a packet to the destination, which after receiving it, generates and sends a route reply packet to the source. The route reply packet is not broadcasted, but rather sent using a

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hop-by-hop unicasting. The route reply mechanism is based on a source routing concept, i.e. the reply packet follows the same path on which the route request came from. RREP Time 2 Node density=300 (nodes/km ) 1

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0.8

0.6

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0.2

0 0

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Number of Nodes

Fig. 8. Route reply time for 802.11 and BeamMAC protocol

As Figure 8 shows, the network area has a negative impact on the route discovery process, as well. On the one hand, considering the small network scenario, we confirm that there is an insignificant reduction of the route reply time with beamforming antennas. On the other hand, considering the large network scenario, we notice a superior performance of the BeamMAC protocol. The route reply time has been reduced by about 30%–40% in the case of the BeamMACUCA4 and the BeamMAC-UCA10, respectively. Due to the previous analysis of the flooding speed, we can see here that having faster message propagation ensures quicker delivery to the desired destination. This in turn, helps in achieving better route reply times.

5

Conclusion

Our work outlines the positive impact that the beamforming antennas have on the information dissemination in wireless multihop networks. Our study is performed by simulating realistic network scenarios, considering the very popular 802.11 MAC protocol and a simplified version of the BeamMAC protocol. In addition, we use parameters adopted directly from the IEEE 802.11 standard [12]. Results presented in this paper represent a performance comparison of the broadcast mechanism in multihop networks. Together with the findings in [7] and [9], we provide a thorough analysis of the parameters related to the network topology as well as to the message dissemination in these networks. Although our approach includes a simple flooding model and a simple sourcerouting based route discovery process, we show that the beamforming antennas outperform the omnidirectional antennas. They provide faster message dissemination and faster route discovery process. In addition, we identify their downsides (e.g. void transmission) when implemented in small network scenarios. However,

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in large network area scenarios the beamforming antennas have proven to be superior. This approach could be the worst case analysis when there is no other network information available. As soon as more topology related information is available, nodes can use sophisticated location finding algorithms to adapt or optimize their radiation direction. Moreover, this particular study can be of further help in service discovery scenarios in wireless multihop networks. By simply defining a threshold when the service announcement or service query is successful (e.g. 80% of nodes receive the packet), looking into Figures 4–6 we can obtain the time it takes for a certain service to be properly advertised. We strongly believe that the implementation of beamforming antennas has an enormous potential in wireless multihop networks. Therefore, more in-depth analysis is required which will investigate the actual routing and will look into issues related to cross–layer optimization.

Acknowledgment The authors would like to thank Imad Aad from DoCoMo Euro-Labs and Christian Bettstetter (previously with DoCoMo, now with University of Klagenfurt) for various discussions and very useful comments.

References 1. R. Vilzmann, C. Bettstetter, C. Hartmann: BeamMAC: A New Paradigm for Medium Access in Wireless Networks, International Journal of Electronics and ¨ Volume 60, Number 1, (Jan. 2006) 3–7. Communications (AEU), 2. M. Takai, J. Martin, A. Ren, R. Bagrodia: Directional Virtual Carrier Sensing for Directional Antennas in Mobile Ad Hoc Networks, In Proc. 3rd ACM MobiHoc, Switzerland, (June 2002) 183–193. 3. R. Roy Choudhury, N. H. Vaidya: Ad Hoc Routing Using Directional Antennas, Technical Report, Coordinated Science Laboratary, University of Illinois at Urbana-Champaign (Aug. 2002). 4. H. Singh, S. Singh: A MAC Protocol based on Adaptive Beamforming for Ad Hoc Networks, In Proc. IEEE PIMRC, China, (Sept. 2003) 1346–1350. 5. H. Singh, S. Singh: Smart-802.11b MAC Protocol for Use with Smart Antennas, In Proc. IEEE ICC, France, Volume 6, (June 2004) 3684–3688. 6. Y.-B. Ko, V. Shankarkumar, N. H. Vaidya: Medium Access Control Protocols using Directional Antennas in Ad hoc Networks, In Proc. IEEE Infocom, Israel, (March 2000), 13–21. 7. C. Bettstetter, C. Hartmann, C. Moser: How Does Randomized Beamforming Improve the Connectivity of Ad Hoc Networks?, In Proc. IEEE ICC, Korea, (May 2005), 3380–3385. 8. R. Vilzmann, C. Bettstetter: A Survey on MAC Protocols for Ad Hoc Networks with Directional Antennas, In Proc. EUNICE Open European Summer School, Spain, (July 2005), 268–274. 9. R. Vilzmann, C. Bettstetter, D. Medina, C. Hartmann: Hop Distances and Flooding in Wireless Multihop Networks with Randomized Beamforming, In Proc. ACM MSWIM, Canada, (Oct. 2005), 20–27.

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10. Constantine A. Balanis: Antenna Theory, Analysis and Design, John Wiley & Sons, Inc., 2nd Edition, (1997). 11. M. Matsumoto, T. Nishimura: Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator, ACM Transactions on Modeling and Computer Simulation, Volume 8, Number 1, (1998), 3–30. 12. IEEE Standards Board: Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, (1999), http://www.ieee802.org/11/. 13. C. Bettstetter: Mobility Modelling, Connectivity, and Adaptive Clustering in Ad Hoc Networks, PhD Thesis, Technische Universit¨ at M¨ unchen, Germany, (Oct. 2003). 14. Algorithmic Solutions: LEDA - Library of Efficient Data Types and Algorithms, (Dec. 2005), http://www.algorithmic-solutions.com/enleda.htm. 15. V. Mizorov: Routing in Ad Hoc Networks with Beamforming Antennas, Master Thesis, RWTH Aachen University, (Dec. 2005). 16. T. Korakis, G. Jakllari, L. Tassiulas: A MAC protocol for full exploitation of directional antennas in ad hoc wireless networks, In Proc. 4th ACM MobiHoc, USA, (June 2003), 98–107. 17. W. Weichselberger, G. L. de Echazarreta: Comparison of Circular and Linear Antenna Arrays with respect to the UMTS Link Level, COST 260 Management Committee and Working Groups Meeting, G¨ oteburg, Sweden, (May 2001). 18. N. Razavi-Ghods, M. Abdalla, S. Salous: Characterisation of MIMO Propagation Channels Using Directional Antenna Arrays, in Proc. IEE International Conference on 3G Mobile Communication Technologies (3G2004), London, UK, (October 2004).

Power Amplifier Characteristic-Aware Energy-Efficient Transmission Strategy Kwanghun Han, Youngkyu Choi, Sunghyun Choi, and Youngwoo Kwon School of Electrical Engineering and INMC Seoul National University, Seoul, Korea {khhan,ykchoi}@mwnl.snu.ac.kr, {schoi,ykwon}@snu.ac.kr

Abstract. The energy consumption in transmitting an information bit, i.e., energy-per-bit, has been known to decrease monotonically as the transmission time increases [1]. However, when considering the power amplifier (PA) characteristics, we learn that the energy-per-bit starts to increase as the transmission time becomes long over a certain threshold. This is caused by the fact that, in a wireless device, it is not the transmission power, which determines the energy consumed during transmissions, but the input power to the PA whose output power is used as the transmission power. Based on our new trade-off model between the energy-per-bit and transmission time, we revisit known energy-efficient scheduling algorithms. Finally, we evaluate the impact of the new tradeoff model and the performance of algorithms via simulations.

1

Introduction

For battery-powered hand-held mobile devices, it is a key concern to reduce the energy consumption in order to extend the device’s life time. Since the wireless communication module is a major source of the overall energy consumption in such devices [2, 3], many studies in the literature have tried to minimize the energy consumption by turning off the unused parts of the wireless communication module after finishing packet transmission as quickly as possible [4, 5, 6]. In the meantime, the authors in [1, 7] proposed another approach, which reduces the transmission energy by controlling the transmit power when sending a given amount of data. They showed based on Shannon’s capacity equation that the energy-per-bit monotonically decreases as the transmission time1 increases. According to this trade-off relation, the authors proposed Lazy scheduling algorithm, which minimizes the transmission energy by sending an information bit as slowly as possible, which is accomplished by using low order modulation, low code rate channel coding and low transmission power. However, their model [1] 

1

This research is in part supported by University IT Research Center (ITRC) project, and by the SNU-Samsung 4G collaboration project. Here, the exact meaning of the transmission time is the inverse of spectral efficiency. Assured that it is not confusing, hereafter, we will simply use this term to represent this meaning.

I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 37–48, 2007. c IFIP International Federation for Information Processing 2007 

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accounts for only the transmission energy while circuitry typically keeps consuming energy in order to maintain the transmission module consistently active even when there is no on-going packet transmission. The power required by circuitry is called electronics power, and this is almost constant irrespective of the transmission power. When considering the effect of electronics power, Yu et al. showed that the energy-per-bit does not monotonically decrease with transmission time any more, especially when the electronics power is comparable with the transmit power [8]. Such a situation can indeed happen when the transmission range is extremely small as in the sensor networks, while the transmit power dominates the electronics power in most wireless communication systems. Shuguang et al. verified through in-depth circuit-level analysis [9] that such a trade-off relation is really present in the context of sensor network. Based on this trade-off model, the authors in [8] proposed a packet scheduling algorithm, which aims at minimizing the energy dissipation in multi-hop wireless sensor networks. Then, in a long-range communication, e.g., conventional cellular network, where the transmit power dominates the electronics power, is it still reasonable to think that the energy-per-bit monotonically decreases as the transmission time increases? Our major finding, in this paper, is that even if the electronics power is ignorably small compared with the transmit power (i.e., long-range communications), the energy-per-bit does not monotonically decrease as transmission time increases when the power amplifier (PA) characteristics are considered. In a strict sense, we should note that the actual energy consumption is not caused by the transmission energy but by the energy consumed by PA to generate the transmit power. Accordingly, we revisit the energy-efficient scheduling problems, which are considered in [1, 10], based on our new trade-off model. We expect that if the algorithms derived in this paper are used for uplink scheduling, especially in a cellular network, the lifetime of battery-powered device could be extended. The rest of this paper is organized as follows: In Sect. 2, we derive the tradeoff model between the energy-per-bit and transmission time considering the PA characteristics. In Sect. 3, we formulate the energy-efficient scheduling problems, and then present not only two offline algorithms, called Modified Lazy scheduling and Modified Move Right scheduling, but also the online version of each offline algorithm, respectively. In Sect. 4, we evaluate the performance of the algorithm via simulation. Finally, in Sect. 5, we conclude the paper with some remarks on the future work.

2

Revised Trade-Off Model

The PA efficiency is defined as the ratio of the output power to the power provided by direct current (DC) voltage source. Since the PA output power is equivalent to the transmit power in the context of communication system, we denote the output power by Ptx as shown in Fig. 1.

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DC voltage source

P in

P tx

Fig. 1. A diagram for power amplifier

Let us denote the power efficiency by η(Ptx ) (< 1), which is typically nondecreasing with Ptx [11, 12]. Then, Ppa , which represents the actual power consumed by PA, is represented as Ppa =

Ptx , 0 ≤ Ptx ≤ Ptx,max , η(Ptx )

(1)

where Ptx,max is the maximum output power, a design parameter of a PA.2 Due to the dependence of η on Ptx , (1) implies that as we reduce Ptx by Δ, the decrement of Ppa is not linearly proportional to Δ, but is altered by the operating range of Ptx . Under an Additive White Gaussian Noise (AWGN) channel with noise power N , the optimal channel coding gives Shannon’s capacity as follows: C=

αPtx 1 log2 (1 + ), 2 N

(2)

where α represents the power loss due mainly to the path loss. Although the actual transmission rate should be less than C, for the convenience of discussion, we just regard C as the achievable rate. When we denote the time necessary to transmit one information bit by t = C1 , the energy-per-bit, Er (t), is given by Er (t) = tPpa = t

Ptx N 2 , Ptx = (2 t − 1). η(Ptx ) α

(3)

If η(Ptx ) is simply modeled by a constant, Er (t) is monotonically decreasing and convex in t as shown in [1,7]. Now, using a proposed power efficiency model in [13], we replace η(Ptx ) with  η(Ptx ) = ηmax 2

Ptx , Ptx,max

(4)

In fact, the additional power provided by PA amounts to Ptx − Pin , and hence those, who are interested in the PA performance itself, typically use a metric called powerin . Since the PA gain defined as added efficiency (PAE), which is defined as PtxP−P pa typically ranges from 20 to 30 dB, Ptx − Pin  Ptx , and hence PAE can be thought to be nearly equal to the power efficiency. Ptx Pin

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where ηmax is the maximum PA efficiency achieved when Ptx = Ptx,max . Accordingly, we obtain a new energy-per-bit Er (t) as follows:  Ptx Ptx,max t. (5) Er (t) = ηmax We present two theorems, which show the property of the trade-off relation between Er (t) and t. For the purpose of comparison, we denote by Ec (t) the energy-per-bit obtained when the power efficiency is considered constant, e.g., η = ηmax as in the literature. Theorem 1. Er (t) is neither monotonically decreasing nor convex in t. 1

Proof. It can be shown that as t becomes much smaller than 1, Er (t) ∼ 2 t t and 2 Ec (t) ∼ 2 t t. Therefore, Er (t) is also monotonically decreasing and convex in t as Ec (t). On the other hand, √ as t approaches infinity, Ec (t) approaches a constant ln 2 i.e., 2N while E (t) ∼ t. Thus, Er (t) becomes an increasing and concave r αηmax function in the region of large t. Since Er (t) changes from a decreasing convex function to an increasing concave function in the range of t from 0 to infinity, we can prove that there exist both minimum and inflection points of Er (t). Theorem 2. When we denote t yielding the minimum and inflection points of Er (t) by t∗ and to , respectively, t∗ < to . √  2 N Ptx,max Proof. From (5), Er (t) = β 2 t − 1t, where β = √αηmax . Differentiating

−2 r t g(t), where g(t) = (1 − lnt 2 )2 t − 1. Er (t) by t, we obtain dE dt = β(2 − 1) Since Er (t) becomes an increasing function when t is large, g(t) < 0 when t < t∗ , and g(t) > 0 when t > t∗ . 2 d 2 Er − 32 2t ln 2 r t 2 t3 k(t), where Differentiating dE dt again, we obtain dt2 = β(2 − 1) 2 k(t) = (2 ln 2 − 1)2 t − 2 ln 2. From k(to ) = 0, to = log ( 22 ln 2 )  1.0849. Since 2

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Figure 2 plots both Ec (t) and Er (t). Referring to the parameters of RF2162PA [13], we set Ptx,max to 1.41 W and ηmax to 0.5. Assuming that the received N tx signal-to-noise ratio (SNR), αP N , ranges from 0.11 dB to 20 dB, we set α appropriately in order that Ptx does not exceed Ptx,max at the highest SNR (i.e., 20 dB). Obviously, we see that Er (t) becomes quite different from Ec (t). This observation tells us that the energy-efficient scheduling algorithm should be revisited based on the new trade-off model. This motivation is differentiated from other approaches [7, 8] because the trade-off model, which considers only the effect of electronics power, just accounts for the short-range communication like sensor network, while the electronics power can be ignored in the energy consumption of many other communication systems.

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Energy Efficient Uplink Scheduling

In this section, we consider the energy efficient uplink scheduling problem in cellular systems. Based on our trade-off model, we derive offline and online algorithms. 3.1

Problem Definition

In cellular systems, most subscriber stations are battery-powered while the base station is AC-powered. Accordingly, the energy efficient transmission strategy can be beneficial, especially for uplink transmissions. In order to highlight the impacts due to our new trade-off model, we restrict the discussion to the scenario of a point-to-point communication. Let us denote by w(τ ) the amount of energy required to transmit a packet over a time duration τ by subscriber stations. We assume that M packets should be transmitted within time [0, T ), which can be considered the time allocated to a subscriber station by the scheduler. For the purpose of analytical simplicity, all packets are assumed to be of equal size. We denote the arrival time of the ith packet by ti and the packet interarrival time by di = ti+1 − ti . Without loss of generality, the first packet is assumed to arrive at time zero, i.e., t1 = 0. The scheduler determines both the packet transmission duration τ = (τ1 , · · · , τM ) and the transmission start time s = (s1 , · · · , sM ). Based on this system description and assumption, we formulate an energy-efficient scheduling problem constrained by the total allowed transmission time for a group of packets, which is equivalent to the problem considered in [1].

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Problem 1. Find the scheduling, τ and s, which minimizes the total transmission energy: M min W (τ ) = i=1 w(τi ), s.t. ti ≤ si , ∀i ∈ {1, ..., M }, sM + τM ≤ T. For the purpose of notation, we denote this problem by ESP-I. As shown in Problem 1, the transmission of the last M th packet should be completed within time T . However, since Problem 1 does not take care of the delay, which an individual packet would experience, if T is quite large, the scheduling result may not be desirable for some types of traffic. Note that packets often have transmission delay bound, and hence packets exceeding a certain delay bound would be considered a delivery failure or discarded. This is quite typical for packets out of real-time multimedia applications. Therefore, we consider another problem formulation of energy-efficient scheduling with constraints of per-packet delay bound, and denote the problem by ESP-II. Given a vector of per-packet delay bound q = (q1 , · · · , qM ), where qi represents the maximally allowed transmission time for the ith packet, ESP-II can be written as follows: Problem 2. Find the scheduling, τ and s, which minimizes the total transmission energy: M min W (τ ) = i=1 w(τi ), s.t. ti ≤ si , ∀i ∈ {1, · · · , M }, si + τi ≤ qi , ∀i ∈ {1, · · · , M }. 3.2

Offline Algorithm

Modified Lazy Scheduling Algorithm. In order to solve ESP-I, Lazy scheduling algorithm was originally developed, and it holds optimality and feasibility (see the detailed algorithm and proofs in [1]). It achieves transmission energy reduction by lowering the transmission power and increasing the transmission time as much as possible under the strictly convex and monotonically decreasing energyper-bit function. Now, since the energy-per-bit function is changed in our model, we develop a modified Lazy scheduling algorithm, which is an extended version of the Lazy scheduling. In order to devise modified Lazy scheduling, we consider the two lemmas induced from the trade-off relationship described in Section 2. Lemma 1. There exists a packet transmission time τmax , which minimizes the transmission energy consumption. Proof. From Theorem 2, there exists a transmission time-per-bit t∗ , which yields the minimum energy-per-bit value. Accordingly, we can obtain the packet

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transmission time τmax , which minimizes the energy consumption needed to transmit a packet, by multiplying the packet size and t∗ together. Lemma 1 tells us that we do not need to consider the range of τ longer than τmax in the optimization problem. The reason is that using τ (> τmax ) does not help minimizing the energy consumption nor satisfying the delay constraint. Lemma 2. When the range of τ , which we are interested in, is upper-bounded by τmax , w(τ ) can be regarded as a convex function of τ . Proof. According to Theorem 2 in Sect. 2, Er (t) is convex when the transmission time-per-bit t is less than t∗ since t∗ is less than the inflection point to . Therefore, w(τ ) is also convex in τ when τ < τmax . Our modified Lazy scheduling algorithm consists of two parts. The first part is called minimum energy transmission part, where the scheduler finds the packets which can be transmitted with the minimum energy packet transmission time τmax . The second part is called legacy Lazy scheduling part, where the Lazy scheduling is conducted for the set of the remaining packets. The modified algorithm is summarized in Algorithm 1. Algorithm 1. Modified Lazy Scheduling si ⇐ ti , i ∈ {1, ..., M } and si+1 = T tsum ⇐ s1 and smax ⇐ 0 for i = 1 to i ≤ M do tsum ⇐ tsum + τmax if tsum ≤ si+1 then smax ⇐ i and tsum ⇐ si+1 for i = 1 to i ≤ smax do si+1 ⇐ max{si+1 , si + τmax } and τi ⇐ τmax if smax < M then Do Lazy scheduling beginning from the (smax + 1)th packet

Modified Move Right Algorithm. In order to solve ESP-II, we modify the Move Right scheduling algorithm [10]. Originally, Move Right algorithm was developed to solve ESP-I when the non-identical energy-per-bit transmission function is used for each packet. However, we modify this algorithm to deal with the constraints of per-packet delay bound. The main idea of the original Move Right algorithm is to find the optimal transmission start time with an iterative manner, and this notion of iteration is maintained in our proposed algorithm as well. The modified algorithm has two additional constraints: one is a delay bound for the feasibility and the other is a transmission duration bound for the minimum transmission energy. Initially, si and τi are set to ti and min{si+1 − si , qi − si , τmax }, respectively. For a pair of packets, which arrive subsequently, we find s2  (s2 ≤ s2  ≤ s2 +τ2 ), τ1  , and τ2  such that w(τ1  )+w(τ2  )

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is minimized. This operation proceeds until the last two packets. In order to get the optimum value, the algorithm repeats this process until the scheduling results converge. The detailed algorithm is described in Algorithm 2, where the superscript k−1 k−1 k−1 k in τik and ski indicates the kth iteration. f (τik−1 , τi+1 , si si+1 ) returns the k k k k ) when updated set of values (τi , τi+1 , si+1 ), which minimize w(τi k ) + w(τi+1 k−1 k−1 k k k k k τi +τi+1 is fixed, where τi , τi+1 , and si+1 satisfy τi ≤ τmax , τi+1 ≤ τmax , and k−1 k−1 k−1 k ski+1 ≤ sk−1 +τik−1 , i+1 +τi+1 ≤ min{si+1 +τmax , qi+1 }, respectively. If si+1 > si k k k (τi , τi+1 , si+1 ) are not changed from the values at the (k − 1)th iteration. The optimality is also shown in [10] and this is maintained as well in our algorithm since we only consider the convex region of w(τ ) given when τ is less than or equal to τmax . Algorithm 2. Modified Move Right Scheduling k ⇐ 0 and f lag ⇐ 0 ski ⇐ ti , i ∈ {1, ..., M } τik ⇐ min{ski+1 − ski , qi − ski , τmax }, i ∈ {1, ..., M } while f lag = 0 do k ⇐k+1 τ k ⇐ τ k−1 and sk ⇐ sk−1 for i = 1 to i ≤ M − 1 do if ski+1 = ski + τik then k−1 k−1 k−1 k (τik , τi+1 , ski+1 ) = f (τik−1 , τi+1 , si si+1 ) k k−1 then if τ = τ f lag ⇐ 1

3.3

Online Algorithm

Online Extension of Modified Lazy Scheduling Algorithm. For the extension to online algorithm, we assume that packets arrive according to the Poisson distribution with mean rate λ. Our goal is to achieve the optimal performance in an average sense. To do so, we need a more tractable form of the scheduling result achieved by the algorithm and this was derived in [1]  offline  k 1 ∗ as τj = maxk∈{1,...,M−(j+bj )} k+bj i=1 Ci , where M is the total number of packets arriving during [0, T ), j is the current packet to be sent, and Ci , i ∈ {1, ..., M − j − bj } is the inter-arrival time between the (j + i − 1)th packet and the (j + i)th packet. bj is the number of packets backlogged at that time when the jth packet is transmitted. From this expression, one can derive   1 k , where b is the curD a random variable τ ∗ (b, t) = maxk∈{1,...,M} k+b i i=1 rent backlog, M is a random variable representing the number of packet arrivals during [t, T ), and Di is the average inter-arrival time when M = i. Finally, the transmission duration of the current packet is determined by E[τ ∗ (b, t)]. However, we simply modify it to τ ∗ = min{τmax , E[τ ∗ (b, t)]} for our algorithm by considering τmax .

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Online Extension of Modified Move Right Algorithm. Online extension of modified Move Right scheduling can also be achieved by the similar method used for the online modified Lazy scheduling case. In [10], the authors derived the online algorithm using a look-ahead buffer. In other words, the scheduler waits for gathering some packets during a determined time. However, for ESPI, this look-ahead buffer adds a constant value to the total transmission delay, and hence it can cause the actual duration of transmission to be shorter, which means that more energy consumption is required. Accordingly, instead of using the notion of the look-ahead buffer, we make use of the assumption that for a given time interval, the packets arrive with the same inter-arrival time, which is determined by the ratio of the given time interval to the average number of packet arrivals during that interval. Then, we run Move Right scheduling to decide the transmit duration of the current packet using the information of b backlogged packets and the expected packet arrivals, where each packet is assumed to have the same delay margin from its own arrival time.

4

Simulation Results

In this section, we evaluate the proposed algorithms using an MATLAB-based simulator. We assume that the size of a packet is 10 kbits and the system bandwidth is 106 symbols/sec. A simulation run lasts for 10 sec, and during the last 0.5 sec, no packet is assumed to arrive in order to prevent the transmission energy from divergence. For other parameters, we use the same values mentioned in Sect. 2. Whenever a result needs to be averaged, we repeat the simulation runs as many as 10 times. First of all, we compare Lazy and modified Lazy scheduling for the same packet arrival patterns under the proposed trade-off model. As shown in Fig. 3, when the arrival rate is less than 150 packets/sec, Lazy scheduling tends to send each packet with a transmit duration longer than τmax , and hence more energy is consumed. In the meantime, modified Lazy scheduling limits the transmit duration up to τmax , which yields the minimum energy consumption. However, as the packet arrival rate increases, the difference of energy-per-bit between two algorithms becomes marginal since both algorithms will yield the same result if the optimal transmit duration is less than τmax . Second, Fig. 4 compares the online modified Lazy scheduling algorithm with corresponding offline version. The discrepancy between two algorithms becomes larger as the packet arrival rate increases. This is due to the fact that the online algorithm only minimizes the average energy consumption. Finally, Fig. 5 shows the energy per bit achieved by offline and online modified Move Right scheduling algorithm. In this simulation, we assume that the perpacket delay bound, qi , is given by 200 msec for every packet. When the packet arrival rate is less than 90 packets/sec, the delay bound does not affect the energy-per-bit much because the energy optimal transmit duration is determined as a value less than the delay bound. However, as the packet arrival rate increases,

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the delay bound tends to limit the transmit duration, and hence the energy-perbit also increases. This remark can be confirmed by comparing them with the modified Lazy scheduling result, which does not impose per-packet delay bound constraint.

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In this work, we show that the characteristic of power amplifier leads to a non-convex energy-per-bit curve. Based on this trade-off model, we propose modified Lazy scheduling and modified Move Right scheduling algorithms, which were originally proposed in [1, 10], to solve the energy minimization problem, where the delay constraint is imposed on either a group of packets or each packet. Since the transmit power in the uplink of a cellular network should be controlled in order to deal with the near-far problem and the inter-cell interference, it is our on-going work to solve both the energy-efficient scheduling and power control problem jointly in the multi-cell environment.

References 1. Prabhakar, B., et al.: Energy-Efficient Transmission over a Wireless Link via Lazy Packet Scheduling. In: Proc. IEEE INFOCOM. (April 2001) 2. Stemm, M., et al.: Reducing Power Consumption of Network Interfaces for Handheld Devices. In: Proc. MoMuC. (September 1996) 3. Flinn, J., Satyanarayanan, M.: Energy-aware adaptation for mobile applications. In: Proc. ACM SOSP. (December 1999) 4. Krashinsky, R., Balakrishnan, H.: Minimizing Energy for Wireless Web Access with Bounded Slowdown. In: Proc. ACM MobiCom. (September 2002) 5. Anand, M., et al.: Self-tuning wireless network power management. In: Proc. ACM MobiCom. (September 2003) 6. Qiao, D., Shin, K.G.: Smart Power-Saving Mode for IEEE 802.11 Wireless LANs. In: Proc. IEEE INFOCOM. (March 2005)

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7. Schurgers, C., et al.: Power Management for Energy-Aware Communication Systems. ACM Trans. Embedded Computing Sys. 2(3) (2003) 431–447 8. Yu, Y., et al.: Energy-Latency Tradeoffs for Data Gathering in Wireless Sensor Networks. In: Proc. IEEE INFOCOM. (March 2004) 9. Cui, S., et al.: Energy-constrained Modulation Optimization. IEEE Trans. Wireless Commun. 4(5) (2005) 10. Gamal, A.E., et al.: Energy-Efficient Scheduling of Packet Transmissions over a Wireless Networks. In: Proc. IEEE INFOCOM. (2002) 11. J¨ ager, H., et al.: Broadband High-Efficiency Monolithic InGap/GaAs HBT Power Amplifiers For 3G Handset Applications. IEEE MTT-S Inter. Microwave Sympo. Digest 2 (2002) 1035–1038 12. Pedro, J.C., et al.: Linearity versus Efficiency in Mobile Handset Power Amplifiers: A Battle without A Loser. Microwave Engineering Europe (August 2004) 13. Corte, F.D.: Power Management for Energy-Aware Communication Systems. RFDesign Magazine (May 2000)

Energy Efficient Throughput Optimization in Multi-hop Wireless Networks Dan Xu and Xin Liu Computer Science Department, University of California Davis, CA 95616, USA {xud,liu}@cs.ucdavis.edu

Abstract. Throughput, fairness, and energy consumption are often conflicting objectives in multi-hop wireless networks. In this paper, we propose the notion of lexicographical maxmin energy efficiency throughput fairness that achieves throughput fairness per unit energy. Compared with maxmin throughput fairness and maxmin time fairness, the proposed scheme allocates more bandwidth to nodes with relay requirements and provides satisfactory bandwidth to nodes far from the sink. We design an optimal bandwidth allocation algorithm to achieve the proposed fairness objective. Simulation results show that the proposed scheme results in more balanced throughput among users when they exhaust energy resources, compared to other fairness schemes.

1

Introduction

One of the most challenging issues in bandwidth allocation is the conflict between fairness and throughput. In [1], the authors indicate in multi-rate 802.11 MAC, throughput-based fairness degrades network throughput considerably since most channel access time is occupied by low bit rate links. Time-based fairness proposed in [2] allows each user to fairly share time resources, which results in low throughput on low capacity links. In [3], the authors argue in multi-hop WLANs[4], maxmin throughput fairness can improve network throughput without penalizing low capacity users, and maxmin time fairness leads to an even higher network throughput by protecting high bit rate links. In multi-hop networks, some nodes need to serve as routers and relay traffic for other nodes. Routers handle more traffic and thus consume much more energy than descendant nodes. If nodes are energy constrained, such as in sensor networks or when using devices on battery power (e.g., laptops or PDAs), energy consumption needs to be considered in bandwidth allocation among users. This observation motivates the work in this paper. We consider a multi-hop wireless network where all nodes need to connect to a wired sink or AP (access point) while taking into account energy consumptions. When energy is a constraint, maxmin throughput fairness is unfair to routers 

The work was in part supported by NSF through CAREER Award #0448613 and Grant #0520126, and by Intel through a gift grant.

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because they consume more energy and die much faster than other nodes. Consider the example illustrated by Fig. 1; nodes 2 and 3 choose node 1 as their router since in (a) they both have low bit rates and therefore low throughput if directly connected to the sink. To simplify the example, we assume at each node, transmitting one unit of data costs 2J of energy, receiving one unit of data needs 1J, and no energy is consumed in an idle state. Then in (b) where node 1 is a router, it costs 8J per unit time to transmit the same amount of data as node 2 or 3, which only consume 2J per unit time. Therefore, node 1 will have a much shorter lifetime and consequently much less aggregate throughput compared with that of itself in a) and nodes 2 or 3 in b). On the other hand, maxmin time fairness severely penalizes nodes far away from the sink. This is because, in order to fairly share a router’s time, a child node’s throughput is about 12 of that allocated to the router. The larger the number of network hops, the less the bandwidth leaf nodes receive. For example, consider a chain topology with 20 nodes and a sink as shown in Fig. 2. Each node chooses the node in front of it as its router. Assume each link’s bit rate is 11Mbps. In b), by maxmin time fairness, routers receive much more bandwidth 0.282 20

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compared to their descendants. The leaf node 20 only receives a bandwidth of 1 27kbps, which is less than 20 of that of node 1. Motivated by such limitations, we propose the notion of lexicographical maxmin energy efficiency throughput fairness, which achieves maxmin throughput fairness per unit energy. With this objective, a router is allocated more bandwidth when it consumes more energy per unit time to relay traffic for other nodes. In other words, routers are compensated for providing service for other nodes. Although a router has a shorter lifetime, it can still achieve a high total throughput before using up its battery power. Another benefit is illustrated in Fig. 2, using maxmin energy efficiency throughput fairness, a router can receive higher throughput than its child nodes. Meanwhile, even the leaf node can still receive a satisfactory throughput, which is 185kbps in the example illustrated by Fig. 2. That is, maxmin energy efficiency throughput fairness provides a better balance among users than both maxmin throughput fairness and maxmin time fairness when energy is the constraint. Our contributions are as follows. We observe the limitations of maxmin throughput fairness and maxmin time fairness when energy is constrained and propose maxmin energy efficiency throughput fairness that allocates more bandwidth to routers while still not penalizing the bandwidth of children nodes severely. To achieve the objective, we design an iterative optimal bandwidth allocation algorithm. We also propose and implement a maxmin energy fair scheme for comparison. Our results show that maxmin energy efficiency throughput fairness results in more balanced throughput among all nodes when they deplete their energy compared with that of the maxmin throughput fair, maxmin time fair, and maxmin energy fair schemes. The rest of paper is organized as follows. In Section 2, we describe the network model and state the maxmin energy efficiency throughput fairness. To achieve the defined fairness objective, we design an optimal bandwidth allocation algorithm and validate its correctness in Section 3. Section 4 is performance evaluation. We present related work in Section 5 and conclusions in Section 6.

2 2.1

Formulation Network Model

We consider a wireless multi-hop network where each node chooses only one pre-determined first-hop router to be connected to the sink or AP. Therefore, the network topology can be modeled by a tree structure rooted at the sink. In sensor networks or mesh networks, nodes are often static and thus we consider a relatively stable network topology in this paper. Consider a node i, ai,Pi denotes achievable link rate between node i and its parent, which is denoted by Pi . Notice a sink has no parent node. We use an indicator function Ii to denote whether a node is a sink or not, where Ii = 1 if i

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D. Xu and X. Liu Table 1. Notions of main variables bi bandwidth of node i the set of child nodes of node i Ci Pi the first hop router of node i the subtree rooted at node i Ti total bandwidth of subtree Ti Bi Ii Ii = 1 if i is a non-sink node, Ii = 0 if i is a sink actual bit rate from node j to i aj,i energy consumed per unit time in transmit state of node i eti energy consumed per unit time in receive state of node i eri energy consumed per unit time in idle state of node i eii Wi workload of i, i.e., the sum of time length of receive and transmit state time length of idle state of node i tii Ei total energy consumption of node i 2 e bi energy efficiency throughput of node i bandwidth vector of the subtree Ti Bi E2 Bi energy efficiency throughput vector of subtree Ti

is a non-sink node, Ii = 0 otherwise. Let Ci be the set whose first-hop router is i and Ci+ be the set Ci ∪ {i}. Let the subtree rooted at node i be Ti and |Ti | be the number of nodes in Ti . Let bi denote the bandwidth allocated to node i, and Bi be the aggregate bandwidth of subtree Ti . The notions used in this paper are listed in Table 1 for reference. The time fraction of node i consumed to transmit i bi its own traffic is aIi,P . Here the time fraction represents the workload added to i node i. Notice node i also needs to relay traffic for its child node j ∈ Ci . The B I B B time fraction to relay j’s traffic is aj,ij + aii,Pj , while aj,ij is the time consumed to i receive j’s packets. Since the time fraction at each node can not exceed 1, the feaB I B i bi sible bandwidth allocation condition is given as j∈Ci ( aj,ij + aii,Pj ) + aIi,P ≤ 1. i i Similar models are widely used in previous literature [3][8][12]. In such models, the effect of inter-link interference can be ignored or taken into account in the achievable link rate ai,Pi , as in this article. In wireless networks, a node may transmit, receive, or stay idle (we ignore the sleeping state in this paper although all studies in this article can be extended to include the sleeping state). Energy consumed in all three states is taken into account in this paper. Let eti , eri , and eii be the energy consumptions per unit time of node i in transmit, receive, and idle states, respectively. These parameters are similar for the same kind of wireless terminals. In [5], the authors have measured these parameters for various wireless adapters. The reported values for a 802.11 WLAN module are used in our simulations. 2.2

Maxmin Energy Efficiency Throughput Fairness

As illustrated in the example in Fig. 1, a router node consumes much more energy, and therefore has much less overall throughput than its descendant nodes when maxmin throughput fairness is implemented. On the other hand, a node with multiple hops is severely penalized when maxmin time fairness is used. The maxmin energy efficiency throughput fairness is motivated by such limitations and formulated in this section.

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Consider a non-sink node i. Its energy consumption per unit time is

Ei =

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(1)  B B bi In (1), 1 − j∈Ci ( aj,ij + ai,Pj ) − ai,P is the idle time of node i, denoted as i i tii , where tii ≥ 0. A non-sink node i consumes Ei unit of energy per unit time and achieves a bandwidth of bi . We define its energy efficiency bandwidth as e2 bi = Ebii , which denotes the bandwidth per energy unit. Suppose there are n non-sink nodes in the network. The energy efficiency bandwidth vector is defined as E2 B=( Eb11 , Eb22 , . . . , Ebnn ), where Eb11 ≤ Eb22 ≤ . . . ≤ Ebnn . We give Definition 1 as: Definition 1(Maxmin Energy Efficiency Throughput Fairness). A feasible bandwidth allocation B is maxmin energy efficiency throughput fair if its energy efficiency bandwidth vector E2 B=( Eb11 , Eb22 , . . . , Ebnn ) is lexicographically equal or larger than that of any other feasible bandwidth allocation. Informally, a feasible bandwidth allocation is maxmin energy efficiency throughput fair if and only there is no way to increase energy efficiency throughput of any node without decreasing the energy efficiency throughput of some nodes with equal or already less energy efficiency throughput. The objective of Definition 1 is to provide maxmin fairness of the bandwidth per unit energy. Intuitively, it first allocates the bandwidth per energy unit among all nodes equally. When some nodes are not able to consume the allocated bandwidth within per unit energy, the bandwidth per unit energy can be evenly shared by the rest of the nodes. A desirable property is that a router’s energy efficiency throughput is not less than that of its child nodes. By maxmin energy efficiency throughput fairness, routers that spend more energy can get more bandwidth. If we view the energy as the cost that each node must pay for communications and the bandwidth as the revenue, the more a node contributes, the higher throughput it gets. Although routers have a shorter lifetime, they can still transmit a large amount of data before using up battery power. Therefore, compared with maxmin throughput fairness, the aggregated throughput of a router is significantly improved when it depletes its energy. This mechanism is a good incentive to encourage each node to serve others. ti times of Since maximum energy consumption at node i does not exceed eerj any other node j, maximum throughput allocated to a certain router is not excessively higher than its descendants. Compared with maxmin time fairness, the proposed fairness objective provides a satisfactory throughput to leaf nodes, even with a large number of network hops, as shown in Fig. 2. Maxmin energy efficiency throughput fairness provides the fairest overall throughput after each node depletes energy resource.

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3.1

Algorithm Design

We design an optimal bandwidth allocation algorithm named E2 TBA (Maxmin Energy Efficiency Throughput Fairness Bandwidth Allocation) to achieve the defined fairness objective. The structure of E2 TBA is based on the idea of Pump-Drain first proposed in [3]. We use Pump-Drain to convert the problem of maxmin energy efficiency throughput fairness bandwidth allocation, which can be modeled as a serial Quasi-optimization problem, to a simper problem of solving a non-linear equation set. Then we give an approximate algorithm to obtain the solution numerically. E2 TFA runs in the recursive and distributed way: a sink initializes E2 TFA, then E2 TFA recursively calls E2 TFA in the up-bottom order. After E2 TFA execution at a node j ∈ Ci returns, node i will perform Pump-Drain within Ti to achieve maxmin energy efficiency throughput fairness among all the nodes in Ti . To perform Pump-Drain, each node i maintains the following information that is locally reported by its children nodes. After performing Pump-Drain, node i also reports the information to its parent node. • The bandwidth assigned to each node k in Ti , namely bk . • The distinct amounts of energy efficiency bandwidth assigned to Ti , which are sorted in the array λi in a non-decreasing order. |λi | is the up-to-date number of the elements of λi . • In array ξi , the kth element ξi [k] is a set of nodes whose energy efficiency bandwidth is equal to λi [k]. • The structure of Ti . The details of E2 TFA are as follows. Pump: Initially, the energy efficiency bandwidth of each node is zero(Bandwidth of each node is set to zero). After the execution of E2 TFA returns from a child node of Ti . Pump is executed at node i in the following steps. I. If node i is a sink, let bi keep the value of 0 and there is no need to perform Pump. However, Drain maybe needed since bandwidth of its children nodes may make i overloaded. If node i is a non-sink node, Pump goes to Step II. II. For a non-sink node i, after the execution of E2 TFA at j ∈ Ci returns, the bandwidth allocation within Tj is maxmin energy efficiency throughput fair and node j is saturated. The aggregated bandwidth of Tj is Bj , whose time B B share at node i is aj,ij + ai,Pj . The energy efficiency bandwidth of node j i

is e2 bj =

bj Ej .

At node i, the time fraction left to support its own bandwidth is

Energy Efficient Throughput Optimization in Multi-hop Wireless Networks

1− is:



Bj j∈Ci ( aj,i

55

B

+ ai,Pj ), then the bandwidth of node i that can be supported i

⎛

⎞   Bj Bj ⎠ + φ = ⎝1 − ai,Pi aj,i ai,Pi

(2)

j∈Ci

With the bandwidth of φ, there is no idle time at node i, and the corresponding energy efficiency bandwidth of node i is e2 bi =

φ φ = eri eti Ei j∈Ci ( aj,i + ai,P )Bj + i

When



φ e e + a ti )Bj + a ti φ

eri j∈Ci ( aj,i

i,Pi

eti ai,Pi

φ

(3)

≥ λi [|λi |], i.e., energy efficiency bandwidth

i,Pi

of node i is larger than that of any other node in Ti , let bi = φ. Pump stops and there is no need to perform Drain. Otherwise, Pump goes to Step III. φ III. When  < λi [|λi |], we let the energy efficiency e e e ( ri + ti )B + ti φ j∈Ci

aj,i

ai,P i

j

ai,P i

bandwidth of node i equal to λi [|λi |]. Node i gets the bandwidth ϕ by solving the following equation, λi [|λi |] = 

Then ϕ =

λi [|λi |]



ϕ eri j∈Ci ( aj,i

eri eti j∈Ci ( aj,i + ai,P i e 1−λi [|λi |] a ti i,Pi

)Bj

+

eti ai,Pi

)Bj +

eti ai,Pi

ϕ

,

(4)

. Now node i also has the largest energy

efficiency bandwidth among all the nodes in Ti . Since ϕ > φ, node i must be overloaded, Pump stops and Drain is needed to decrease the bandwidth of Ti to make the bandwidth allocation feasible. Drain: The objective of Drain is to decease the bandwidth of each node in ξi [|λi |] to make the workload of node i feasible, i.e., let Wi =1. Meanwhile, the energy efficiency bandwidth of each node should still stay the same. However, since in ξi [|λi |], deceasing the bandwidth of a node will probably result in the decrease of energy consumption of itself and all the ancestor nodes, decreasing the bandwidth of each node while keeping their energy efficiency bandwidth the same is a non-trivial job. In ξi [|λi |], there are three kinds of nodes: first, the nodes without any children in ξi [|λi |], we use k to denote them; the second is those with children in ξi [|λi |], we denote these with l; the last is node i itself. Then mathematically, the above problem can be solved by the equation set (5). The equation in {}* appears in (5) only when i is a non-sink node. Notice in (5) the idle time and idle energy consumption of node i is 0, since i is saturated before Drain is completed. In (5), the bandwidth of each node is decreased to make the workload of node i equal to 1, while keeping energy efficiency bandwidth the same, which is denoted by η. When Wi = 1 is satisfied, if η ≥ λi [|λi | − 1], then Drain is done. If η < λi [|λi | − 1], simply decreasing

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the bandwidth of nodes in ξi [|λi |] is not enough, the bandwidth of nodes in ξi [|λi | − 1] should also be decreased. Then Drain is performed by two steps: first, decrease the bandwidth of each node in ξi [|λi |] to make their energy efficiency bandwidth equal to λi [|λi | − 1], which can be done through replacing η by λi [|λi | − 1] in (5) and deleting the final equation; second, combine the set ξi [|λi |] and ξi [|λi | − 1] and do the same operation described by (5). If at this time the current λi [|λi |] is still smaller than the current λi [|λi | − 1], repeat the above two steps. ⎧ bk −δk =η  ⎪ e e e (b −δ ) ⎪ ( a rk + a tk )Bj + tka k k +eik tik ⎪ j∈C ⎪ k j,k k,Pk k,Pk ⎪  ⎪ B −δk ) j ⎪ ⎪ tik = 1 − j∈Ck ( aBj,k + ak,Pj ) − (bakk,P ⎪ ⎪ k k ⎪ ⎪ .. ⎪ ⎪ ⎪ . ⎪ ⎪ ⎪ bl −δl ⎪ =η   e e e (b −δ ) ⎪ ⎪ ( a rl + a tl )(Bj − δm )+ tla l l +eil til ⎪ j,l l,Pl l,Pl ⎪ j∈C m∈ξ [|λ |]&m∈T ⎨ l i i l  (5)  (aj,l +al,Pl )(Bj −m∈ξi [|λi |]&m∈Tl δm ) (bl −δl ) ⎪ til = 1 − − al,P ⎪ aj,l al,Pl ⎪ l ⎪ j∈Cl ⎪ ⎪ ⎪ . ⎪ .. ⎪ ⎪ ⎪ ⎪ ⎪ bi −δi ∗ ⎪ {  eri eti  e (b −δ ) = η} ⎪ ⎪ (a +a )(Bj − δk )+ tia i i ⎪ j,i i,P i,P ⎪ i i j∈Ci k∈ξi [|λi |]&k=i ⎪     ⎪ ⎪ Bj − δn Ii ( Bj − δn ) ⎪ ⎪ j∈Ci n∈ξi [|λi |]&n=i n∈ξi [|λi |]&n=i i −δi ) ⎩ j∈Ci + + Ii (b =1 aj,i ai,P ai,P i

i

(5) is a non-linear equation set which definitely has an optimal solution. However, numerically, there is only an approximate algorithm to solve (5). Here we design an efficient distributed algorithm to perform Drain which can get approximate optimal numerical results.

Algorithm 1. The procedure of Drain of E2 TFA for (η = λi [|λi |]; η = η − Δ; η > λi [|λi | − 1]) do E2 TFA Drain (initialnode, η, initialnode) end for if initialnode s workload is still larger than 1 then Let λi [|λi |] = λi [|λi | − 1] and ξi [|λi |] = ξi [|λi |] ∪ ξi [|λi | − 1] Algorithm is performed from beginning again end if /* Here Δ is a small value which decides precision*/

3.2

Correctness Validation

Proposition 1. E2 TFA achieves maxmin energy efficiency throughput fairness. Proof is available at[6].

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57

Algorithm 2. Function E2 TFA Drain (i, η, initialnode) if i is initialnode then Let all the parameters including bandwidth, idle time as what they are before the first time the function called end if for ∀j ∈ ξi [|λi |] do if parent[j] is i then E2 TFA Drain (j, η, initialnode) end if end for if i is not initialnode then Decease bandwidth of node i by δi , which is calculated by the first equation in (5). Update parameters of each node in ξi [|λi |], including aggregate subtree bandwidth, idle time, which varied resulted from the decrease δi . else {i is initialnode and i is not a sink} Decease bandwidth of node i by δi , which is calculated by the first equation in (5), but here idletime is 0. end if

4

Evaluation

In this section, we evaluate the performance of E2 TFA and compare it with other fairness schemes including maxmin throughput fairness bandwidth allocation(MMFA), maxmin time fairness bandwidth allocation(MTFA) and maxmin energy fairness bandwidth allocation(MEFA). MMFA and MTFA have been studied in [3]. We propose MEFA for comparison. In MEFA, each router’s energy resource is fairly shared by all its descendants and itself. The idea of MEFA is similar with that of MTFA. Therefore, MEFA should have similar performance to MTFA. In E2 TFA, routes are predetermined. Because finding an optimal routing that yields best throughput is NP-hard, we implement two heuristic schemes. The first is the tree construction algorithm proposed in [3], which can iteratively improve throughput. We call it ITCA here. ITCA provides good performance for networks with a small number of hops but works slowly when the number of hops increases. Therefore, we also deploy a shortest distance routing (SDR) scheme, where a node chooses its first-hop router which is the nearest one among the nodes that have a shorter distance with the sink. SDR is efficient in large wireless networks. In the simulation, we consider an area of 150m ∗ 150m. The link bit rate is determined as follows: it is 11Mb/s when the distance between a transmitter and its receiver is smaller than 50m, 5.5Mb/s when distance is smaller than 80m, 2Mbps when smaller than 120m, and 1Mbps when larger than 120m. Unit energy consumptions in the transmit, receive, and idle states are 1.9J/s, 1.55J/s, and 0.75J/s, respectively [5]. We conduct simulations in the following two scenarios.

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• Scenario A: 4 sinks are located at each corner and 30 nodes are randomly located in the square. ITCA is used. • Scenario B: 1 sink is located at a corner and 25 nodes are randomly located in the square. SDR is used. First, we study the aggregate throughput of each node when it depletes energy. The initial energy of each node is set to be 100J. We compare MMFA, MTFA, MEFA and E2 TFA in both Scenario A and B. When a node runs out its energy, it quits the networks and the four schemes are executed for the rest of the nodes. As showed in Fig. 3, in both scenarios, E2 TFA provides the fairest aggregate throughput among all nodes. In Scenario A, using MMFA, routers only transmit a small amount of data before they deplete their energy resources. While in B, the aggregate throughput of leaf nodes in MTFA and MEFA is very low, since in Scenario B there is only a sink, the number of network hops is large, throughput of leaf nodes is severely penalized by MEFA and MTFA. Although leaf nodes have a longer lifetime, their aggregate throughput is still very low. Notice that routers have higher aggregate throughput, throughput, and energy efficiency throughput in MTFA and MEFA, which is contrary to that in MMFA. In Fig. 4, in both scenarios, MMFA results in fairest throughput(bi ) among all the nodes. On the other hand, MTFA allocates much higher throughput to routers than children nodes. In Scenario B, throughput of leaf nodes allocated by MTFA is only 14 of that given by MMFA. However, in the same scenario, compared with MTFA, E2 TFA allocates much more throughput to the leaf node, which is about 3 times more than that of MTFA. Meanwhile it still allocates similar high throughput to a router. In both scenarios, E2 TFA gives higher throughput to routers without severely penalizing any node. In Fig. 5, we show that E2 TFA achieves the fairest throughput per unit energy( Ebii ), which is the objective of E2 TFA. By MMFA, children nodes have smaller energy consumption and therefore have high energy efficiency throughput. MTFA and MEFA gives routers excessively high throughput, which result in a higher energy efficiency throughput for routers although they have relatively higher energy consumption. This aslo illustrates that MTFA is severely biased towards nodes near the sink.

Fig. 3. Each node’s aggregate throughput

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59

Fig. 4. Throughput of each node

Fig. 5. Energy efficiency throughput

5

Related Work

In [3], the authors consider both maxmin throughput fairness and maxmin time fairness in multi-hop WLANs and design an optimal bandwidth allocation algorithm for each objective. In [8][9][10][11], the authors study MAC layer scheduling or bandwidth allocation for ad hoc networks. In [12], the authors study maxmin fairness bandwidth allocation in multi-AP single-hop WLANs through association control. Since the problem is NP-hard, algorithms to determine user-AP associations are proposed that attain near-optimal maxmin fairness. In [13], the authors study maximum and maxmin fairness bandwidth allocation in multichannel wireless mesh networks. All the above works do not consider energy constraints. In [14], the authors consider maxmin fairness rate allocation in sensor networks. Flow split is allowed and thus the problem can be solved by a serial LP with lifetime constraints.

6

Conclusion

In this paper, we study throughput fairness and optimization in energy-constrained multi-hop wireless networks. We observe that maxmin throughput fairness biases against routers with heavier traffic while maxmin time fairness biases against nodes with more hops to the sink. Motivated by such observations, we propose the notion

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of lexicographical maxmin energy efficiency throughput fairness with the following properties. First, the proposed fairness objective allocates more bandwidth to routers that relay packets for others and therefore encourages them to serve others; second, the throughput discrepancy between routers and their descendants is bounded. Therefore, leaf nodes can still receive satisfactory throughput even in a large network; third, by combining energy consumption and throughput, our scheme results in the most balanced aggregate throughput when all nodes use up the energy resources. We develop a distributed algorithm to achieve the above objective and validate its advantages through extensive simulations.

References 1. M. Heusse, F. Rousseau, G. Berger-Sabbatel, and A. Duda, “Performance anomaly of 802.11b,” in IEEE Infocom, 2003. 2. G. Tan and J. Guttag, “Time-based fairness improves performance in multi-rate wireless lans,” in USENIX Annual Technical Conference, 2004. 3. Q. Dong, S. Banerjee, B. Liu, “Throughput Optimization and Fair Bandwidth Allocation in Multi-Hop Wireless LANs,” in IEEE Infocom, 2006. 4. S. Lee, S. Banerjee, and B. Bhattacharjee, “The case for a multi-hop wireless local area network,” in IEEE Infocom, 2004. 5. O.Kasten, “Energy Consumption,” available at http://www.inf.ethz.ch/personal/ kasten/research/bathtub/energy consumption.html 6. Dan Xu and Xin Liu, “Energy Efficient Throughput Optimization in Multi-hop Wireless Networks,” http://www.cs.ucdavis.edu/˜liu/. 7. T. Nandagopal, T.-E. Kim, X. Guo, and V. Bharghavan, “Achieving mac layer fairness in wireless packet networks,” in ACM MobiCom, 2000. 8. L. Tassiulas and S. Sarkar, “Maxmin fair scheduling in wireless networks,” in IEEE Infocom, 2002. 9. S. Lu, H. Luo and V. Bharghavan, A new model for packet scheduling in multihop wireless networks,in Proceedings of ACM MobiCom, 2000. 10. X. L. Huang and B. Bensaou, “On max-min fairness and scheduling in wireless ad-hoc networks: Analytical framework and implementation,” in Proceedings of in ACM MobiHoc, 2001. 11. A. Penttinen, I. Koutsopoulos and L. Tassiulas, “Low-complexity distributed fair scheduling for wireless multi-hop networks,” in IEEE Wiopt, 2005. 12. Y. Bejerano, S.-J. Han, and L. E. Li, “Fairness and load balancing in wireless lans using association control,” in Proceedings of ACM MobiCom, 2004. 13. J. Tang, G. Xue, W. Zhang, “Maximum throughput and fair bandwidth allocation in multi-channel wireless mesh networks,” in IEEE Infocom, 2006. 14. Y. Hou, Y. Shi, H. Sherali, “Rate Allocation in Wireless Sensor Networks with Network Lifetime Requirement,” in Proceedings of ACM MobiHoc, 2004.

Election Based Hybrid Channel Access Xin Wang1 and J.J. Garcia-Luna-Aceves1,2 Computer Engineering Department, University of California, Santa Cruz, Santa Cruz, CA 95064, USA 2 Palo Alto Research Center (PARC) 3333 Coyote Hill Road Palo Alto, CA 94304, USA {wangxin,[email protected]}

1

Abstract. We propose an Election based Hybrid Channel Access (EHCA) protocol for ad hoc network to achieve high throughput and bounded channel access delay at the same time. EHCA reduces the contentions during the channel scheduling formation through fair node elections, which are based on the topology information. Only the elected nodes contend for the channel and broadcast the scheduling result. Numerical analysis and simulation results show that EHCA outperforms alternative designs.

1

Introduction

The analysis about the capacity of wireless networks [5] demonstrated that perfect scheduling is the ultimate way to achieve the capacity in the MAC layer. However, in a distributed ad hoc network it is impossible to use perfect channel scheduling, and the random channel access has to be used to some extent. We propose the Election based Hybrid Channel Access (EHCA) protocol to attain both high channel utilization and bounded channel access delay. The former is important for serving data-centric applications, while the latter is critical for voice-related applications. In EHCA, channel access period is divided into four time sections. The first section is used to exchange the neighbor information. After that, all nodes do fair elections to reduce the number of nodes which will contend for the channel access. The nodes which fail in the election will follow the scheduling result of the nodes elected. In the third section, the channel scheduling is distributed in the two-hop range and contention-free transmissions happen in the fourth section. We evaluate the performance of EHCA through analysis and simulation. Compared with existing hybrid channel access scheme [3] and 

This work was supported in part by the Baskin Chair of Computer Engineering at UCSC, the National Science Foundation under Grant CNS-0435522, and the U.S. Army Research Office under grant No.W911NF-041-1-0224. Any opinions, findings, and conclusions are those of the authors and do not necessarily reflect the views of the funding agencies.

I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 61–72, 2007. c IFIP International Federation for Information Processing 2007 

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X. Wang and J.J. Garcia-Luna-Aceves

IEEE 802.11, EHCA can achieve a much higher throughput and smaller channel access delay at the same time. The rest of the paper is organized as follows. We describe the related work in Section 2. We introduce the details of the proposed approach in Section 3. We analyze the properties of EHCA in Section 4. We evaluate the performance of EHCA and compare it with alternative designs in Section 5. We conclude the paper in Section 6.

2

Related Work

Medium access control (MAC) protocols of ad hoc network can be classified into contention-based channel access and contention-free channel access. In contention-based MAC protocols, each node either detects the transmission collision (collision-detection) or tries to avoid the transmission collision through random back-offs (collision-avoidance). Based on its observation of the channel status, each node contends for the channel access in a distributed fashion. Contention-based MAC protocols may experience throughput degradation at high traffic loads and due to their best effort nature, they can not provide Quality-of-Service (Qos) support for real-time applications. In contention-free MAC protocols, a set of timetables for individual nodes or links is prearranged. Each node/links can only transmit in their assigned time/frequency slots, so that the transmissions from these nodes/links are collision-free within the effective range of the transmissions. Dynamic transmission scheduling protocols can exploit spatial reuse of the wireless channel and have higher channel utilization than static scheduling approaches, e.g. TDMA. Based on whether the schedule scheme needs the topology information, the scheduling-based channel access can be further divided into topology dependent/independent scheduling. In topology dependent scheduling, global topology information is required to form the correct channel scheduling. Arikan [1] has shown that the problem of establishing an optimal interference-free schedule where the optimal is considered in term of throughput, is NP complete. Chlamtac [4] first proposed a topology-transparent scheduling algorithm for wireless ad hoc networks. It uses polynomials over a Galois field to assign time slots, which guarantees each node can transmit successfully at least once in a frame. This approach can provide a minimum performance guarantee for each node. It just needs the information of overall number of nodes in the network and the number of neighbors of each node. The frame length is also much smaller than the classic TDMA approach. Konstantinos [8] proposed probabilistic policy to increase the system throughput under various traffic loads. Ju [7] proposed an approach based on code theory to optimize the performance of Chlamtac’s algorithm in terms of minimum throughput and maximum delay. However, Carlos [11] has shown that the throughput of topology-transparent scheduling is at most the same with the slotted ALOHA.

Election Based Hybrid Channel Access

63

Hybrid channel access is proposed to take the advantages of contentionbased channel access and topology-dependent scheduling. Nodes first use the contention-based channel access to exchange the neighbor information to build the channel scheduling or reserve time slots in the scheduling-based transmission period. The examples of hybrid channel access protocol are NAMA [3] and CATA [13]. NAMA uses a hash function, which takes the node identifier and the current time slot number as input to derive a random priority for every neighbor within two hops. If a node has the highest priority, it can access the channel within the corresponding time slot. The advantage of NAMA is that it completely eliminated the communication overhead with regard to building the dynamic channel access schedule, except for collecting the two-hop neighbor information. However, NAMA has the following problems [2]: first, a node may probabilistically derive low priority for a long period of time and never get access to the channel; second, there may be chain effects to the channel access opportunities, in which the priorities of nodes cascade from high priority to low priority across the network. Chain effects will reduce the spatial reuse of the whole system; third, the channel bandwidth may also be wasted when a node does not have data to send in the allocated time slot. Because of the wasted bandwidth causing starvation to the nodes with traffic, NAMA interacts badly with certain applications that are sensitive to the delay, such as TCP congestion control [12] and AODV route update mechanisms [9]. In CATA, the transmission period is composed of a contention period and a group transmission period. During the contention period, nodes contend for the channel access and reserve a space in the group-transmission period. Then during the group-transmission period, one or more nodes can transmit data packets without collisions. The problem of CATA is that when there is a large number of nodes, the length of the contention period may not be long enough for each node to reserve a slot in the group transmission period. In this paper, we propose a hybrid channel access protocol which reduces the control overhead during the scheduling formation through nodes elections. Compared with NAMA and CATA, it can provide a bounded channel access delay and only nodes with traffic can access the channel. Since it reduces the number of contending nodes through elections, it allows more nodes to successfully reserve the channel through contentions and is more suitable for mobile scenarios.

3

Election Based Hybrid Channel Access (EHCA)

We assume that each node is synchronized on slot systems and nodes access the channel based on slotted time boundaries. Each time slot is numbered relative to a consensus starting point. We divide the channel access period into four different sections, as Figure 1 shows:

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Fig. 1. Channel access period

3.1

Neighbor Information Exchange Period

The neighbor information exchange period is used to maintain the neighbor information, send the reservation requests and distribute the reservation information in the two-hop range. All nodes adapt the 802.11 Distributed Coordination Function (DCF) to contend for the channel access during the neighbor information exchange period. It can be further divided into two sections: one-hop broadcast period and one-hop re-broadcast period. Each node will do the following in the one-hop broadcast period: – If a node does not want to reserve a slot in the scheduling-based transmission period, just send a HELLO packet to maintain the neighbor information. – Otherwise, a node needs to send a RESERVE REQUEST packet which indicates the receiver of the transmission (NULL for broadcast packet). The format of the RESERVE REQUEST is (src, dest, type). The type field indicates the previous scheduling is a failure or not. – Node i will classify the set of the RESERVE REQUEST information it has collected during the one-hop broadcast period as one-hop link set li1 . – Each node will choose the node with the largest MAC address in its onehop range as the leader of the network. The leader information is used for the time synchronization across different networks, which will be further discussed in Section 3.5. Then in the one-hop re-broadcast period, node i will forward the li1 to its neighbors, which guarantees the RESERVE REQUEST will be distributed in the two-hop range. We define the RESERVE REQUEST information node i has 2 received from node j during the one-hop re-broadcast period as lij . The final RESERVE REQUEST information node i has collected (li ) is: 2 li = {li1 ∪ lij

Ni1

∀j ∈ Ni1 }

(1)

where is the set of node i’s one-hop neighbors. After one-hop re-broadcast, each node will compare the MAC address of its two-hop neighbors with its current one-hop leader, then update the node with the largest MAC address in its two-hop range as the network leader. We denote Nmax1 as the maximum number of one-hop neighbors. Nmax1 is a predefined value to control the node density in the network. The length of the neighbor information exchange period Tne needs to be long enough to allow every nodes to broadcast twice. In this paper, we set Tne as 2Nmax1 × Tb , where Tb is the maximum time needed to send a broadcast packet using 802.11 DCF, including carrier sensing and exponential back-off.

Election Based Hybrid Channel Access

65

At the end of the neighbor information exchange period, we use one-hop link contender election to reduce the possible contentions in the channel reservation 2 period. Each node i will compare the li1 with lij for its every neighbor j. If node 1 2 1 2 i finds li = li ∪ lij and li = lij , it means node i and j have the exactly same set of one-hop links, which constitute the total RESERVE REQUEST information node i has collected, then node i will compare the MAC address of i and j. If i has a smaller MAC address, it will give up doing channel reservation and follow the scheduling result of the node j. We define the node with a larger MAC address as contender. Consider the case in which a lot of nodes are close to each other, this approach elects the node with the largest MAC address as the contender and it will do the scheduling for all the one-hop links, which reduces the possible channel access contentions. 3.2

Contention-Based Channel Reservation Period

During the contention-based channel reservation period, we extend the 802.11 DCF to form the channel scheduling in a distributed fashion. We define Dmax as the maximum delay a frame can tolerate, which is dependent on specific application. Nmt is the number of maximum transmissions a frame can support in order to satisfy Dmax . The priority of node i (iprio ) is the overall number of links it has collected in the neighbor information exchange period: iprio = |li |

(2)

The node priority will be broadcasted along with the scheduling results during the reservation information exchange period (section 3.3), then each node compares the node priority it has received. If for node i, there are two nodes j and k (j, k ∈ Ni1 ) with the same highest priority (larger than iprio ), i will define the contention link set (li1 cont ) as follows: 2 2 li1 cont = li1 ∩ lij ∩ lik 2 2 |li1 cont | = |li1 ∩ lij ∩ lik |

(3)

The contention priority of node i (icont prio ) is the number of links in the contention link set (li1 cont ): icont prio = |li1 cont |

(4)

The length of the back-off time (Tbackof f ) is decided by the number of links it has observed and the type of links, as Equation 5 shows:  Tsif s + Random × Ts if |li1 cont | > 0 (5) Tbackof f = Tsif s + (2Nmt − |li |) × Ts if |li1 cont | = 0 Each node keeps carrier sense the channel for a Short Inter Frame Space time (Tsif s ), which is defined in IEEE 802.11 [6]. If the channel is idle and |li1 cont | > 0, the back-off time equals to Tsif s + Random × Ts , where Random is

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a random variable uniformly distributed in [0, Nmt ], Ts is the minimum time slot length defined in IEEE 802.11 [6]. When |li1 cont | = 0, the back-off time equals to Tsif s + (2Nmt − |li |) × Ts . Through this approach, we divide the back-off period into two sections. One section is for the contention links while the other is for the remaining two-hop links, as Figure 2 shows. A node which has observed contention link set always has a shorter back-off period than than a node which has not.

Fig. 2. Node back-off scheme

During the back-off period, nodes which have contention links will access the channel and broadcast its scheduling result before the nodes which have not. In other words, contention links are scheduled before the normal links. After the scheduling for the contention links is formed, the node which can observe the largest number of remaining two-hop links will have the shortest Tbackof f . It will first access the channel and build the channel scheduling for the rest links. When a node gets the channel access, it will send an ordered set which indicates the corresponding scheduling as (sourcen , destn , type). After receiving the scheduling results from neighbor j, a node will first compare the jprio and jcont prio . The scheduling results of contention link set li1 cont is decided by the node with the highest contention priority (N odecont prio ). The scheduling results of rest links (li − li1 cont ) is decided by the node with the highest node priority (N odeprio ). If all the link schedules of a node are already formed by its neighbor with a higher priority, a node will give up its attempt to contend the channel. We give a simple example to show how the channel scheduling is formed, as Figure 3 shows. We assume node D is the node with the highest priority 4, which can observe links AB, BD, DE and EG. Then node D will first access the channel and broadcast the scheduling result of those four links to nodes {B, C, E, F }, which will distribute the scheduling information to nodes A and G during the reservation information exchange period (Section 3.3). We also consider the case that two nodes observe the same number of links, their node priorities (N odeprio ) are the same and their channel accesses will experience a collision. For example, we assume the nodes priorities and the contention link sets in Figure 3 are: – – – –

Aprio = Dprio = Gprio = 6 Bprio = Cprio = Eprio = Fprio = 2 1 1 lB cont = lC cont = {AB, DB} 1 1 lE cont = lF cont = {DE, GE}

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Fig. 3. Channel scheduling formation example

In the first round of scheduling, node A and D will have the same Tbackof f and collide at hidden terminals B and C, node D and G will collide at hidden terminals E and F . We use failed-link contender election to solve this problem. as Algorithm 1 shows. We define li1 f ail as the set of links which are collected by node i during 2 one-hop broadcast period with type failure. lij f ail is the set of links node i has received from node j during one-hop re-broadcast period with type failure. Then at the end of neighbor information exchange period, we compare the li1 f ail and 2 1 2 lij f ail for each neighbor j. If li f ail ⊂ lij f ail , node i will not schedule the failed 2 links, just follow the schedule result of node j. If li1 f ail = lij f ail , we compare the iprio and jprio , the one with a higher priority will be elected as the contender. If iprio = jprio , we further compare the MAC address to break the tie. Now when we revisit the previous example, node B and C will elect one node as contender. According to the backoff scheme we have introduced, this contender will access the channel before nodes A and D to build the scheduling for contention link set {AB, DB}. Then nodes A and D just need to schedule the rest four links. It is the same case for nodes {D, E, F, G}. The length of the contention-based channel reservation period (Tcr ) needs to be long enough to for nodes with the same highest contention priority to send their reservation packets, which is the worst case for the contention-based channel reservation. In this paper, based on the simulation experiment, we set Tcr as 6 × (Tmax backof f + Tr ), where Tmax backof f is the maximum back-off time and Tr is the needed to send a reservation packet. 3.3

Reservation Information Exchange Period

During the reservation information exchange period, nodes broadcast the scheduling results they have received and the related N odeprio to the neighbors, thus the scheduling results are distributed in the two-hop range. If a node receives a different channel scheduling with the same priority, it will mark the type of corresponding link as failure.

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Algorithm 1. Failed-link contender election algorithm /* First step, get the contend link sets */ 1: for each node j, k ∈ Ni1 do 2: if j prio == k prio == max(Ni1 prio ) 3: && max(Ni1 prio ) > i prio then 4:  /* node j and node k are the highest among all node i’s one-hop neighbors */; 2 2 ∩ lik ; 5: li1 cont = li1 ∩ lij 2 2 ∩ lik |; 6: |li1 cont | = |li1 ∩ lij 7: end if 8: end for /* Second step, elect the contender for the failed links */ 9: for each node j ∈ Ni1 do 2 10: if li1 f ail ⊂ lij f ail then 11: contender = j; 12: end if 2 13: if li1 f ail == lij f ail then 14: if iprio ! = jprio then 15: contender = max prio(i, j); 16: else 17: contender = max mac address(i, j); 18: end if 19: end if 20: end for

The length of the reservation information exchange period (Tre ) needs to be long enough to allow every node to broadcast once, which is half of the neighbor information exchange period (Tre = Nmax1 × Tb ). 3.4

Schedule-Based Transmission Period

In schedule-based transmission period, each node will follow the channel scheduling with the highest priority to send its own packets. The length of the schedulebased transmission period (Tst ) equals to Nmt × Tdata , where Tdata is the time needed to send a data packet with the maximum payload length. When a node experiences a collision during the schedule-based transmission, it will mark the type of corresponding link as failure. 3.5

Network Merge Consideration

Under mobile scenarios, when two networks which are in different time sections merge into one, they need to synchronize on one time section to form the correct scheduling. We address this problem by leader election. We get the network leader information during the neighbor information exchange period (section 3.1). Then we add the leader, N odepriority and current time section information in the header of each frame sent after the neighbor information exchange period. The basic principle is to detect the network merge by identifying the leader of the network, then letting the network with the fewer transmissions to synchronize on the

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time section of the network with more transmissions. If two network have the same number of transmissions, all nodes will follow the network leader with a larger MAC address. If two networks merge before neighbor information exchange period and both of them have not formed the leader and priority information, they can finally form a new network, although it may not have all the transmission information. If one network is already in the time section after the neighbor information exchange period while the other is not, the latter will synchronize on the time section of the former.

4

Performance Analysis

1 Through fair node election, each node in EHCA can reserve  Nmax2 +1  of the schedule-based transmission period and access the channel in up to two time frames, which are at the order of Θ(Nmax1 ) slots. We compare the per-node throughput and maximum channel access delay (dmax ) of EHCA with other channel access schemes through numerical analysis, as Table 1 shows, where Nmax2 is the maximum number of nodes in the two-hop range. N is the overall number of nodes in the network. It demonstrates that EHCA achieves a good balance between throughput and delay.

Table 1. Comparison with existing channel access schemes

Protocol

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dmax (unit:slot)

EHCA Θ(Nmax1 ) NAMA [3] ∞ TDMA Θ(N ) 2 2 Topology Nmax2 log2 N (N Nmax2 ) O( log ) O( log ) 2 2N Nmax2 log2 N max2 transparent [4]

5

Performance Evaluation

We have implemented the EHCA and NAMA under Qualnet [10]. We use the simulation setting that 50 nodes are uniformly distributed across a 400 × 400 square meters area. Each node uses 802.11a as the physical layer and the transmission rate is 54 Mbps. Packets are served in First-In First-Out (FIFO) order. The duration of the simulation is 90 seconds. The transmit power is set to 16 dBm, receive sensitivity to -69 dBm. We set Nmax1 equal to 20 and Nmt equal to 400. The simulations are repeated with ten different seeds to average the results for each scenario.

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Static Topology

We use twenty Constant Bit Rate (CBR) flows with varying inter-packet times to evaluate the performance for real time applications. The packet length of the CBR flow is 512 bytes. The senders and destinations are more than two-hops away from each other. This ensures that the metrics measured are reflective of multi-hop traffic. The simulation results are shown in Figure 4. Throughput

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5.2

Dynamic Topology

We use the Random-WayPoint as the mobility model and the way point speeds randomly varying from 1 to 10 meters/second. The pause time is 10 seconds. DSR is used as the routing protocol. The results are shown is the Figure 5. Through the comparisons of Figure 4(a) - 4(d) and Figure 5(a) - 5(d). We can see that under light traffic loads, EHCA performs similar to IEEE 802.11 and NAMA, but with the increase of the traffic load, the contention-based protocol begins to perform badly. EHCA also outperforms NAMA because NAMA does not have enough spatial reuse. The end to end delay of EHCA remains almost constant. 5.3

Interaction With TCP

We generate a traffic scenario which integrates the CBR traffic and TCP traffic to evaluate the interaction between EHCA and TCP. Twenty FTP flows are

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pumped into the network along with twenty CBR flows. The sources and destinations of the FTP flows are randomly chosen such that they are more than 2 hops away from each other. The results are shown in Figure 6(a) - 6(b), which indicate that EHCA performs well with TCP traffic.

6

Conclusion

This paper introduced an election based hybrid channel access (EHCA) protocol. The advantage of EHCA is that reduces the number of contention nodes through node elections, thus reducing the additional control overheads during the channel scheduling formation. EHCA can achieve high system throughput and bounded

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channel access delay at the same time. It is particularly suited for multi-hop ad hoc networks over which both voice and data services must be provided. We have shown through analysis and simulation that EHCA outperforms TDMA, IEEE 802.11 and existing hybrid channel access scheme.

References 1. E. Arikan. Some Complexity Results about Packet Radio Networks. IEEE Transactions on Information Theory, 30(4):681–685, Jul 1984. 2. L. Bao. MALS: Multiple Access Scheduling Based on Latin Squares. In IEEE MILCOM 2004, October 31-November 3, 2004. 3. Lichun Bao and J. J. Garcia-Luna-Aceves. A New Approach to Channel Access Scheduling for Ad Hoc Networks. In ACM Seventh Annual International Conference on Mobile Computing and networking(Mobicom), 2001. 4. I. Chlamtac and A. Farago. Making Transmission Schedules Immune to Topology Changes in Multi-hop Packet Radio Networks. IEEE/ACM Transactions on Networking, 2(1):23–29, February 1994. 5. P. Gupta and P. R. Kumar. The Capacity of Wireless Networks. IEEE Trans. on Inf. Theory, 46:388–404, March 2000. 6. IEEE Standard for Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, Nov 1997. 7. Ji-Her Ju and Victor O. K. Li. An Optimal Topology-Transparent Scheduling Method in Multi-hop Packet Radio Networks. IEEE/ACM Transactions on Networking, 6(3):298–306, June 1998. 8. Konstantinos Oikonomou and Ioannis Stavrakakis. Analysis of a Probabilistic Topology-Unaware TDMA MAC Policy for Ad-Hoc Networks. IEEE JSAC Special Issue on Quality-of-Service Delivery in Variable Topology Networks, 22(7):1286– 1300, September 2004. 9. C. Perkins, E. Belding-Royer, and S. Das. RFC 3561- Ad hoc On-Demand Distance Vector (AODV) Routing, Jul 2003. 10. Qualnet Simulator. Scalable Network Technologies, http://www.scalable-networks. com/. 11. Carlos H. Rentel. Network Time Synchronization and Code-based Scheduling for Wireless Ad Hoc Networks. Ph.D. Thesis, Carleton University, January 2006. 12. T. Socolofsky and C. Kale. RFC 1180 - A TCP/IP Tutorial, Jan 1991. 13. Z. Tang and J.J. Garcia-Luna-Aceves. A Protocol for Topology-Dependent Transmission Scheduling. In Proceedings of IEEE Wireless Communications and Networking Conference(WCNC), September 21-24, 1999.

Asynchronous Data Aggregation for Real-Time Monitoring in Sensor Networks Jie Feng, Derek L. Eager, and Dwight Makaroff Department of Computer Science, University of Saskatchewan, Saskatoon, SK S7N 5C9, Canada {jif226,eager,makaroff}@cs.usask.ca

Abstract. Real-time monitoring applications for sensor networks can require high sampling rates and low-delay forwarding of the sensor values to a sink node at which the data is to be further processed. High data collection rates can be efficiently supported by aggregating data as it is being forwarded to the sink. Since aggregation requires that some sensor data be delayed at intermediate nodes, while waiting for other data to be received, a key issue in the context of real-time monitoring is how to achieve effective aggregation with minimal forwarding delay. Previous work has advocated synchronous aggregation, in which a node’s position in the aggregation tree determines when it transmits to its parent. This paper shows that asynchronous aggregation, in which the time of each node’s transmission is determined adaptively based on its local history of past packet receptions from its children, outperforms synchronous aggregation by providing lower delay for a given end-to-end loss rate. Keywords: sensor networks, aggregation protocols, real-time monitoring, performance evaluation.

1

Introduction

Data aggregation is an important technique for reducing sensor network traffic and energy consumption [1,2,3,4,5,6]. Various aggregation protocols have been proposed for different applications, such as monitoring and periodic data collection [7,8,9], dynamic event detection[10], and target tracking[11]. This paper considers data aggregation in the context of sensor networks supporting realtime monitoring, specifically real-time monitoring systems where sensor data is sampled periodically and forwarded to a single sink node. A high sampling rate and a low delay in forwarding data to the sink are required in such systems so as to maintain a current “view” of the environment being monitored. Aggregation protocols for sensor networks with periodic traffic transmit sensor values over a tree or cluster topology, rooted at the sink [12,7,8,9]. Previous work has advocated synchronous aggregation protocols, in which a sequence of time intervals are statically defined for each round (collection of one set of sensor values), with each interval dedicated to transmissions from particular sensor nodes. TAG is an example of an aggregation service using synchronous I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 73–84, 2007. c IFIP International Federation for Information Processing 2007 

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aggregation [7]. In TAG, each node, beginning with the sink node, informs its children in the aggregation tree of the interval during which it will be receiving data. A child’s transmission interval is fixed as the receiving interval of its parent, and the child’s own receiving interval is chosen as the immediately preceding interval. Thus, all of the sensors at the i’th level of the aggregation tree, 1 ≤ i ≤ H, share transmission interval H − i, where H denotes the height of the tree and where the first interval in a round is numbered as interval zero. All intervals are of identical duration. A potential disadvantage of synchronous aggregation is increased delay, since the interval duration must be conservatively chosen so as to provide a high probability that each node will be able to successfully transmit its data to its parent prior to the end of its transmission interval. A second potential disadvantage is that the constraints imposed on node transmission times may result in suboptimal use of spatial multiplexing. Solis and Obraczka have described and evaluated two asynchronous aggregation protocols, called periodic simple and periodic per-hop aggregation [8]. In periodic simple aggregation, each node waits for a period of time equal to the round duration, aggregating all of the data received from its children over that period, before transmitting to its parent. This approach does not provide low delay; in fact, data generated during one round may not be received at the sink for a number of rounds equal to the height H of the aggregation tree. Periodic per-hop aggregation is similar to periodic simple aggregation in that nodes may wait for a period of time equal to the round duration before transmitting to their parent, but each node may transmit earlier if data is received and aggregated from all children prior to the end of the round. Again, this approach may result in long delays, with the data generated in one round not being received at the sink until some subsequent round. These simple asynchronous protocols were found to yield poorer performance than synchronous aggregation. In this paper, improved asynchronous aggregation protocols are designed through use of more aggressive methods for determining when a node should transmit to its parent. If a node receives data from all of its children prior to sending its own data to its parent, in a given round, all of this data is aggregated and sent to the parent at that point. A node will also transmit to its parent if the time it has been waiting for its children exceeds an adaptively determined timeout value. In this case, any “late arrivals” from its children are simply dropped. The choice of timeout value is critical, since a long timeout value may cause excessive delay, while substantial data loss may be incurred if the timeout value is too short. In the proposed protocols, timeout values are adaptively determined based on local history of past packet receptions. The performance of the new asynchronous protocols, as well as that of synchronous aggregation, is evaluated using simulation. Asynchronous aggregation is found to outperform synchronous aggregation. Performance comparisons of the asynchronous protocols show that adaptation of timeout values based on a weighted average of history information from multiple rounds is preferable to adaptation based only on the immediately previous round. It is also found that randomizing the transmission times of leaf nodes to avoid congestion at

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the beginning of each round, and the duration of the randomization interval, have a great impact on delay and end-to-end loss rate. A method is proposed for adaptively determining the duration of the randomization interval. The remainder of the paper is organized as follows. The new asynchronous aggregation protocols are presented in Section 2. Section 3 presents simulation results evaluating the performance of the new asynchronous protocols and of synchronous aggregation. Section 4 concludes the paper.

2

Asynchronous Aggregation

The main goal is to design asynchronous aggregation protocols that maximize aggregation efficiency by ensuring that as much aggregation occurs as possible, while still providing timely arrival of aggregation results at the sink. Three asynchronous protocols are proposed in the following subsections, beginning with the simplest of these protocols, and then making enhancements that yield improved performance as shown by our performance results in Section 3. The proposed protocols run above the network layer. Aggregation is performed as data packets are forwarded to the sink. The union of the routes to the sink forms an aggregation tree with the sink as its root node. For simplicity, it is assumed that a node can aggregate data from its subtree, together with its own data, into a fixed-size packet. 2.1

Basic Asynchronous Aggregation Protocol

In our basic asynchronous protocol, each non-leaf node sets a timeout in each round, establishing the maximum time it will wait to receive data from its children. The timeout value is determined adaptively, based on the timings of packet receptions from its children in the immediately preceding round. The node transmits its data packet for this round to its parent (aggregating its own data with whatever it has received from its children) either when it hears from all of its children, or when the timeout expires. For simplicity, it is assumed that all nodes agree on the same base time T0 defining the beginning of the first round. (In Section 3.5, however, it is shown that the proposed protocols are tolerant of substantial variability in the values of T0 used at different nodes.) To avoid concurrent transmissions, each node i (other than the sink node) picks a random value ri between 0 and R at T0 , where R is a protocol parameter. At time T0 + ri , node i sends a packet containing its sensor data for the first round to its parent. At each subsequent round j, each node i that is a leaf in the aggregation tree sends a packet containing its sensor data at time T0 + ri + (j − 1) × t, where t is the time between successive sensor readings at each node (i.e., the inverse of the sensor sampling rate). Each non-leaf node operates as follows. Let Lji denote the time by which non-leaf node i receives the last packet for round j. Let T Oij denote the timeout for round j at node i. Node i sets its timeout for the second round to T Oi2 = L1i + t.

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For round j + 1, j + 1 > 2, the timeout of node i is updated as follows: 1. If node i received data packets for round j from all of its children before T Oij , it sets the timeout for round j + 1 to T Oij+1 = Lji + t + e (since a packet from each child should arrive approximately once every time t). The protocol parameter e allows for some variance in the times at which packets are successfully transmitted. 2. If the timer for round j went off before node i received packets from all of its children, node i sets the timeout for round j + 1 to T Oij+1 = T Oij + t. If node i receives one or more packets for round j after time T Oij (“late arrivals”), it updates T Oij+1 to Lji + t. Such late arrivals have been received too late to be aggregated in node i’s round j transmission to its parent, and are simply dropped, since only up-to-date data is of interest in real-time monitoring. The choice of the protocol parameter e impacts the timeliness of the arrivals of data packets at the sink, and the number of late arrivals at the intermediate nodes in the aggregation tree. If e is set too small, timeouts may be set too aggressively, and data packets that experience normal variability in transmission times may arrive after the expiry of the respective timeout and be dropped. When e is set too large, latency may build up as nodes wait for data packets that will never be received owing to transmission failures. Our experiments show, however, that e can be set to a fixed value that yields good performance over a wide range of conditions. In contrast, we find that tuning the parameter R according to the particular network scenario can yield substantial improvements in performance. A method is proposed in Section 2.3 to adaptively determine the value for R. The above protocol supports adaptivity to dynamics in the topology of the aggregation tree, as long as nodes have some mechanism for dynamically altering when necessary their set of child nodes and their parent. The timing of transmissions can be quickly adjusted according to the above rules. 2.2

Asynchronous Aggregation Protocol with EWMA

While the basic protocol is straightforward, it may cause a “timeout chain” phenomenon under certain circumstances. Suppose, for example, that a node 1 has only one child, node 2, and only one grandchild, node 3. Suppose that node 2 receives the packet for round j from node 3 at time Lj2 , and sets its timeout for round j + 1 to Lj2 + t + e. Suppose further that the aggregate sent by node 2 arrives at node 1 after a transmission delay d, causing node 1 to set its timeout for round j + 1 to Lj2 + d + t + e. If the round j + 1 packet from node 3 is not successfully received by node 2, node 2 will time out and send its packet for round j + 1 at time Lj2 + t + e. If the transmission delay of this packet exceeds d, node 1 will also time out, causing the packet to be a late arrival and be dropped. The main reason for the above phenomenon is that the timeout for the next round at a node is set too aggressively when packets are received from all children prior to timeout expiry. In the second asynchronous protocol that we propose, an Exponentially Weighted Moving Average (EWMA) strategy is used to adjust the

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timeout value in this case. Specifically, if a node i heard from all of its children before timeout in round j, it sets its timeout for round j + 1 to T Oij+1 = (1 − δ) × (T Oij + t) + δ × (Lji + t + e)]. The parameter δ controls how quickly the protocol reacts to changes in the network. The above adjustment method bears some similarity to the Additive Increase Multiplicative Decrease (AIMD) algorithm in TCP. Both react slowly to “good news” while aggressively to “bad news”. In our case, the timeout for the next round is adjusted cautiously when packets are received from all children prior to timeout expiry, but more aggressively when there is a late arrival. 2.3

Adaptive Asynchronous Aggregation Protocol

It is important to randomize the transmission times of leaf nodes to avoid congestion at the beginning of each round. The parameter R controls the duration of the randomization interval. Choosing an appropriate value of R requires balancing the risk of congestion (if R is set too small) versus increased delay (if R is set too large). The best value is network dependent. In our third asynchronous aggregation protocol, R is determined adaptively. Based on the observation that the “asynchronous with EWMA” protocol achieves good performance when the ratio of R to the average data collection delay D is within a certain range, the adaptive protocol works by calculating the average data collection delay at the sink and adjusting R when the ratio is out of range. The data collection delay for a round is defined as the maximum delay from when a sensor value is captured, until the corresponding aggregate arrives at the sink. Although sensor values may be captured at somewhat different times at the various nodes, in our simulation implementation the capture times are approximated for each node and round j as T0 + (j − 1) × t. The average data collection delay is calculated as D = αD + (1 − α)D∗ , where ∗ D is the latest measurement for the data collection delay and α is a parameter determining the weight given to the previous value of the average. Suppose the desired range of R/D is [β −Δ, β +Δ]. When the sink observes that R/D is out of range, it updates R as follows. If R/D < β −Δ, R is updated to R = D×(β +Δ). If R/D > β + Δ, R is updated to R = D × (β − Δ). With suitable parameter value selections, changes to R with this protocol would be relatively rare, and we do not model any particular technique for communicating changes in R from the sink to the other network nodes.

3 3.1

Comparative Evaluation Synchronous Aggregation

The synchronous aggregation protocol used here for comparison uses a similar synchronization structure as that in TAG [7] and the cascading timeout protocol [8]. In particular, it is assumed that each node i knows its hop count to the sink, hi , and accordingly chooses its transmission interval within each round. Let I be the duration of the interval. For each round j, node i picks a random value

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rij between 0 and λ × I, 0 ≤ λ ≤ 1, aggregates the data it has received for this round and sends out its packet at T0 +t×(j −1)+(H −hi )×I +rij . Randomizing transmissions over λ × I yields better performance than when all nodes at the same tree level attempt to transmit at the same time. Parameter λ is set to 0.8 in all experiments. Alternative values were tried, but did not yield better performance. The duration of the interval is the decisive performance factor once the network configuration is fixed. In the performance evaluation experiments, different interval durations are used to explore the best achievable performance. 3.2

Goals, Metrics, and Methodology

The performance of the asynchronous protocols and the synchronous protocol is evaluated through ns2 simulation. The primary metrics are the end-to-end loss rate, equal to the ratio of the number of samples not included in the aggregates arriving at the sink to the total number of samples the nodes generate, and the maximum data age, which measures how old the data at the sink can be by the time the next samples arrive. The maximum data age is approximated by t plus the average data collection delay. An additional metric for which some results are presented is the average number of MAC layer data packet transmissions per round, which may yield insight into relative energy usage. Different sensor networks are generated by randomly scattering nodes in square areas with different sizes. The sink is located in the center of the network unless otherwise stated, and the aggregation tree is constructed as a shortest path tree. The physical layer packet loss rate is specified as a simulation input parameter. The uniform random error model is used for all experiments except those in which the two-state Gilbert error model is used to simulate channel errors (Section 3.5). An 802.11 MAC layer is simulated, without RTS/CTS [13], with a transmission range of 40 meters and rate of 2Mbps, and a fixed packet size of 52 bytes. A data packet is retransmitted up to three times before being discarded if an ACK is not received. 3.3

Parameter Analysis

While the asynchronous protocols have more protocol parameters than the synchronous protocol, experimental results show that e and δ can be easily fixed at 0.1 second and 0.05 respectively for all network settings. For adaptive aggregation, α, β, and Δ are fixed at 0.875, 0.7, and 0.15 respectively. Fig. 1 shows the impact of e on end-to-end loss rate and maximum data age. Fixing e at 0.1 second yields good performance for different physical layer loss rates. Experiments are also conducted with different sensor networks and the results show that good performance is achieved for all sensor networks when e is 0.1 second. Similar results are obtained showing that the chosen values of the other parameters (δ, α, β, and Δ) yield good performance across all of the simulated network configurations. Figures showing the impact of these parameters are omitted.

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The performance of the synchronous protocol is very sensitive to the choice of the duration of the interval. Experimental results show that link quality and aggregation tree structure have a great impact on the choice of I. In practice, it may be difficult to set this parameter in a manner yielding consistently good performance. 3.4

Principal Performance Comparison

Fig. 2 shows the performance of the aggregation protocols at three different sampling rates. Each point for basic asynchronous and asynchronous with EWMA is achieved at a specific R. For t = 0.25, R ∈ [0, 0.1, 0.2, 0.25]. For t = 0.5 and 0.75, R ∈ [0, 0.1, 0.2, 0.3, 0.4, 0.5] and [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.75] respectively. Similarly, each point for the synchronous protocol is achieved at a specific I. Two different values, 0 and t, are used as the initial value for R in adaptive asynchronous. For all three sampling rates, asynchronous aggregation achieves lower maximum data age than synchronous aggregation for a given end-to-end loss rate. The performance of basic asynchronous and asynchronous with EWMA is very close when t is 0.5 and 0.75 second. Fig. 2 shows that both protocols get end-toend loss rate close to 1% at similar maximum data age. At such a low end-to-end loss rate, almost all packet transmissions are triggered when a parent hears from all children. The timeout strategy doesn’t have much impact. When t is 0.25 second, the end-to-end loss rate gets higher and the difference between the two protocols becomes bigger as more packet transmissions are triggered by timeout. Fig. 3 shows the performance of the considered protocols with alternative sink placement. The same sensor network as for Fig. 2 is used, but with the sink at the corner. Fig. 3 (compare with Fig. 2) shows that the maximum data age of the synchronous protocol substantially increases when the sink is located at the corner while that of the asynchronous protocols stays around the same. A close look at the tree structure shows that the aggregation tree with the sink at the corner is more than twice as long as the one with the sink in the center, but the maximum number of nodes at the same tree level is quite similar in both cases.

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Thus, for synchronous aggregation, a similar interval duration is required in both cases, but twice as many intervals are required when the sink is at the corner. Another observation from Fig. 2 and Fig. 3 is that with the same 0.5 and 0.75 second sampling periods, asynchronous with EWMA performs much better than basic asynchronous with the sink at the corner. The reason for the difference can be traced back to the tree structure as well. When the sink is located at the corner, the sink only has four children and only one of these children has three children. Moreover, only one of these three grandchildren of the sink

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has its own children. The performance of basic asynchronous is very susceptible to the “timeout chain” phenomenon mentioned in Section 2.2 with such a tree structure. The number of late arrivals now differs enough to make a more significant difference in the end-to-end loss rate. The relative difference between basic asynchronous and asynchronous with EWMA, however, doesn’t vary much with different sink placement when t is 0.25 second. This is because packet losses due to congestion now play an important role in the network. The loss caused by the defects of basic asynchronous is less dominant. Fig. 4 shows the average number of MAC layer data packet transmission per round of the considered protocols with 10% and 30% physical layer loss rate. Fig. 4 shows that the performance improvements shown in Fig. 2 and Fig. 3 are achieved without impact on the number of MAC layer packet transmissions. The number of MAC layer data packet transmissions is very similar with all of the considered protocols, and in fact even slightly better with the asynchronous protocols when the end-to-end loss rate is low. 3.5

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Fig. 5 shows that the maximum data age and the end-to-end loss rate of both synchronous and asynchronous aggregation get worse as the physical loss rate increases. Asynchronous aggregation outperforms synchronous aggregation for different physical layer loss rates. When the number of nodes is fixed, the performance of the asynchronous protocols is not very sensitive to the size of the area. For the synchronous protocol, the average data collection delay increases as the tree gets longer and skinnier with a lower density. The maximum data age increases accordingly. As shown in Fig. 6, the performance improvement asynchronous aggregation achieves over synchronous aggregation increases as the size of the area increases.

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When the size of the area is fixed, the maximum data age for all of the considered protocols increases as the number of nodes increases. As seen in Fig. 7, the asynchronous protocols outperform the synchronous protocol for different numbers of nodes. For both synchronous and asynchronous aggregation, it was assumed that there is a common base time T0 that defines the beginning of the first period at all sensor nodes. Here this assumption is relaxed by assuming that there is some variable clock shift away from this common base time, so that different nodes consider the first period to begin at somewhat different times. Fig. 8 (compare with Fig. 1(b)) shows that the asynchronous protocols are much more tolerant of clock shift than the synchronous protocol. Fig. 9 considers the impact of a more bursty physical layer packet loss process on the relative performance of the aggregation protocols. The two-state Gilbert error model is used, with a “good” state in which there is no physical layer packet loss, and a “bad” state in which there is a 40% physical layer packet loss rate. When in each state, after a time duration of 5 seconds on average,

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a transit decision is made with 20% probability of moving to the other state. Each link independently transits between the two states. As seen in the figure, the relative performance of the various protocols is qualitatively consistent with that observed in the earlier experiments. Similar results have been obtained with other settings of the Gilbert error model parameters.

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This paper presents three asynchronous protocols and compares them against each other and against synchronous aggregation for the context of real-time monitoring systems. Simulation results show that asynchronous aggregation outperforms synchronous aggregation in its ability to keep data “current” while achieving a low end-to-end loss rate. Results also show that the per-node transmission adaptation strategy is crucial in asynchronous aggregation.

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References 1. Intanagonwiwat, C., Govindan, R., Estrin, D.: Directed diffusion: a scalable and robust communication paradigm for sensor networks. In: MobiCom ’00, Boston, MA (2000) 56–67 2. Krishnamachari, B., Estrin, D., Wicker, S.B.: The impact of data aggregation in wireless sensor networks. In: ICDCSW ’02, Vienna, Austria (2002) 575–578 3. Intanagonwiwat, C., Estrin, D., Govindan, R., Heidemann, J.: Impact of network density on data aggregation in wireless sensor networks. In: ICDCS ’02, Vienna, Austria (2002) 457–458 4. He, T., Blum, B.M., Stankovic, J.A., Abdelzaher, T.: AIDA: Adaptive applicationindependent data aggregation in wireless sensor networks. Trans. on Embedded Computing Sys. 3(2) (2004) 426–457 5. Shrivastava, N., Buragohain, C., Agrawal, D., Suri, S.: Medians and beyond: new aggregation techniques for sensor networks. In: SenSys ’04, Baltimore, MD (2004) 239–249 6. Nath, S., Gibbons, P.B., Seshan, S., Anderson, Z.R.: Synopsis diffusion for robust aggregation in sensor networks. In: SenSys ’04, Baltimore, MD (2004) 250–262 7. Madden, S., Franklin, M.J., Hellerstein, J.M., Hong, W.: TAG: a tiny aggregation service for ad-hoc sensor networks. SIGOPS Oper. Syst. Rev. 36(SI) (2002) 131– 146 8. Solis, I., Obraczka, K.: The impact of timing in data aggregation for sensor networks. In: ICC ’04, Paris, France (2004) 3640–3645 9. Madden, S., Szewczyk, R., Franklin, M.J., Culler, D.: Supporting aggregate queries over ad-hoc wireless sensor networks. In: WMCSA ’02, Washington, DC (2002) 49–58 10. Fan, K.W., Liu, S., Sinha, P.: On the potential of structure-free data aggregation in sensor networks. In: INFOCOM ’06, Barcelona, Spain (2006) 11. Zhang, W., Cao, G.: DCTC: dynamic convoy tree-based collaboration for target tracking in sensor networks. IEEE Trans. Wireless Commun. 3(5) (2004) 1689– 1701 12. Heinzelman, W.R., Chandrakasan, A., Balakrishnan, H.: Energy-efficient communication protocol for wireless microsensor networks. In: HICSS ’00, Maui, HI (2000) 8020–8029 13. Xu, K., Gerla, M., Bae, S.: Effectiveness of RTS/CTS handshake in IEEE 802.11 based ad hoc networks. Ad Hoc Netw. 1(1) (2003) 107–123

A Novel Agent-Based User-Network Communication Model in Wireless Sensor Networks Sang-Sik Kim and Ae-Soon Park Electronics and Telecommunications Research Institute {pstring,aspark}@etri.re.kr

Abstract. Wireless sensor networks generally have three kinds of objects: sensor nodes, sinks, and users that send queries and receive data via the sinks. In addition, the user and the sinks are mostly connected to each other by infrastructure networks. The users, however, should receive the data from the sinks through multi-hop communications between disseminating sensor nodes if such users move into the sensor networks without infrastructure networks. To support mobile users, previous work has studied various user mobility models. Nevertheless, such approaches are not compatible with the existing data-centric routing algorithms, and it is difficult for the mobile users to gather data efficiently from sensor nodes due to their mobility. To improve the shortcomings, we propose a view of mobility and propose a model to support a user mobility that is independent of sinks. The proposed model, finally, is evaluated by simulation of delivery ratio, latency, and network lifetime. Keywords: User Mobility Support, Wireless Sensor Networks.

1 Introduction Wireless sensor networks typically consist of three objects, as shown in Fig. 1: user, sink, and sensor node [1]. Firstly, a user is an object that disseminates an interest in the sensor field and collects data about the interest from sensor nodes. Secondly, a sink is an object that collects data. The sink receives an interest from a user and disseminates the interest inside sensor fields. The sink receives sensing data from sensor nodes and forwards the sensing data to the user. Lastly, a sensor node is an object that generates data about the interest and delivers the data to a sink. As shown in Fig. 1, the user and the sinks are mostly connected to each other by infrastructure networks. The users, however, should receive the data from the sinks through multi-hop communications between sensor nodes if such users move around the sensor networks without infrastructure networks. Recently, applications transmitting data to moving users inside sensor fields, such as rescue in a disaster area or maneuvers in a war zone, have been on the rise in large-scale sensor networks [5]. (Firefighters and soldiers are users gathering data from sensor networks.) To support mobile users in wireless sensor network, previous work has studied various user mobility models. But, until now, only three models supported the mobility I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 85–96, 2007. © IFIP International Federation for Information Processing 2007

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of users for those applications: the direct user-network communication model, the GPS-based user-network communication model, and the topology-control-based usernetwork communication model.

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The direct user-network communication model (D-COM) is shown in Fig. 2. It supports the mobility of a user on the assumption that the user communicates directly with sinks through infrastructure networks, namely, the Internet, such as communication systems in traditional sensor networks [1]. And, users can communicate directly with the networks via the sinks. But, in applications such as rescues in a disaster area or maneuvers in a war zone, circumstances without infrastructure networks, except sensor networks, are more prevalent. Hence, the assumption that a user and a sink can communicate directly through the Internet is not entirely accurate. The GPS-based user-network communication model (G-COM) is seen in Fig. 3. G-COM is source-based topology [5], [6], [7]. In G-COM, sensor nodes proactively construct a GRID system with GPS receivers. G-COM assumes that all sensor nodes have their own GPS receivers and an ability that constructs a GRID when a stimulus is detected. A sensor node, i.e. source, with a stimulus is going to make a GRID in a sensor field. Once a GRID is set up, mobile user floods its interests within a cell only where the user is located. When a sensor node on a GRID receives interests, it sends interests to the source along a GRID path and data from the source are forwarded to the user along the reverse path. The topology-control-based user-network communication model (T-COM) is seen in Fig. 4. It also identifies a user with a sink. This model supports the mobility of the user by reflecting the movement of the user [8], [9]. In T-COM, the user and sensor nodes construct a tree that is rooted at the user. The user always maintains the tree and gathers data from sensor nodes. Intuitively, G-COM and T-COM seem to be suitable for the aforementioned applications. But, these models also have various problems. First of all, they cannot use existing effective data collection algorithms [2], [3], [4] between a sink and sensor nodes based on the data in static sink sensor networks because of low protocol compatibility. Accordingly, such algorithms can hardly be exploited if users in sensor networks have mobility.

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The other problem is that the cost of the overhead to reorganize the network topology and reconstruct dissemination paths from sensor nodes to the mobile user is expensive. In G-COM, all sensor nodes make the topology based on location information. Accordingly, each sensor node must have its own GPS receiver. The cost of GPS receivers is decreasing, but the overall cost is still high. In T-COM, similarly, user mobility causes topology reconstruction. Users in T-COM have a tree that is rooted at each mobile user. If users move into a new location, then the root of trees must be changed, as seen in Fig. 4. This leads to enormous overhead to sensor nodes with constrained energy. Hence, this paper proposes a novel agent-based user-network communication model (A-COM). A-COM collects data through a temporary agent and delivers the data to mobile users. In A-COM, if a user intends to obtain data while moving, the user appoints a sensor node to act as an agent, and the agent forwards interests to the sink via a sensor network. The sink, having received interests from the user, collects data from sensor nodes using the existing data collection algorithm in static sink sensor networks [2], [3], [4]. The collected data are finally forwarded to the user. (If there is no sink, the agent directly disseminates interests to the whole networks and collects data.) Table 1. Taxonomy of Mobility Type Mobility Type

Compatibility Feasibility GPS Control Control Help of with Existing receivers Overheads Overheads to infrastructure Static Sink for sensors according to support networks Routing Protocols user mobility multiple users D-COM High Low Needless Low Low Mandatory G-COM Low Middle Mandatory Middle Low Needless T-COM Low High Needless High High Needless A-COM High High Needless Low Low Needless

A-COM has various advantages, as can be seen in Table 1. First of all, A-COM has the compatibility with existing static sink routing protocols without infrastructure networks. In addition, the users in A-COM do not make a topology (tree or GRID) and communicate only with agents. So, the users, while moving, are free from

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topology control. The user’s freedom saves much energy, and enables more users to participate in the proposed model even if the sensors have no GPS receivers. Our simulation verifies that the lifetime of sensor networks is prolonged because the user’s freedom decreases the energy consumption of the sensor nodes. Also, we verified that the performance of the data delivery ratio and the delay never decreases. Nevertheless, the movement of the user is supported by only sensor nodes without infrastructure networks. The rest of this paper is organized as follows. Section 2 describes the proposed model. Simulation results are presented in Section 3 to evaluate the effectiveness of our design and to analyze the impact of important parameters. Section 4 concludes the paper.

2 Model Analysis In our model, if a user intends to obtain data while moving, the user appoints a sensor to act as an agent and forwards an interest to the agent. If there is one or more sink(s), the agent forwards interests to sensor networks via sink(s). The number of sinks, however, depends on the network policy. A network administrator might want to set a single or more sinks in the sensor field, or alternatively the sensor field may be hazardous as he cannot reach the field. Hence, we consider three scenarios according to the number of sinks and describe the scenarios based on following assumptions. • A user can communicate with static sinks only through sensors because networks within sensor fields are infrastructure-less networks. • It is possible that multiple sinks are deployed in sensor networks and are connected to each other via the Internet. How to connect a sink with other sinks is out of the range of this paper, but this helps maximize the efficiency of gathering data. • Multiple static sinks are located in the outskirts of sensor fields. • The data which one sink collects is aggregated by the sinks. The aggregated data is shared by every multiple static sinks through the infrastructure network, namely, Internet. • The interest from a user describes how many times the sink forwards the gathered data set to a user.

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2.1 Scenario 1: Sensor Fields with Only One Sink Dissemination of sink announcement message. In the initial stage of the sensor network, the network administrator sets a sink in a suitable position: center, outskirt, or a special position according to his or her policy. If a sink is located in an arbitrary position in sensor fields, it floods a sink announcement message to announce itself inside the whole sensor field (Fig. 5). As a result of the flooding announcement message, every sensor node knows the hop counts and next hop neighbor sensor node to the sink. Dissemination of the user interest. While moving inside the sensor fields, if a user wants to collect data, the user selects the nearest node as a first agent, as shown in Fig. 6. The user delivers an interest to the first agent. The first agent, to which the user has delivered the interest, forwards the interest to the next hop neighbor node toward the sink. The next hop sensor node, which has had the interest delivered to it, also forwards the interest to the next hop neighbor node toward the sink. This process continues until the sink receives the interest of the user. Also, a route for the interest from the sink to the user has been established through this process. Based on our assumptions, the established route vanishes from the network when the described period in the interest is over. Data collection of sink. A sensor network with a static sink is a network where sensing data from sensor nodes should be transmitted to the static sink through multihop communication. So, existing routing algorithms for a static sink can be used (e.g., routing algorithms collecting data by periods, routing algorithms collecting a minority event, or routing algorithms detecting a moving object.) Hence, the network administrator can support a suitable routing protocol for users, and besides, a user can select and use the most appropriate routing algorithm with a static sink according to the policy of the networks. Such research has already been advanced [2], [3], [4]. So we will not mention it further in this paper. Rather, we use one of the existing routing algorithms to collect data in this paper. In Fig. 7, the static sink can forward interests from users to sensors and gather data from sensor networks according to the existing routing protocols. If all data are gathered by routing protocols, the static sink aggregates all data and forwards an aggregated data to the first agent. Mobility support of the user. A user may move to another place after sending an interest to the first agent. In this case, the user selects another agent that can communicate with the first agent. Also, the user makes a new connection between the newly selected agent and the original agent. (While moving inside the sensor field, the user can make more agents and connections.) These agents and connections are used for forwarding the aggregated data from the sink. Data propagation of sink. A sink delivers the aggregated data to the first agent through the reverse path of interest forwarding. The first agent delivers the aggregated data to the last agent through the connection of agents. The last agent delivers the

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aggregated data to the user. As shown in Fig. 8, the user can surely receive the aggregated data from the sink. 2.2 Scenario 2: Sensor Fields with Multiple Sinks Separation of the sensor fields. Basically, the difference between Scenario 1 and Scenario 2 is only the number of sinks. If there are more than one sink in the sensor field, this means a separation of the sensor fields. As a result of sink announcement message dissemination in this case, all sensor nodes know the nearest sink according to the hop counts. Accordingly, Interest dissemination of the user targets the nearest sink from the agent, as shown Fig. 9. The targeted sinks can be changed whenever the user wants to send its interests (see Fig. 10). Nevertheless, mobility support of the user and data propagation of the sink is still the same with Scenario 1. In addition, users may not be able to recognize how many static sinks are in the sensor fields. This means that the proposed model is independent of the number of sinks. Interest

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Data sharing of multiple static sinks. As shown in Fig. 1, a sink in typical sensor networks takes charge of the function as a gateway for a connection with infrastructure networks [1]. Various papers in relation to multiple static sinks also indicate the connection between a sink and an infrastructure network and the connection between all sinks as an assumption [10], [11].

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Therefore, in this paper, it is assumed that each sink placed in the edge of a sensor field can communicate with the other sinks via the infrastructure networks. Hence, the proposed model of this paper collects data by one sink through sensor fields. And the aggregated data of the collected data will be shared by multiple static sinks through the infrastructure network. Advantages with multiple static sinks. The proposed model can obtain various advantages with multiple static sinks. First of all, a user can receive the data from the nearest sink to its position. Therefore, short hops communications between a user and a sink are possible. This saves energy, enhances the data delivery ratio, and reduces delay. Also, because a user requires a dissemination of interests through multiple static sinks, the locations of data collection are diverse. It relieves the hot spot problem, which has carried a disproportionate amount of traffic to sensor nodes near the sink [13]. As a result, the lifetime of the sensor networks will increase because a balance of energy consumption of the sensor nodes is made possible. 2.3 Scenario 3: Sensor Fields with No Sink Hazardous sensor fields. Sensor fields without a sink are a special type of sensor networks. If the sensor field is hazardous such that network administrator cannot reach the field (e.g., a battlefield), the sensor field may not have any sinks. In a battlefield, users (or soldiers) may move into a sensor field that has no sink and gather data from sensors. In this case, users must gather data for themselves. Dissemination of sink announcement message. Because there is no sink in the sensor field, the sensor network cannot perform the sink announcement message dissemination process for itself. In this case, users appoint the nearest sensor node as first agent, and the first agent disseminates the sink announcement message. As shown in Figs. 11 and 12, users that want to gather data from sensors examine nearby sensor nodes whether there is a sink in the sensor field or not. If there is no sink, users appoint the nearest sensor node as first agent. Once a sensor node becomes the first agent, it acts as the sink of Scenario 1. Hence, other processes such as sink announcement message dissemination, interest dissemination of the user, mobility support of the user, and data propagation of the sink are the same as in Scenario 1. New Agent Move Report

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Advantages with idle sensor network. Based on our assumptions, the proposed model in this scenario may create many first agents periodically. The first agents must return to the original state after the described period. This means that the first agents are appointed whenever users want to send their interests. Then, the first agents are reactively selected and perform all processes for user mobility. In the whole network, therefore, the sensor network can remain in an idle state in case there is no user in the sensor field. From the standpoint of the whole network, this is a positive effect because there is no control of messages and interests in the idle state sensor network.

3 Performance Evaluation In this section, we evaluate the performance of a proposed model through simulations. We first describe our simulation model and simulation metrics. We next evaluate how environmental factors and control parameters affect the performance of a proposed algorithm. 3.1 Simulation Model and Metric

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We evaluate the proposed model in Qualnet, a network simulator [12]. A sensor node’s transmitting and receiving power consumption rate are 0.66 W and 0.39 W. The transceiver in the simulation has a 50 m radio range in an outdoor area. Each interest packet is 40 bytes long, and the data packet has 64 bytes. The sensor network consists of 100 sensor nodes, which are randomly deployed in a 300m x 300m field. We consider three scenarios for the proposed model according to the number of sinks. Hence, the number of sinks and users is changed for this evaluation. The multiple static sinks are located in the outskirts of sensor fields. And the user, which follows a random waypoint model of 10m/s speed and 10 second pause time, moves into the sensor field. The user disseminates an interest at an interval of every 10 seconds. Every sensor node receives the interest and generates only one sensing data for the interest. This is defined as one interest round. Namely, one interest round is 10 seconds. The simulation lasts for 500 seconds.

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We use metrics to evaluate the performance of the proposed algorithm. The network lifetime is defined as the number of the interest round when the first sensor node dies. The data delivery ratio is the ratio of the number of successfully received reports by a user to the total number of reports generated by every sensor node. The delay is defined as the average time between the time a user transmits an interest and the time the user receives the report. We compare three mobility types (D-COM, G-COM, and T-COM) in Table 1 with the proposed model in the simulation. 3.2 Impact of the Number of Static Sinks

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Scenarios 1 and 2 of A-COM can be compared with the D-COM because G-COM and T-COM have no static sink. We first study the impact of the number of sinks on A-COM’s performance. The number of sinks varies from 1, 2, 3, 4 to 5. And there is only one user in the sensor field. In this part, we compare Scenarios 1 and 2 to D-COM regarding lifetime, delay, and delivery ratio. A difference between A-COM and the D-COM is how to communicate between a user and a sink. Fig. 13 shows the number of interest rounds, namely, network lifetime. As shown in Fig. 13, the number of interest rounds shows little difference between A-COM and D-COM. This means that A-COM can manage sensor fields as well as D-COM without infrastructure that connects users with sinks. In addition, the lifetime is increased according to the number of sinks. This is a side effect of multiple sinks. Multiple sinks separate the sensor field, and besides, users only use the nearest sink to send interests and receive replies. Users can use the shortest path to communicate with multiple sinks. As a result of the shortest communication, the lifetime in A-COM is enhanced according to the number of sinks. The delay is also enhanced by this side effect of multiple sinks. A-COM basically has some delay due to multi-hop communication between users and sinks. However, the delay is diminished according to the number of sinks, as shown in Fig. 14. Nevertheless, the data delivery ratio of A-COM is comparable with D-COM, as shown in Fig. 15. This also proves that the proposed model can manage sensor fields as well as D-COM without infrastructure.

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3.3 Impact of the Number of Users The number of users only results in path increase between users and sinks. D-COM uses direct communication between users and sinks, and A-COM uses multi-hop communication. A-COM has more paths and consumes more energy. (e.g., five users in A-COM consumes five times of the energy that is consumed by one user.) However, it is a tradeoff between energy and infrastructure. Although A-COM has more energy consumption and delays than D-COM, the merit of A-COM is infrastructure-less communication systems. Scenario 3 of A-COM can be compared with G-COM and T-COM because Scenario 3 of A-COM, G-COM, and T-COM have no static sinks. There are no sinks, and the number of users varies from 1, 2, 3, 4 to 5. In this part, we compare Scenario 3 of A-COM to G-COM and T-COM regarding lifetime, delay, and delivery ratio. G-COM and T-COM make and change the topology proactively, but Scenario 3 of A-COM reactively makes and shares it among users. Generally, users move about the sensor field only and generate its interest occasionally. Hence, sensors in Scenario 3 can save considerable energy. Alternatively, sensors in G-COM and T-COM maintain a topology continuously. Fig. 16 shows each lifetime of these sensor networks. As shown in Fig. 16, the lifetime of T-COM is considerably low due to frequent topology change and that of G-COM is relatively low due to GRID maintenance. In Fig. 17, G-COM has little delay due to proactive GRID topology by the GPS receiver. T-COM proactively creates the topology, but frequent topology changes of TCOM delay data delivery considerably. The delay of Scenario 3, as shown in Fig. 17, however, is only a little high due to the reactive first agent selection and topology construction. In the case of the data delivery ratio, A-COM and G-COM in Fig. 18 are similar except for T-COM. The reason is frequent topology change. Topology change messages disturb the data delivery ratio. 3.4 Impact of the Number of Sensor Nodes Evaluating A-COM with other models according to the number of sensors is of no real consequence. It is closely related to the performance of routing protocols that are used in the network. Hence, we do not evaluate the proposed model with this factor. 100

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3.5 Impact of the User Mobility We lastly evaluate the impact of user speed on A-COM. We vary the maximum speed of a user from 8, 10, 12, 14 to 20m/s. We assume that there is one user in the sensor field. In this part, we compare Scenario 3 to G-COM and T-COM because D-COM is independent of user speed. Fig. 19 shows the delay in data delivery, which slightly increases as the user moves faster. The delay depends on a movement operation that is processed by the user. The faster a user moves, the more the time is needed to establish a connection between the user and the network. Nevertheless, the delay of A-COM is comparable with G-COM because A-COM creates only one communication path between the user and its first agent. The delay of T-COM, on the other hand, is relatively higher than the others due to frequent topology changes. And, Fig. 20 shows the data delivery ratio when the user’s moving speed changes. The data delivery ratio of A-COM is slightly decreased according to the delay. But the data delivery ratio remains around 0.8 - 0.9; nevertheless, the user moves faster. Besides, the data delivery ratio of G-COM remains high because the GPS receiver may help the user with geographical routing. On the other hand, the data delivery ratio of T-COM is relatively lower than the others because it has too many topology changes when moving. The results in Fig. 19 and Fig 20 mean that A-COM is fast and stable without GPS receiver.

4 Conclusion and Further Work In this paper, we propose a novel agent-based user-network communication model to support the mobility of users in wireless sensor networks. In the proposed network model, the user can receive data with a higher data delivery ratio and in a faster time without infrastructure. We verified that the lifetime of sensor networks is prolonged because the reactive path construction decreases the consumption of sensor nodes. Also, we verified that performance of the data delivery ratio and the delay never falls; nevertheless, communication between the user and the network for guaranteeing movement of the user is supported by only sensor nodes without infrastructure networks. There is further work that is related to this research. In a mobile environment, many sensor nodes can shift from one place to another frequently. The mobile sensor node environment makes more dynamic sensor networks. The issue of node mobility requires further study.

References 1. I.F. Akyildiz, et al., "A survey on sensor networks," IEEE Communications Magazine, Vol. 40, pp. 102-114, Aug. 2002. 2. C. Intanagonwiwat, et al., "Directed diffusion: A scalable and robust communication paradigm for sensor networks," ACM Mobicom, 2000. 3. C. Schurgers and M.B. Srivastava, "Energy efficient routing in wireless sensor networks," IEEE MILCOM 2001.

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4. W. R. Heinzelman, et al., "Adaptive Protocols for Information Dissemination in Wireless Sensor Networks," ACM Mobicom, 1999. 5. F. Ye, et al., “A Two-Tier Data Dissemination Model for Large-scale Wireless Sensor Networks,” ACM MobiCOM, Sept. 2002. 6. S. Kim, et al., “SAFE: A Data Dissemination Protocol for Periodic Updates in Sensor Networks,” Distributed Computing Systems Workshops 2003. 7. H. L. Xuan and S. Lee, “A Coordination-based Data Dissemination Protocol for Wireless Sensor Networks,” IEEE ISSNIP, Dec. 2004. 8. K. Hwang, et al., "Dynamic sink oriented tree algorithm for efficient target tracking of multiple mobile sink users in wide sensor field," IEEE VTC, Sep. 2004. 9. S. R. Gandham, et al., "Energy Efficient Schemes for Wireless Sensor Networks with Multiple Mobile Base Stations," IEEE GLOBECOM, Dec. 2003. 10. H. Ferriere, et al., “Efficient and Practical Query Scoping in Sensor Networks,” IEEE International Conference on Mobile Ad-hoc and Sensor Systems, Oct. 2004. 11. E. I. Oyman and C. Erso, “Multiple Sink Network Design Problem in Large Scale Wireless Sensor Networks,” IEEE ICC, Jun. 2004. 12. Scalable Network Technologies, Qualnet, [online] available: http://www.scalablenetworks.com. 13. Hui Dai and Rechard Han, “A node-centric load balancing algorithm for wireless sensor networks,” IEEE GLOBECOM, Dec. 2003.

Realistic Mobility and Propagation Framework for MANET Simulations Mesut G¨ une¸s, Martin Wenig, and Alexander Zimmermann Chair of Computer Science, Informatik 4, RWTH Aachen University {guenes,wenig,zimmermann}@i4.informatik.rwth-aachen.de

Abstract. Two main steps on the way to more realistic simulations of mobile ad-hoc networks are the introduction of realistic mobility and sophisticated radio wave propagation models. Both have strong impact on the performance of mobile ad-hoc networks, e.g. the performance of routing protocols changes with these models. In this paper we introduce a framework which combines realistic mobility and radio wave propagation models. Our approach consists of a zone-based mobility generator and a high accuracy radio wave propagation model. For the mobility generation a wide variety of well understood random mobility models is combined with a graph based zone model, where each zone has its own mobility model. To achieve a realistic radio wave propagation model a ray tracing approach is used. The integration of these two techniques allows to create simulation setups that closely model reality.

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Introduction

A mobile ad-hoc network is created by a collection of nodes which communicate using radio interfaces and do not rely on any pre-installed infrastructure. Furthermore, it is supposed that ad-hoc networks are inherently adaptive and auto-configured. Therefore, ad-hoc networks offer immense flexibility. In recent years the interest in the deployment of ad-hoc networks for real world scenarios grew. Still the number of real world ad-hoc networks is quite low and most of the testbeds [1] consist only of a small number of nodes. The development and testing of new algorithms and methods nowadays relies heavily on network simulations. Simulating wireless networks, and especially mobile adhoc networks, is not a trivial task and consequently there have been discussions about the validity of presented simulation results [2,3]. This work does not deal with the methodological background used to analyze the output of the simulation, instead it deals with the simulator’s accuracy. A key factor of accurate simulation results are accurate simulation models. To the belief of the authors the main weak points are 1) the unrealistic assumptions concerning the radio wave propagation [2], 2) the currently used simplistic mobility models [4,5] and 3) the assumed workload of the network. This work proposes a solution to the first two mentioned problems. I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 97–107, 2007. © IFIP International Federation for Information Processing 2007

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Our contribution in this work is an integrated framework which allows the definition and control of the movement and the radio wave propagation model in higher detail than previous approaches. We propose a generation process which based on partitioning the simulation area into zones with different independent mobility models together with a high accuracy radio wave propagation model. The need for such a generation framework might be illustrated by a quick literature overview: Taking the publications of the MobiHoc conferences of the last two years as an example, it is obvious that there is a need for better tool support for simulation designers. Out of 52 papers 35 presented simulation results (around 67%). Six papers did not give any information about the used mobility model, 10 used random waypoint to model mobility and 14 considered static scenarios. Only two papers showed results obtained from considering more than one mobility model. Only two papers mention the used radio wave propagation model, ten papers gave no indication about the used model and 22 used a fixed radius. Assuming that all papers which did not specify their propagation model used a fixed range it can be concluded that all papers used circular, bidirectional links. None of the presented papers used a small scale (fading) model. The structure of the paper is as follows: In section 2 mobility and radio wave propagation models are presented. In section 3 our approach is discussed in detail and in section 4 some simulation results obtained with ns-2 are discussed.

2 2.1

Related Work Random Mobility Models

There are many random mobility models proposed in literature. Detailed descriptions of these models are given in [6,7,8,9,10]. The most simple random mobility model is called Random Walk. In this model, a node selects randomly a direction and speed from predefined ranges [ϕmin : ϕmax ] and [vmin : vmax ], respectively. Each movement is bounded either by travel time or distance. The Random Waypoint mobility model is an extension of Random Walk and integrates a pause time between two consecutive moves. A disadvantage of this model is the concentration of nodes in the center of the simulation area [11]. Besides these entity mobility models, there are group mobility models which specify how a set of nodes move in respect to each other [6]. In the Nomadic Community Mobility Model, all mobile nodes move to the same location in the same order but by using different entity mobility models. The Reference Point Group Mobility model specifies the movement of the group as well as the movements of the nodes within the group. There are also models which match the characteristics of car movements. In the Freeway model, there is at least one lane in each direction of a street. The nodes move on the lanes. The speed of a node depends on other nodes on the same lane. In the Manhattan model the lanes are organized around blocks of buildings. A node can change its direction only at intersections. All mobility models discussed so far share the assumption that there are no obstacles. In [12] a refinement of random mobility models by integrating obstacles

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is proposed. The obstacles represent buildings. Upon the definition of buildings, paths between them are calculated. The mobile nodes are randomly distributed on the paths and the destinations of the nodes are selected randomly among the buildings. The nodes move on the defined paths from building to building. Additionally, the communication characteristic is also affected by the obstacles. A mobile node inside a building cannot communicate with a mobile node outside the building. 2.2

Models from Cellular Network Research

In cellular networks the geographical area is divided into cells. There is a base station in each cell which provides communication service for the nodes. The mobility models in this area describe the mobility of the nodes regarding the cell topology, i.e., when a node moves from a particular cell to another cell. In [13] a hierarchy of such models with regard to metropolitan, national, and international mobility is presented. Their results cannot directly be applied to MANET simulations, since here movements have to be described with higher granularity. 2.3

Mobility Models from Real User Traces

The best input for simulations would be derived from real traces. However, it is very difficult for the research community to obtain those data. Therefore, there are few studies reported which are based on real data [14]. In [15] the authors describe how real user traces can be used to build simulation models. It is based on the trace collection at Darthmouth College. Their interesting research can be used as input for our mobility generator. But using it to evaluate our models is not meaningful, since we could set up our model to deliver similar results by simply creating a similar geometry and using their parameters as input. 2.4

Radio Wave Propagation

Radio channels are more complicated to model than wired channels. Their characteristics may change rapidly and randomly and they are dependent on their surrounding (buildings, terrain etc.). Nevertheless, most wireless network simulators use very simplified propagation models. In general, propagation models can be characterized into two groups: large-scale and small-scale propagation models. Large-scale models characterize how the transmission power between two nodes changes over long distances and over a long time. Small-scale models account for the fact that small movements (in the order of the wavelength) may have large influence on the transmission quality. Also, due to multipath propagation, the signal varies heavily even if the nodes do not move. Common used propagation models are the Free Space model, the Two-Ray Ground model and the Shadowing model [16]. In addition, Ricean and Rayleigh fading are often used as small-scale models [17]. None of these models is able to correctly model complex scenarios with obstacles. One way to overcome this

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limitation is the use of ray tracing technologies. In [18] an approach using this technique is described. It allows the definition of obstacles in a graphical editor and this scenario description is used in the simulation to feed a ray tracing algorithm. The algorithm is started once for every new position the node takes up. The authors state that this approach slows down the simulation by a factor of up to 100. Also, no movement information is generated by this tool. Other approaches [19,20] either do not scale well or their accuracy is highly dependent on the selected grid resolution of the calculated scenario. Additionally, these models have been developed for fixed wireless networks.

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Generation Framework

The proposed framework named CosMos addresses the generation of i) realistic mobility patterns, and ii) accurate radio wave propagation information for the specific scenario. The whole process needs three steps. First the designer has to create a scenario for the desired simulation setup. In the next two steps the energy density maps for the radio wave propagation model are precomputed and the movement files are generated. 3.1

Scenario Creation

The scenario consists of movement zones (MZ) and obstacle zones (OZ). Both can basically be described as polygons and they divide the simulation area into smaller parts. The designer assigns a mobility model to each MZ. All models have their own set of parameter (e.g. maximum speed) and are independent of each other. When MZs overlap nodes can change from one zone to the other. The probability to leave the current zone can also be set by the designer. The obstacles have three parameters: their height, their reflection, and transmission coefficients. The position of the zones can be set up by the designer as wished, e.g to model an indoor scenario. The values for the mobility models must be decided individually according to the intended scenario. Here, only very limited experience has been gathered by researchers. The approach presented in [15] can be integrated in our framework. For the radio wave propagation model there have been measurements which can be used, e.g. [16]. Another approach is to perform own measurements and use these as input for the ray tracer. 3.2

Mobility Generator

The movement zones create a weighted and directed graph: the zones are the vertices (V), there is an edge between two vertices if the corresponding movement zones overlap. The set of edges (E) has weights attached to them. The function w : E → − (0 . . . 1) defines weights for all edges of the graph G(V, E). The weight wi,j of a directed edge ei,j ∈ E from zone i to zone j corresponds to the probability for nodes to leave zone i to zone j.

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Initially all nodes are distributed randomly in the movement zones. During the generation process nodes move inside the zones according to the mobility model of their current zone. If a node decides to leave to a neighbouring zone (depending on the exit probability) it moves towards the overlapping region of the two zones. When it arrives there, the mobility model of the new zones takes over and the node starts to move according to the new mobility model. Our approach allows the calculation of the spatial distribution of nodes on the simulation area as well as the distribution of nodes on the movement zones. Since initially all nodes are distributed randomly in all movement zones, there will be a point in time in which zones with a high exit probability will ‘loose’ some nodes to the zones with a lower exit probability. After a while, the distribution of nodes should become stable. Figure 1 shows a small example with three movement zones: two large rectangles on each side and a narrow street connecting them. Zone A has a higher exit probability than Zone B. The street is only used to travel from zone A to B and vice versa. 1

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Fig. 1. Visualizing the steady state

Figure 1(a) shows the (long-term) spatial probabilities of the simple scenario. It shows the probability of a node being at a specific place over a simulation run of 10000 seconds. Figure 1(b) shows that initially all zones contain approximately one third of all nodes. During the simulation run the distribution slowly changes: all nodes in the street zone leave this zone to one of the neighbouring zones. The distribution stabilizes when most of the nodes are inside the zone with the lower exit probability. Nevertheless, still nodes travel from one zone to the other, but the long term average remains relatively constant from second 2000 onwards. If this ‘steady-state’ behaviour is important for the considered simulation scenario then the first seconds will have to be cut off. The proposed framework per default creates several independent variants of the movements according to the given models. This helps the researcher to conduct simulations with independent replications.

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Radio Wave Propagation Model

The radio wave propagation model used in this work is based on a ray tracing approach. The obstacles defined in CosMos are used as input for the ray tracer. Triggering a ray tracing run for every position of the current sender is unfeasible in mobile ad-hoc networks. Instead, our approach uses a set of predefined starting points for the ray tracing approach. The ray tracer is then started once for each of this points creating an energy distribution map for each one. During the simulation the energy distribution between the sender and the receivers is calculated using weighted interpolation, as detailed below. The ray tracer accounts for the following propagation phenomenas: reflection, diffraction, and scattering. To use the generated energy distribution maps during the simulation, we modified the ns-2 network simulator [21]. We added a propagation model which reads in a given set of maps and the corresponding starting points. During the simulation, whenever a node nt wants to transmit a packet, a k-nearest neighbor search is started1 . This search finds the k nearest starting points and their corresponding energy distribution maps to the sender’s position. For each node inside the maximum interference range of an unobstructed radio wave the transmission power is calculated. The formula used for the weighted interpolation is given below: k−1 si i=0 posi −post p 1 i=0 posi −post p

st−r = k−1

,

where st−r is the signal strength between the transmitter node nt and the receiver node nr . The position of the transmitter is given as post , posi denotes the position of the starting point of the i-th closest map. Note that si is the predicted signal strength of map i at the position of the receiver posr . The exponent p controls how much influence is given to further away maps2 . The benefits of our approach are that it is not necessary to rerun the ray tracing algorithm during simulation time, it is not necessary to divide the simulation area into evenly sized squares, and the accuracy can be increased in areas with a lot of obstacles, simply by adding more starting points. A real-time evaluation tool has been developed to show the result of the interpolation. Our approach increases the simulation speed and allows the designer to choose between high accuracy and reduced memory needs [22].

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Results

In this Section we discuss some simulation results created with ns-2. The simulation scenario was created with CosMos. The presented Scenario models the office building in which the authors’ chair is in. The intention of the studies was 1 2

Our experiments showed k equal to 3 gave good results. In our experiments p was set to 3.

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Fig. 2. Indoor scenario

to show the impact of the mobility and radio wave propagation models on the performance of MANET routing protocols. Figure 2 shows the scenario outline. Only the ground floor is modeled here. All nodes are equipped with IEEE 802.11 radio interfaces with a transmission rate of 11 Mbit/s and a transmission power of 0.1 mW. The receiving threshold was set to -88 dBm, a value taken from the specification of the Cisco Aironet 1240AG Series access point. The AODV implementation of the university of Uppsala [23] and the current version of DSR [11] in ns2 were used. Thirty connections between randomly selected nodes were started, each one offering 32 kBytes of load. Movements inside of offices are seldom and relatively slow (max. speed was set to 1 m/s). Movements inside of the hallways on the other hand are faster and follow the freeway model (max. speed was set to 2 m/s). Since we had detailed plans of our building, we were able to model it with high detail. To check the accuracy of the radio wave propagation model, we conducted some measurements with real-life systems and compared the results to the calculated values. The mean error between the predicted values and the calculated is 3.5 dB which is as good as the results for approches mentioned in section 2. We conducted simulations using the AODV and the DSR routing protocols in which the following combinations were considered: CosMos mobility model together with Two-Ray Ground propagation model and CosMos mobility model with ray tracing propagation model. Figure 3 shows a comparison of the throughput achieved using AODV and DSR in the presented scenario. It is clear to see that the measured values without the ray tracer propagation model can be considered as equal. But using the ray traced propagation model, the DSR protocol suffers more heavily from performance loss. AODV seems to be able to cope better with the situation. The decreasing performance for larger number of nodes can be explained by the higher number of hops between sender and destination.

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The routes are getting longer because the node density is higher and farther away nodes can also be reached. The reason for the worse performance of DSR compared to AODV seems to be a larger number of discovered paths which were actually already invalid (stale paths) when they should be used for the first time. Figure 4 compares the average end-to-end delay for packets between source and destination. As expected, the values using TwoRay Ground can again be considered as equal. Using the ray tracer the delay of course grows due to longer routes, higher number of transmission errors, and thus higher routing overhead. Again, we see a strong influence on DSR. As a rule of thumb, one can say that if more than 90% of all packets have a delay of less than 150ms, VoIP is possible with reasonable quality. If scenarios with more than 60 nodes are considered, DSR is not able to fullfil this criterion. This is yet another example why accurate simulation models are absolutely neccesarry. If one would have based the decission on the simple simulation setup both algorithms would have been judged as equal but in reality only AODV is actually able to fullfil the delay bound. 35

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Another result of our simulation study is that the mobility model is more important for larger scenarios. The smaller the simulation area compared to the transmission range of the nodes, the smaller the influence of the mobility model. We also measured the run-time of the simulations with and without our propagation model. Table 1 shows the times for the indoor simulation. The increase in run-time is relatively small since during the simulation runtime only lookups in the kd-tree have to be done. The preprocessing time, namely the time needed to create the energy distribution maps, is dependent on the complexity of the scenario. For the presented indoor scenario 112 starting points were used and the ray tracer needs around 12 seconds for each point (shooting 50000 photons).

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Conclusion

In this paper we have introduced a mobility and radio wave propagation scenario generator for MANET. The goal was to aid researchers in the design of realistic simulation scenarios. The framework is very general and can be deployed to design scenarios with special requirements. Our approach combines a wide variety of well understood random mobility models with a graph based zone model and a sophisticated ray traced radio wave propagation model. Each zone can have a different mobility model. The framework allows to generate the mobility definition and the ray tracer results from one common scenario. So the combination of realistic movement models and accurate radio wave propagation models becomes an easy task for the researcher. Furthermore, our approach allows the calculation of the spatial distribution of nodes on the simulation area as well as the distribution of the nodes on the defined zones. This allows us to figure out the time when the stationary state is reached. Since, trustworthy MANET simulations should begin when the stationary state is reached.

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References 1. G¨ une¸s, M., Bouazizi, I.: From Biology to Technology: Demonstration Environment for the Ant Routing Algorithm for Mobile Ad-hoc Networks. In: Tenth Annual Int. Conference on Mobile Computing and Networking (ACM MobiCom 2004), Philadelphia, USA (September 2004) 2. Kotz, D., Newport, C., Gray, R.S., Liu, J., Yuan, Y., Elliott, C.: Experimental evaluation of wireless simulation assumptions. Technical Report TR2004-507, Dept. of Computer Science, Dartmouth College (June 2004) 3. Pawlikowski, K., Jeong, H.D.J., Lee, J.S.R.: On credibility of simulation studies of telecommunication networks. IEEE Communications 40(1) (January 2002) 132– 139 4. Bettstetter, C., Hartenstein, H., Perez-Costa, X.: Stochastic properties of the random waypoint mobility model: epoch length, direction distribution, and cell change rate. In: MSWiM ’02: Proc. of the 5th ACM int. Workshop on Modeling, Analysis and Simulation of Wireless and Mobile Systems, NY, USA, ACM Press (2002) 7–14 5. Bettstetter, C., Resta, G., Santi, P.: The node distribution of the random waypoint mobility model for wireless ad hoc networks. IEEE Trans. Mobile Computing 2(3) (2003) 257–269 6. Hong, X., Gerla, M., Pei, G., Chiang, C.C.: A group mobility model for ad hoc wireless networks. In: Proc. of the ACM Int. Workshop on Modeling and Simulation of Wireless and Mobile Systems (MSWiM). (August 1999) 53–60 7. Camp, T., Boleng, J., Davies, V.: A survey of mobility models for ad hoc network research. Wireless Communications and Mobile Computing (WCMC): Special issue on Mobile Ad Hoc Networking: Research, Trends and Applications 2(5) (2002) 483–502 8. Sanchez, M.: Mobility models. http://www.disca.upv.es/misan/mobmodel.htm (2005) 9. Bai, F., Sadagopan, N., Helmy, A.: The important framework for analyzing the impact of mobility on performance of routing for ad hoc networks. AdHoc Networks Journal - Elsevier Science 1(4) (November 2003) 383–403 10. Lin, G., Noubir, G., Rajaraman, R.: Mobility models for ad hoc network simulation. In: Proc. of the 23rd Conference of the IEEE Communications Society, Hon Kong, IEEE, IEEE (March 7-11 2004) 11. Johnson, D.B., Maltz, D.A.: Dynamic source routing in ad hoc wireless networks. In: Mobile Computing. Volume 353. Kluwer (1996) 12. Jardosh, A., Belding-Royer, E.M., Almeroth, K.C., Suri, S.: Towards realistic mobility models for mobile ad hoc networks. In: The Ninth Annual Int. Conference on Mobile Computing and Networking (ACM MobiCom 2003), San Diego, USA, ACM (September 14-19 2003) 13. Lam, D., Cox, D.C., Widom, J.: Teletraffic modeling for personal communications services. IEEE Communications Magazine 35 (Feb. 1997) 79–87 14. Hsu, J., Bhatia, S., Takai, M., Bagrodia, R., Acriche, M.J.: Performance of mobile ad hoc networking routing protocols in realistic scenarios. In: MilCom 2003, Boston, Massachusetts (October 13-16 2003) 15. Kim, M., Kotz, D., Kim, S.: Extracting a mobility model from real user traces. In: Proc. of the 25th Joint Conference of the IEEE Computer and Communications Societies, Barcelona, Spain, IEEE Computer Society Press (April 2006)

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16. Rappaport, T.S.: Wireless Communications, Priciples & Practice. Prentice Hall (1999) 17. Punnoose, R.J., Nikitin, P.V., Stancil, D.D.: Efficient simulation of ricean fading within a packet simulator. In: Vehicular Technology Conference. (Sep. 2000) 18. Dricot, J.M., Doncker, P.D.: High-accuracy physical layer model for wireless network simulations in ns-2. In: Proc. of the Int. Workshop on Wireless Ad-hoc Networks. (2004) 19. Catedra, M., Perez, J., de Adana, F.S., Gutierrez, O.: Efficient ray-tracing techniques for three-dimensional analyses of propagation in mobile communications: application to picocell and microcell scenarios. Antennas and Propagation Magazine 40(2) (Apr 1998) 15–28 20. Schmeink, M., Mathar, R.: Preprocessed indirect 3D-ray launching for urban microcell field strength prediction. In: AP 2000 Millennium Conference on Antennas and Propagation. (April 2000) 21. Fall, K., Varadhan, K.: The ns-2 manual. Technical report, The VINT Project, UC Berkeley, LBL and Xerox PARC (2003) 22. Schmitz, A., Wenig, M.: The effect of the radio wave propagation model in mobile ad hoc networks. In: MSWiM ’06: Proc. of the 9th ACM international workshop on Modeling, Analysis and Simulation of wireless and mobile systems, Torremolinos, Spain, ACM Press (2006) 23. Wiberg, B., Nordstr¨ om, E.: Ad-hoc on-demand distance vector routing - for real world and simulation. http://core.it.uu.se/core/index.php/AODV-UU (October 2006)

Localization for Large-Scale Underwater Sensor Networks Zhong Zhou1 , Jun-Hong Cui1 , and Shengli Zhou2 1 2

Computer Science & Engineering Dept, University of Connecticut, Storrs, CT, USA, 06269 Electrical & Computer Engineering Dept, University of Connecticut, Storrs, CT, USA, 06269 {zhong.zhou,jcui,shengli}@engr.uconn.edu

Abstract. In this paper, we study the localization problem in large-scale underwater sensor networks. The adverse aqueous environments, the node mobility, and the large network scale all pose new challenges, and most current localization schemes are not applicable. We propose a hierarchical approach which divides the whole localization process into two sub-processes: anchor node localization and ordinary node localization. Many existing techniques can be used in the former. For the ordinary node localization process, we propose a distributed localization scheme which novelly integrates a 3-dimensional Euclidean distance estimation method with a recursive location estimation method. Simulation results show that our proposed solution can achieve high localization coverage with relatively small localization error and low communication overhead in large-scale 3-dimensional underwater sensor networks.

1 Introduction Recently, there has been a rapidly growing interest in monitoring aqueous environments for scientific exploration, commercial exploitation and coastline protection. The ideal vehicle for this type of extensive monitoring is a distributed underwater system with networked wireless sensors, referred to as Underwater Wireless Sensor Network (UWSN) [1,9]. For most UWSNs, localization service is an indispensable part. For example, in the long-term non-time-critical aquatic monitoring service [9,13], localization is a must-do task to get useful location-aware data. Location information is also needed for geo-routing which is proved to be more efficient than pure flooding in UWSNs [20]. In this paper, we investigate the localization issue for large-scale UWSNs. Localization has been widely explored for terrestrial wireless sensor networks, with many localization schemes being proposed so far. Generally speaking, these schemes can be classified into two categories: range-based schemes and range-free schemes. The former covers the protocols that use absolute point-to-point distance (i.e., range) estimates or angle estimates to calculate locations [12,14,6,5,18,15], while the latter makes no assumptions about the availability or validity of such range information [7,17,16,11,19]. Although range-based protocols can provide more accurate position estimates, they need additional hardware for distance measures, which will increase the network cost. On the other hand, range-free schemes do not need additional 

This work is supported in part by the NSF CAREER Grant No.0644190.

I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 108–119, 2007. c IFIP International Federation for Information Processing 2007 

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hardware support, but can only provide coarse position estimates. In this paper, we are more interested in accurate localization, which is requested by a range of applications, such as estuary monitoring and pollutant tracking [9]. Moreover, in UWSNs, acoustic channels are naturally employed, and range measurements using acoustic signals are much more accurate than using radio [9,20]. Thus, range-based schemes are potentially good choice for UWSNs. Due to the unique characteristics (such as low communication bandwidth, node mobility, and 3-dimensional node deployment) of UWSNs [1,9], however, the applicability of the existing range-based schemes is yet to be investigated. There are also several schemes proposed for the localization service in underwater acoustic networks [4,3,21,10]. These solutions are mainly designed for small-scale networks (usually with tens of nodes or even less). For large-scale UWSNs, hundreds or thousands of sensor nodes are deployed in a wide underwater area. Directly applying these localization schemes proposed for small scale underwater networks in large-scale networks is often inefficient and costly. In this paper, for the first time, we explore the localization problem in large-scale UWSNs. We propose a hierarchical approach, dividing the whole localization process into two sub-processes: anchor node localization and ordinary node localization. Many existing approaches can be used in anchor node localization. For ordinary node localization, we propose a novel distributed method based on a 3-dimensional Euclidean distance estimation method and a recursive location estimation method. Simulation results show that our localization scheme can achieve high localization coverage with accurate location estimation and low communication overhead in large-scale 3-dimensional underwater sensor networks. The rest of this paper is organized as follows. In Section 2, we describe our localization scheme. Simulation results are then presented in Section 3. And finally we draw conclusions in Section 4.

2 Localization for Large-Scale UWSNs 2.1 Overview We consider a typical UWSN environment as shown in Fig. 1. There are three types of nodes in the network: surface buoys, anchor nodes, and ordinary nodes. Surface buoys are nodes that drift on the water surface. These buoys are often equipped with common GPS and can get their absolute locations from GPS or by other means. Anchor nodes are those who can directly contact the surface buoys to get their absolute positions. These nodes can also communicate with ordinary nodes and assist them to do localization. Ordinary nodes are those who can not directly talk to the surface buoys because of cost or some other constraints but can communicate with the anchor nodes to estimate their own positions. To handle the large scale of UWSNs, we propose a hierarchical localization approach. In this approach, the whole localization process is divided into two sub-processes: anchor node localization and ordinary node localization. At the beginning, only the surface buoys know their locations through common GPS or by other means. Four or more buoys are needed in our system. These buoys work as the “satellites” for the whole network, and anchor nodes can be localized by

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Fig. 1. A typical large-scale underwater sensor network setting

these surface buoys. Using surface buoys to locate underwater objects has been extensively investigated and many existing systems, such as [4] and [3], can be employed in the anchor node localization process. In this paper, we will not contribute to this part. Instead, we mainly tackle the problem of ordinary node localization, for which we propose a distributed range-based scheme, novelly integrating a 3-dimensional Euclidean distance estimation method and a recursive location estimation method. We describe this scheme in the following section. 2.2 Ordinary Node Localization In 3-dimensional UWSNs, for a range-based localization scheme, ordinary nodes have to estimate their distances to more than 4 anchor nodes and calculate their locations by triangulation methods, which are commonly used in GPS systems. In a large-scale UWSN, however, not all ordinary nodes can directly measure their distances to 4 or more anchor nodes, thus some multi-hop distance estimation methods have to be developed. In [18], the authors proposed and compared three multi-hop distance estimation methods: DV-Hop, DV-Distance and Euclidean. Even for two dimensional terrestrial sensor networks, the performance of DV-Hop and DV-Distance degrades dramatically in anisotropic topologies, while the Euclidean method can achieve much more accurate results and behave more consistently in both anisotropic and isotropic networks than other methods [18]. In a UWSN, since the sensor nodes are constantly moving due to many environment factors, the network topology may change unpredictably with time and space. Thus, the Euclidean method is expected to be more suitable for UWSNs than other approaches. In our scheme, we employ a hybrid approach based on a 3-dimensional Euclidean distance estimation method and a recursive location estimation method to get the ordinary node positions. When combined with the recursive method, the inherent problems of the Euclidean method such as high communication cost and low localization coverage can be greatly alleviated. Next, we first discuss these two methods, examining why they can be seamlessly integrated together. Then we describe the ordinary node localization process in detail.

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3-Dimensional Euclidean Distance Estimation. In [18], a Euclidean distance propagation method is proposed for two dimensional sensor networks. Here, we extend it into 3-dimensional networks. We use an example to illustrate the method. Referring to Fig. 2, if an ordinary node E wants to estimate its distance to anchor node A, it needs to know at least three (onehop) neighbors (e.g., B, C, and D) which have distance estimates to A. Note that nodes A, B, C and D should not be co-plane and any three nodes out of A, B, C, D and E should not be co-line. Moreover, E needs to know its two-hop distance estimates, that is, E should have the length information of EB, BA, EC, CA, ED, DA, DB, DC, and BC. The 3-dimensional Euclidean distance estimation works as follows: First, node E uses edge BA, CA, BC to construct the basic localization plane. Since the lengths of edges DB, DA and DC are already known (to E), the position of D can be easily estimated. There exist at most two possible positions for D. Because E knows the lengths of edges ED, EB and EC, corresponding to the two possible positions of D, there will be at most four possible solutions for E’s position. The choice among these four possibilities is made locally by voting when E has more immediate neighbors with estimates to A. If it cannot be decided, the distance estimate to A is not available until E gets more information from its neighbors.

Fig. 2. 3-dimensional Euclidean estimation

Recursive Location Estimation. In [2], the authors propose an iterative framework to extend the position estimation from a few reference nodes throughout the whole network. System coverage increases recursively as nodes with newly estimated positions join the reference node set, which is initialized to include anchor nodes. This recursive location estimation method is illustrated in Fig. 3. In the figure, node 1 can get its location information from four neighboring anchor nodes A, B, C and D. If the location estimation error is small enough, node 1 can be regarded as a new reference node for other nodes. Then, it will broadcast its own location information. When node 2 gets to know the locations of C, D, E and 1 as well as the distances to these nodes, it can calculate its own location. On the other hand, if the location estimation error is large, node 1 cannot be treated as a reference node and will not broadcast its location. In our scheme, the following formula is used to estimate the location error δ:

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δ=

  (u − xi )2 + (v − yi )2 + (w − zi )2 − l2 , i

(1)

i

where (u, v, w) are the estimated coordinates of the unknown node, (xi , yi , zi ) are the reference node i’s location, li is the measured distance between the unknown node and node i.

Fig. 3. Recursive location estimation

In order to alleviate the error propagation effect, every reference node in the system has a confidence value η. For the initial reference nodes (i.e., the anchor nodes), η is set to be the largest, while for a new reference node, η is associated with its location error. In our scheme, η is calculated as follows ⎧ 1 ⎪ ⎨

if node is the initial anchor δ η = 1−  others ⎪ ⎩ (u − xi )2 + (v − yi )2 + (w − zi )2

(2)

i

We can see that η is essentially a normalized δ. A critical value λ (referred to as “confidence threshold” later) is set. When η > λ, the unknown node can become a reference node. Otherwise, it will continue to be non-localized. When a node gets to know its distances to more than four nodes, it will choose four according to their η values and calculate its location. Ordinary Node Localization Process. In the ordinary node localization process, there are two types of nodes: reference nodes and non-localized nodes. In the initialization phase, all anchor nodes label themselves as reference nodes and set their confidence values to 1. All the ordinary nodes are non-localized nodes. With the advance of the localization process, more and more ordinary nodes are localized and become reference nodes. There are two types of messages: localization messages and beacon messages. Localization messages are used for information exchange among non-localized nodes and reference nodes, while beacon messages are designed for distance estimates. During the localization process, each node (including reference nodes and non-localized nodes) periodically broadcasts a beacon message, containing its id. And all the neighboring

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Fig. 4. Ordinary node localization process

nodes which receive this beacon message can estimate their distances to this node using techniques, such as TOA (time of arrival). We describe the actions of the two types of nodes as follows. Reference Nodes: Each reference node periodically broadcasts a localization message which contains its coordinates, node id, and confidence value. Non-localized Nodes: Each non-localized node maintains a counter, n, of localized messages it broadcasts. We set a threshold N (referred to as “localization message threshold”) to limit the maximum number of localization messages each node can send. In other words, N is used to control the localization overhead. Besides, each nonlocalized node also keeps a counter, m, of the reference nodes to which it knows the distances. Once the localization process starts, each non-localized node keeps checking m. There are two cases: (1) m < 4. This non-localized node broadcast a localization message which contains all its received reference nodes’ locations and its estimated distances to these nodes. Its measured distances to all one-hop neighbors are also included in this localization message. Besides, this node uses the 3-dimensional Euclidean distance estimation approach to estimate its distances to more non-neighboring reference nodes. After this step, the set of its known reference nodes is updated. Correspondingly, m is updated and the node returns to the m-checking procedure. (2) m ≥ 4. This non-localized node selects 4 reference nodes with the highest confidence values for location estimation. After it gets its location, it computes confidence

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value η. If η is larger than or equal to the confidence threshold λ, then it is localized and labels itself as a new reference node. Otherwise, if η is smaller than λ, the node will take the same actions as described in case (1). The complete localization procedure of an ordinary node is illustrated in Fig. 4.

3 Performance Evaluation In this section, we evaluate the performance of our proposed localization scheme through simulation. 3.1 Simulation Settings In our simulation experiments, 500 sensor nodes are randomly distributed in a 100m × 100m × 100m region. We define node density as the expected number of nodes in a node’s neighborhood, hence node density is equivalent to node degree. We control the node density by changing the communication range of each node while keeping the area of deployment the same. Range (i.e., distance) measurements between nodes are assumed to follow normal distributions, with real distances as mean values and standard deviations to be one percent of real distances. 5%, 10% and 20% anchor nodes are considered in our simulations. Besides our scheme, we also simulate a Euclidean scheme and a recursive scheme for comparison. The recursive scheme here is the same as in [2]. As for the Euclidean scheme, we use the three dimensional Euclidean distance estimation as the distance propagation method and then use the triangulation method to estimate an ordinary node’s position if it gets to know four or more reference nodes. It works almost the same as the Euclidean scheme for two dimensional networks [18]. We consider three performance metrics: localization coverage, localization error and average communication cost. Localization coverage is defined as the ratio of the localizable nodes to the total nodes. Localization error is the average distance between the estimated positions and the real positions of all nodes. As in [18,8], for our simulations, we normalize this absolute localization error to the node communication range R. Average communication cost is defined as the overall messages (including beacon messages and localization messages) exchanged in the network divided by the number of localized nodes. 3.2 Performance in Static Networks In this set of simulations, nodes in the network are fixed. The confidence threshold λ is set to 0.98, and the localization message threshold N is set to 5. We change the node density (i.e., node degree) from 8 to 16 and compare our scheme with the Euclidean scheme and the recursive scheme. The results are plotted in Fig. 5, Fig. 6, and Fig. 7. Localization Coverage. Fig. 5 shows that our scheme outperforms both Euclidean scheme and recursive scheme in terms of localization coverage. This is reasonable since any node which can be located by either Euclidean scheme or recursive scheme can also be located by our scheme. The localization coverage of our scheme increases monotonically with the node density. But when the node density is relatively large, the coverage

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reaches a relatively high value and will not change much after that. For example, when the anchor percentage is 20%, the localization coverage reaches 94% at node density 12 and does not increase much with the node degree lifted. And we can also see that the more the anchors, the higher the localization coverage. For example, if the anchor percentage is 5%, the localization coverage can only reach 0.4 when the node density is 13, but if the anchor percentage is 10%, the localization coverage can reach 0.8 when the node density is 13. This suggests us that in sparse networks, we can increase the number of anchor nodes to achieve higher localization coverage. Localization Error. Fig. 6 plots the relationship between the localization error and the node density. We can observe that when the node density is relatively small, the localization error of our scheme is almost the same as that of the other two schemes. With the increase of the node density, the localization error of our scheme will increase and become a little larger than recursive scheme but much smaller than Euclidean scheme. This is because with the increase of the node density, the localization coverage of our scheme increases much faster than the other two schemes, as leads the growth of the localization error. But this growth is much slower rate than that of the localization coverage. As the node density continues to increase beyond some point, the localization error of our scheme will decrease slowly. This can be explained as follows. When the node density reaches a certain point, most sensor nodes can localize themselves. If we continue to increase the node density, ordinary nodes will get to know more anchor nodes and have more choices to calculate their locations. Thus, the localization error will decrease. But, as show in Fig. 6, this decrease is very limited. For example, when the anchor percentage is 5%, if we increase the node density from 13 to 16, the localization error only decreases from 0.3 to 0.27. Thus, in practice, we cannot expect to reduce the localization error by simply lifting the node density. Fig. 6 also shows us that the localization error will decrease observably with the anchor percentage. For example, at node density 13, when the anchor percentage is 5%, the localization error is 0.3. But when the anchor percentage is enlarged to 20%, it reduces to 0.05. Thus, more anchor nodes can translate into smaller localization errors. Communication Cost. Fig. 7 shows the average communication cost with the changing node density. In the recursive localization scheme, only nodes with known locations broadcast messages and other nodes keep silent. Therefore, the average communication cost of this scheme is very small. For our scheme, when the node density is small, it introduces larger communication cost than the recursive scheme. This is because in our scheme, when the network is sparse, although many nodes exchange beacon messages, they cannot finally localize themselves. In other words, these beacon messages are actually “wasted” in the localization process. But with the increase of the node density, this waste becomes smaller and smaller, and the average communication cost of our scheme becomes closer and closer to the recursive scheme. From the figure, we can also observe that the average communication cost of our scheme decrease with the increase of anchor percentage. Compared with the Euclidean localization scheme, our scheme can always achieve much lower communication cost. This is due to that fact that the recursive component in our scheme help to find more reference nodes much faster than the Euclidean localization scheme.

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(a) Anchor percentage=5%

(b) Anchor percentage=10%

(c) Anchor percentage=20%

Fig. 5. Localization coverage

(a) Anchor percentage=5%

(b) Anchor percentage=10%

(c) Anchor percentage=20%

Fig. 6. Localization error

Discussions. It is shown in [8] that range-based ad hoc localization schemes have high requirements on the node density of the networks. The paper also shows that in a two dimensional network, the node density needs to be at least 11 in order to localize 95% nodes with less than 5% localization error when 20% anchor nodes are present in the network. From Fig. 6(c), we can observe that when there are 20% anchors, our scheme can localize more than 95% nodes with less than 5% localization error if the node density is 12 in a 3-dimensional UWSN. Compared with the results in [8] for two dimensional networks, our scheme can achieve the same performance in 3-dimensional networks, with the connectivity requirement increased from 11 to 12. This indicates the good performance of our proposed scheme. On the other hand, this connectivity requirement of 12 may be still a little high for UWSNs with expensive sensor nodes or sparse deployment. One possible solution is to distinguish between the sensor’s localization range and communication range. This means that we can increase the transmission power for the localization and beacon messages. In this way, the localization connectivity requirement can be satisfied while the contention among data will not increase much. Besides the aforementioned results, we also study the impact of confidence threshold λ, the impact of the localization message threshold N , and the performance in mobile networks. In the following, we briefly summarize our findings for each aspect. Due to space limit, however, we do not include the detailed results in this paper. Interested readers can refer to our technical report [22].

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(b) Anchor percentage=10%

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(c) Anchor percentage=20%

Fig. 7. Average communication cost

Impact of Confidence Threshold: This study suggests us that by changing the confidence threshold, we can control the tradeoff between the localization error, the localization coverage and the average communication cost. For example, with the increase of the confidence threshold, the localization coverage and the localization error will decrease, while the average communication cost will increase. For UWSNs where location information is only used for geo-routing, high localization accuracy is not required [11], but a high localization coverage is desired. For this type of networks, the confidence threshold can be set to a relatively small value. While for UWSNs which require high precise location information, the confidence value should be set to a relatively large value. Some adaptive algorithms can be used to control this important parameter to provide performance guarantees. Impact of Localization Message Threshold: This study tells us that for a network setting, there is a critical value of N . When N is smaller than this value, the localization coverage, the localization error and the average communication cost will increase rapidly. When N is larger than this value, the localization coverage and the localization error will not change much and are relatively stable. But the communication cost will continue to increase. This indicates that beyond the critical value, increasing N will only increase the communication cost and will not bring any benefits. Thus, in practice we need to carefully choose N according to the network environments. In our previously presented simulations, we set N to 5, which is the critical value of N for the considered network setting. Performance in Mobile Networks: We also conduct simulations to evaluate the performance of our scheme in mobile networks, and the results show that the localization coverage and average communication cost are not affected much by the node mobility, while the localization error increases noticeably with the node moving speed. This is mainly due to that fact that the average distance measurement error increases with the average moving speed, as naturally causes the increase of the final localization error.

4 Conclusion In this paper, we presented a hierarchical localization approach for large-scale UWSNs. In this approach, the whole localization process consists of two sub-processes: anchor

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node localization and ordinary node localization. We focused on the ordinary node localization, for which we proposed a distributed scheme which novelly integrates a 3-dimensional Euclidean distance estimation method and a recursive localization method. Simulation results showed that our scheme can achieve high localization coverage with relatively small localization error and low communication cost. Besides, we also investigated the tradeoffs among the node density, the anchor percentage, the localization error, the localization coverage and the communication cost in our scheme. Different networks may have different requirements for these parameters. Via changing the confidence threshold parameter of our scheme, we can well control these tradeoffs.

References 1. I. F. Akyildiz, D. Pompili, and T. Melodia. Challenges for efficient communication in underwater acoustic sensor networks. ACM SIGBED Review, 1(1):3–8, Jul 2004. 2. J. Albowitz, A. Chen, and L. Zhang. Recursive position estimation in sensor networks. In Proceedings of IEEE ICNP, pages 35–41, Nov 2001. 3. T. C. Austin, R. P. Stokey, and K. M. Sharp. PARADIGM: a buoy-based system for auv navigation and tracking. In Proceedings of MTS/IEEE Oceans, 2000. 4. C. Bechaz and H. Thomas. GIB system: The underwater GPS solution. In Proceedings of 5th Europe Conference on Underwater Acoustics, May 2000. 5. P. Biswas and Y. Ye. Theory of semidefinite programming relaxation for sensor network localization. To appear in matehmatical programming. 6. P. Biswas and Y. Ye. Semidefinite programming for ad hoc wireless sensor network localization. In Proceedings of IPSN, pages 46–54, Apr 2004. 7. N. Bulusu, J. Heidemann, and D. Estrin. GPS-less low cost outdoor localization for very small devices. IEEE Personal Communications Magazine, pages 28–34, Oct 2000. 8. K. K. Chintalapudi, A. Dhariwal, R. Govindan, and G. Sukhatme. Ad-hoc localization using range and sectoring. In Proceedings of IEEE Infocom, pages 2662–2672, Mar 2004. 9. J.-H. Cui, J. Kong, M. Gerla, and S. Zhou. Challenges: building scalable mobile underwater wireless sensor networks for aquatic applications. IEEE Network, Special Issue on Wireless Sensor Networking, pages 12–18, May 2006. 10. J. E. Garcia. Ad hoc positioning for sensors in underwater acoustic networks. In Proceedings of MTS/IEEE Oceans, pages 2338–2340, 2004. 11. T. He, C. Huang, B. M. Blum, J. A. Stankovic, and T. Abdelzaher. Range-free localization schemes for large scale sensor networks. In Proceedings of 9th annual internatonal conference on mobile computing and networking, pages 81–95, Sep 2003. 12. Kenneth and D. Frampton. Acoustic self-localization in a distributed sensor network. IEEE Sensors Journals, 6:166–172, Feb 2006. 13. J. Kong, J.-H. Cui, D. Wu, and M. Gerla. Building underwater ad-hoc networks and sensor networks for large scale real-time aquatic application. In Proceedings of IEEE Military Communications Conference (MILCOM’05), Atlantic City, New Jersey, USA, pages 1535– 1541, Oct 2005. 14. A. Mahajian and M. Walworth. 3-D position sensing using the differences in the Timeof-Flights from a wave source to various receivers. IEEE Transactions on Robotics and Automation, 17:91–94, Feb 2001. 15. D. Moore, J. Leonard, D. Rus, and S. Teller. Robust distributed network localization with noisy range measurements. In Proceedings of Sensys, pages 50–61, Nov 2004. 16. R. Nagpal, H. Shrobe, and J. Bachrach. Organizing a global coordinate system from local inforamtion on an ad hoc sensor network. In Proceedings of IPSN, Apr 2003.

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17. D. Nichulescu and B. Nath. DV based positioning in ad hoc networks. Springer, Telecommunication Systems, pages 267–280, Oct 2003. 18. D. Niculescu and B. Nathi. Ad hoc positioning system (APS). In Proceedings of IEEE Globecom, pages 2926–2931, Nov 2001. 19. H. Wu, C. Wang, and N.-F. Tzeng. Novel self-configurable positioning technique for multihop wireless networks. IEEE/ACM Transaction on Networking, pages 609–621, Jun 2005. 20. P. Xie, L. Lao, and J.-H. Cui. VBF: vector-based forwarding protocol for underwater sensor networks. In Proceedings of IFIP Networking, May 2006. 21. Y. Zhang and L. Cheng. A distributed protocol for multi-hop underwater robot positioning. In Proceedings of IEEE International Conference on Robotics and Biomimetics, pages 480– 484, Aug 2004. 22. Z. Zhou, J.-H. Cui, and S. Zhou. Localization for large-scale underwater sensor networks. UCONN CSE Technical Report: UbiNet-TR06-04, http://www.cse.uconn.edu/˜jcui/ publications.html, Dec. 2006.

Location-Unaware Sensing Range Assignment in Sensor Networks Ossama Younis, Srinivasan Ramasubramanian, and Marwan Krunz Department of Electrical & Computer Engineering University of Arizona, Tucson, AZ 85721 {younis,srini,krunz}@ece.arizona.edu

Abstract. We study field-monitoring applications in which sensors are deployed in large numbers and the sensing process is expensive. In such applications, nodes should use the minimum possible sensing ranges to prolong the “coverage time” of the network. We investigate how to determine such minimum ranges in a distributed fashion when the nodes are location-unaware. We develop a distributed protocol (SRAP) that assigns shorter ranges to nodes with less remaining batteries. To handle location-unawareness, we develop a novel algorithm (VICON) for determining the virtual coordinates of the neighbors of each sensor. VICON relies on approximate neighbor distances and 2-hop neighborhood information. Our simulations indicate that SRAP results in significant coverage time improvement even under inaccurate distance estimation.

1 Introduction Sensor monitoring applications require node collaboration to maximize the network “coverage time,” defined as the time during which a specified fraction of the area is continuously monitored. In this work, we focus on applications in which the sensing process is the dominant source of energy consumption and sensing ranges are adjustable. Examples of such applications are those requiring sensors to send continuous longrange pulses for object detection (e.g., RADAR systems). In these applications, sensing is a continuous active process, while communication and processing are only invoked whenever an object of interest is detected. Other example applications are those requiring each sensor to analyze the collected data (e.g., environmental traces or images) before reporting it. Reducing the sensing range in such applications results in significant reduction in the data set to be analyzed, thus conserving energy. Currently, some commercially available sensors are capable of adjusting their sensing levels to control the cost associated with the sensing process (e.g., the Osiris photoelectric sensor [6]). We study how to assign the minimum possible sensing range to every sensor without degrading field coverage. Selecting the optimal sensing ranges for all the sensors is an NP-hard problem [10] (the simplified version of this problem in which each sensor is either ON or OFF is also NP-hard [2]). In previous research that considered nodes with adjustable ranges, greedy techniques were proposed for target monitoring [1] or 

This work was supported in part by the National Science Foundation under grants CNS0627118, CNS-0313234, 0325979, and 0435490.

I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 120–131, 2007. c IFIP International Federation for Information Processing 2007 

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constructing connected covers [10]. However, the problem is more challenging in location-unaware networks in which a sensor is not capable of determining its location or the directions of the incoming signals. This occurs when the sensors can not perform network-wide localization based on location-aware anchor nodes (e.g., in forests or outer space). 1.1 Contributions We develop a distributed sensing-range assignment protocol (SRAP) for locationunaware sensor networks, assuming that every node can tune its sensing range to one of an available set of ranges. In such networks, nodes are not aware of the field “boundary,” and therefore the objective of every sensor is to cover its own maximum sensing region. SRAP employs a novel localized algorithm (VICON) for determining the virtual coordinates of the neighbors of every node prior to range selection1 . At a node v, VICON exploits the 2-hop neighborhood information and the estimated distances between v and its neighbors. VICON employs conservative heuristics to place as many neighbors of v as possible when the estimated distances are inaccurate or the graph of v’s neighbors is disconnected. To prolong the lifetime of every sensor, SRAP assigns sensing ranges based on the remaining sensor batteries. SRAP is also superior to previous work in eliminating redundancy. 1.2 Related Work Under fixed sensing ranges, a node can be either ON or OFF. All previously proposed protocols for this model assumed that node locations or directions of neighbors can be estimated (refer to [8] for a list of these protocols). More recent proposals assumed variable sensing ranges. Cardei et al. [1] proposed centralized and distributed heuristics for maximizing the number of set covers (AR-SC) under this model. Their approach assumes synchronized nodes, base station intervention, and knowledge of node positions. We do not assume any of these capabilities and study a more general model. However, we use the greedy approach in [1] as a baseline for comparison. Zhou et al. [10] proposed another greedy algorithm for selecting a connected cover to optimize query execution under variable sensing and communication ranges. They focused on maintaining both network connectivity and field coverage. Our approach can be integrated with the one in [10] to maintain connected covers in location-unaware networks. The rest of the paper is organized as follows. Section 2 provides the problem formulation. Section 3 introduces the VICON (VIrtual COordinates of Neighbors) algorithm. Section 4 provides details of the SRAP protocol and its properties. Section 5 evaluates the performance of SRAP. Finally, Section 6 gives concluding remarks.

2 Problem Statement Assumptions: Let the maximum transmission range of each node be Rt . We refer to a node within distance ≤ Rt as a “neighbor.” We assume the following: (1) nodes 1

Note that SRAP is independent of VICON.

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are stationary; (2) each node has a set of k usable sensing levels, which correspond to sensing ranges R1 , . . . , Rk , where Rk is the maximum sensing range. Turning off the sensing component corresponds to R0 = 0; (3) energy depletion is proportional to Rim , where 1 ≤ i ≤ k and m is a constant ≥ 1; (4) a node can sense an event within a circular “sensing region” around it; (5) the sensing component in each node is continuously active and the sensing process is energy-intensive. The radio component, however, employs a low duty cycle; (6) neighbor locations and directions of received signals cannot be estimated; and (7) a node can estimate the distance between itself and a neighbor based on well-known techniques such as the time of arrival, received signal strength, etc [9]. For simplicity, we assume that Rt ≥ Rk . We use a conservative approach to estimate neighbor distances in which Rt is divided into a discrete set of nd distances and every range of signal strengths maps to one of these distances. Every node broadcasts the estimated distances to its neighbors so that every node is aware of its 2-hop neighborhood. We account for the inaccuracy in distance estimation in our algorithm presented in Section 3 and evaluate its effect in Section 5. Objectives: Given a set of N deployed sensors, it is required to assign every sensor i, 1 ≤ i ≤ N , the minimum sensing range Rj , where 0 ≤ j ≤ k, such that i’s sensing region is covered. Because the field boundary is unknown to individual sensors, the objective of every sensor is to ensure that its maximum sensing region is covered.

3 The VICON Algorithm In VICON, a node computes “virtual” coordinates of its neighbors. A virtual coordinate space (VCS) of node v’s neighbors is one that keeps the connectivity profile of the real coordinate space (RCS). That is, the distances and angles between the neighbors of v are preserved. However, the VCS can have the neighbors rotated, which does not affect the coverage properties. The problem of assigning neighbor coordinates is a special instance of the “graph embedding” problem, which was studied extensively in the literatures of graph theory and computational geometry [3]. Computing virtual coordinates was also studied in the networking literature, e.g., [5, 7]. In these studies, the objective was to assign coordinates to all the nodes in the network. Such approaches are not suitable for our work for three reasons. First, we do not have anchor nodes in the network since the entire network is location-unaware. Second, basic triangulation techniques do not handle disconnected graphs and fail when distances are inaccurate. Finally, we only require each node to compute the virtual coordinates of its neighbors, and do not need to compute network-wide coordinates. Our approach is a lightweight algorithm that can be easily employed in dynamic networks where new nodes are deployed at any time. We first describe VICON assuming accurate estimates of distances. Then, we extend it to mitigate the negative effects of inaccurate distance estimation. 3.1 Details of VICON Prior to executing VICON, each node is aware of its 2-hop connectivity information (reachability and distances) through neighbor broadcasts. A node v executing VICON

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proceeds as follows. Assume that v has three neighbors v1 , v2 , and v3 , as depicted in Fig. 1(a). Node v assumes that it is positioned at the origin and places its first neighbor (v1 ) at (d1 ,0), where d1 is the distance between v and v1 (see Fig. 1(b)). Using v1 , v2 , v, v1 , and v, v2 , v can compute the angle g1 shown in Fig. 1(a). To determine the virtual coordinates of v2 , v2 is rotated by an angle g1 from the origin in the counter-clockwise direction. Similarly, v3 is rotated in the counter-clockwise direction with an angle g2 and assigned a tentative coordinate. The validity of this coordinate is then tested against all the already-placed sensors to determine whether the original connectivity is preserved. In this example, rotating v3 in the counter-clockwise direction causes it to be a neighbor of v2 , which contradicts with the RCS. Therefore, v3 is rotated by an angle g2 in the clockwise direction. Figure 1(b) illustrates that v is still covered by three nodes that are within g1 + g2 total angle, and are all on one side of v.

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Two problems have to be considered. The first problem is depicted in Figure 2(a), where v’s neighbors form more than one connected component. This results in having a subset of the neighbors unable to find reference nodes that are already placed in the VCS. VICON handles this problem as follows. First, v’s neighbors are divided into groups, where each group represents a connected component (e.g., Fig. 2(a) shows two groups: {v1 , v2 } and {v3 , v4 }). Second, the coordinates of the neighbors in each group are computed independently from the other groups. Finally, each group, other than the first one, is rotated to preserve the RCS connectivity. This is depicted in Fig. 2(b), where the two groups are placed closest to each other while preserving their disjointedness.

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The second problem is that a node may satisfy the connectivity requirements with the already-placed neighbors in both the clockwise or counter-clockwise direction. The

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problem is demonstrated in Fig. 3(a), where node v3 is a neighbor of node v1 but not of v2 or v4 . In the VCS, v1 and v2 are placed first. Node v3 is placed in the counterclockwise direction from v1 (as shown in Fig. 3(b)) and it also satisfies the connectivity of the RCS when placed in the clockwise direction. As a result, v fails to determine a virtual coordinate for v4 . v4

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The above problem can be addressed using the following recursive approach. Assume that node v has a list of Nnbr neighbors. Node v processes these neighbors in sequence and pushes the IDs of the successfully placed neighbors in a stack named FinishedNbr. A neighbor that can be successfully placed in two positions is marked “UNSURE” in FinishedNbr, while a neighbor that can only be placed in one position is marked “SURE.” If v fails to compute coordinates for a neighbor i (2 < i ≤ Nnbr ), then it pops neighbor IDs from FinishedNbr until it finds one referring to an UNSURE neighbor. This neighbor is then placed in the alternative direction, marked SURE, and pushed back in FinishedNbr. VICON then attempts to re-process the pushed-out neighbors. This approach ensures that incorrectly selected coordinates are corrected as more neighbors are placed. In our example depicted in Fig. 3(b), node v3 is marked UNSURE when placed. When v fails to place v4 , it pops v3 from FinishedNbr, places it in clockwise direction relative to v1 , then successfully places v4 . VICON does not preserve the directions of neighbors, which is not a problem since the objective of every node is to determine “how much” area is uncovered, and not “which” area. Pseudo-code and proof of correctness of VICON can be found in [8]. 3.2 VICON Under Inaccurate Distance Estimation Inaccurate distance estimation may cause failures in node placement due to either magnifying or shrinking the angles between a node and its neighbors. We conducted numerical experiments under different settings to study the reasons behind this failure. These experiments revealed two important observations: (1) placement inaccuracy within a maximum inaccuracy I = Rt /nd can be tolerated without sacrificing coverage, and (2) our distance estimation is overconservative for some distances, and less conservative for others. Based on these observations, we extend the basic VICON algorithm as follows. – Assume that the distance d between node v and one of its neighbors u corresponds ˆ to the discrete distance dˆ (dˆ ≥ d). We set u’s distance from v to be d−I/2 to achieve average uncertainty in distance estimation instead of maximum uncertainty.

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– The computed virtual coordinate of a neighbor u is acceptable if it preserves neighborhood within a distance ≤ I of all u’s neighbors. Note that under high densities, the shift in the angles can add up and result in failure to place some neighbors. Thus, the above measures do not ensure that all the neighbors will be eventually placed. In [8], we show the effect of node density on successful neighbor placement.

4 SRAP Protocol Protocol Design: SRAP assigns longer ranges to nodes with higher “weights,” where a dynamic parameter is used to represent the weight of a node (e.g., remaining energy). In addition, SRAP is re-triggered at fixed intervals of time, referred to as the cover update interval tcu , to efficiently balance the load among sensors. The SRAP protocol is executed at every node in the network, typically via timer expiration2. Since sensor clocks are typically unsynchronized, the node with the fastest clock in its 1-hop neighborhood sends a message to its neighbors to trigger the execution of SRAP. Consequently, every node that receives this message sends a similar triggering message prior to executing SRAP. We assume that a node can be in one of two states: DECIDED or UNDECIDED and all the nodes start in the UNDECIDED state. SRAP has three phases: Phase I is for initialization, Phase II is the core operation of SRAP in which a node v decides on a sensing range R, and Phase III is for the optimization of R. A summary of the three phases is shown in Fig. 4. Phase I. In the first phase of SRAP, v computes a real-valued weight wgt(v) as: wgt(v) = E(v)/Emax , where E(v) is the remaining energy in v’s battery and Emax is the maximum battery capacity. A neighbor discovery process is then initiated in which v broadcasts wgt(v). Based on the replies that v receives, it broadcasts its neighborhood table (which includes the estimated neighbor distances). In the second step of this phase, v executes VICON to compute the virtual coordinates of its neighbors (this step is independent of SRAP). The final step is to check whether v has to use its maximum sensing range Rk or not. This is done by having v assume that all its neighbors are using Rk , and check if any part of its sensing region is not covered. If v passes this test, it quits SRAP and uses Rk . Otherwise, v executes Phase II. Phase II. Node v computes its sensing range R based on its weight and the weights of its neighbors. Node v does not make a decision on R unless it has the highest weight among all of its undecided neighbors. This gives a chance for nodes with higher weights to decide first and choose longer ranges. At the same time, v sets a timer T1 (similar for all nodes) for this phase. If T1 expires before a decision is made, v computes its range assuming that all undecided neighbors use R0 . The function Compute R(v) proceeds as follows. Node v first sets its range R to Rk−1 and sets the range of every undecided neighbor u to the largest Rj smaller than [(wgt(u)/wgt(v))1/m × R], where j ≤ k − 1 and m is a constant. Note that 2

SRAP can be triggered asynchronously when detecting events such as node failures or when new nodes are deployed.

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wgt(u)/wgt(v) < 1, which means that v’s undecided neighbors are assumed to use sensing ranges < Rk−1 . Decided neighbors are set to the ranges that they have decided on. If this assignment results in covering the sensing region of v, v sets its range R to Rk−2 and the same process is repeated. If range Ri , 0 ≤ i < k, fails to ensure complete coverage of v’s region, then v uses R = Ri+1 , changes its state to DECIDED, and advertises R to its neighbors3. Phase III. After Phase II, v can terminate SRAP and use its selected R. However, redundancies may have been introduced due to the order of the decision-making process in Phase II. Therefore, we propose an iterative approach for removing redundancies. When the node with the least weight in its neighborhood selects its sensing range, it sends a token to its neighbors, allowing them to proceed with Phase III. A node v starts a timer T2 (of a few seconds granularity) when it receives the first token from one of its neighbors. It waits to receive tokens from all the neighbors with less weights than its own. Once these tokens are available, v computes its final sensing range based on the advertised ranges of its neighbors, and releases a token that advertises the new range of v. If T2 expires before v has received enough tokens, it keeps its range as computed in Phase II and releases its token. Analysis of SRAP: We analyze the SRAP protocol in terms of its correctness, computational complexity, and message overhead. 3

Note that loss of messages in Phase II may only result in more conservative estimation of R. However, termination is not affected.

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Lemma 1. When SRAP terminates, the sensing region of every node with non-depleted battery is completely covered (Coverage property). Proof. When SRAP is executed at node v, two operations affect the final coverage of v’s sensing region: 1. Selection of v’s sensing range in Phase I and II. In Phase I, if v determines that its sensing region can not be completely covered by its neighbors, it sets its sensing range to Rk and terminates SRAP. If v goes through Phase II, it selects its sensing range based on both advertised ranges of its decided neighbors and hypothetical ranges of its undecided neighbors. An undecided neighbor will not be able to select a sensing range less than the largest hypothetical range made by any of its neighbors, unless its region is covered. This ensures that v’s sensing region is completely covered. 2. Reduction of sensing ranges in Phase III. A “hole” in field coverage may occur when two neighboring nodes (e.g., v1 and v2 ) are allowed to reduce their sensing ranges simultaneously. Such scenario implies that both v1 and v2 had all the tokens they need from their neighbors with less weights to start Phase III simultaneously. This is not possible since we assume that the weight is a real number and either v1 or v2 will have less weight than the other. 2 Lemma 2. Every node v selects the minimum sensing range that satisfies coverage of its sensing region if accurate distances are used and the neighbors of v do not form multiple disjoint components (Minimality property). Proof. Let us first assume that the estimated neighbor distances are accurate; i.e., VICON computes virtual coordinates for all the neighbors of v. Also assume that v has selected R = Ri although R = Rj (j < i) was sufficient to have v’s region covered. This may occur in Phase II depending on the order of SRAP execution among neighboring nodes of v. However, when Phase III is executed, v will be able to compute the minimum range R based on its neighbors final decisions. Since nodes getting tokens after v are only allowed to reduce their sensing ranges, the selected R is minimal (this applies to all nodes). Along with selecting covers from higher-weight nodes and refreshing covers, this result has a significant impact on the perceived coverage time. If accurate distances are used for computing virtual coordinates, minimality can only be violated if the neighbors of v form multiple disjoint components. This is unlikely to occur, however, in dense networks. On the other hand, if inaccurate distances are used for obtaining virtual coordinates, minimality can be violated. The redundancy introduced in this case depends on node density and distribution in the field. Message overhead. Four types of message exchange are required: (1) neighbor discovery, which requires O(1) messages, (2) advertisement of node’s weight, which requires only one message whenever SRAP is re-triggered, (3) advertisement of the selected range, which requires O(1) messages, and (4) token exchange, which requires one message. Therefore, the total message overhead of SRAP is O(1) per node. Note that if in future applications more parameters are added to the node weight computation (e.g., mobility, remaining uncovered area, etc.), then a node v’s weight has to be advertised whenever one of v’s neighbors decides its range. This raises the message overhead to O(Nnbr ), where Nnbr is the average number of neighbors per node

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(to ensure connectivity, Nnbr must be = O(log N ) in randomly deployed networks [4]). Note that Phase III may have to be modified in this case since it relies on a parameter that is assumed to be fixed during the range assignment process. Time complexity. The time complexity of SRAP has two components: (1) convergence speed of any node in the network (ignoring the timers in the protocol), and (2) processing complexity. Phase I has O(1) convergence speed. The average-case convergence speed is proportional to the average number of neighbors of any node. The worst-case convergence speed for phases II and III can be proportional to the number of nodes (under very pessimistic distribution of nodes’ remaining battery levels). (In our experiments, we found that the convergence speed of SRAP is significantly less than the worst case.) This justifies the use of timers T1 and T2 to limit the convergence speed and avoid indefinite waits in case of failures. The main processing complexity in SRAP is in testing whether the node’s sensing region is covered. This test is performed once in phases I and III, and every time a neighbor selects its range in Phase II. If we discretize the sensing region into a number of P points, then the complexity of the test is O(P Nnbr ), where Nnbr is the average number of neighbors. The other source of complexity is the VICON algorithm, which 2 is executed only once in static networks. VICON has a complexity of O(αNnbr ) where 5 α = 2 in the worst case since there can exist at most five neighbors of a node that are pairwise non-neighbors. Each of these neighbors can be assigned to at most two positions. Therefore, VICON does not introduce significant computational complexity.

5 Performance Evaluation We study an operational scenario in which a number of sensors send their reports to a base station via multi-hop communication. We assume that nodes that are randomly distributed in a field from (0,0) to (50,50). A base station is placed at (25,25). All the nodes start with full batteries and the network is considered dead when the base station is disconnected. The simulation parameters used in our experiments are as follows: N = 900 nodes, Rt = 5 meters, number of discretized distances nd = 5, k = 4, Rk = 5 meters, battery capacity = 1.0 Joule, communication energy Ecomm = 10−6 Watt, energy consumption parameter m = 2, and cover update interval tcu = 2000 seconds. For radio communications, we assume that a fixed amount of power is consumed from every active node during its operation. We set the energy consumed in communication to correspond to the energy consumed at R1 . We developed a discrete event-driven simulator that is scalable and efficient for largescale networks. We compare SRAP to AR-SC [1]. AR-SC is a distributed protocol proposed for target coverage. However, we extend it to area coverage by discretizing the field into a large number of points. AR-SC gives priority in decision-making (range assignment) to nodes seeing more uncovered targets. This is similar to typical set cover algorithms that aim at reducing the size of the selected set (e.g., [2]). We assume ideal conditions for the operation of AR-SC, which include full node synchronization, optimal sequence of decision-making according to node priorities, and knowledge of the exact node coordinates.

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We also compare SRAP to a generic centralized greedy algorithm (which we refer to as “CentralizedApp”). In CentralizedApp, a centralized entity that is aware of the locations of all the nodes in the network is responsible for range assignment. The network operation is divided into phases of equal duration. Given the energy spent by each sensor at the end of phase i, the minimal cover for phase i + 1 is chosen such that the maximum energy spent by a sensor at the end of phase i + 1 is minimized. The algorithm selects a minimal cover as follows. All the sensors are assumed to employ the maximum sensing range for phase i + 1. The sensors are arranged in the descending order of the expected energy spent at the end of phase i + 1. The algorithm selects the sensor with the highest value (say v). If reducing v’s range by one step (i.e., from Rj to Rj−1 , 0 < j ≤ k) violates coverage, then v’s sensing range is kept at Rj . Otherwise, v’s sensing range is reduced to Rj−1 . The expected energy spent at the end of phase i + 1 is updated, as well as the ordered set of sensors. The procedure is repeated until a minimal cover is obtained. Although, the algorithm is described here as a centralized manner, it may be distributed in a distributed manner using only one-hop neighborhood information. As the sensors reduce their range one step at a time, the worst-case running time of the algorithm is O(N k). We study the operation of SRAP under accurate distance measurements (SRAP-A) and under discretized (inaccurate) distances (SRAP-D). For a fair comparison, we assume that the network boundary is not known by the application employing any of the compared techniques. We assume no packets are lost at the MAC layer. Packet losses may only add some redundancies to field coverage but have no impact on the operation of SRAP. The results provided below are the average of 10 experiments.

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Properties of SRAP and VICON. We first focus on the selection of one cover by any of the compared algorithms. All the nodes are assumed to be alive. We compute the number of nodes selected at the k sensing levels (in addition to R0 = 0), the cost of the selected cover (energy consumed in the network during its operation), and the ratio of successfully placed neighbors per node for SRAP-D. Figure 5(a) demonstrates the number of nodes at each sensing level for different node densities. SRAP shows more collaborative behavior under both accurate and discretized

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distances than AR-SC. CentralizedApp shows the best collaborative behavior because it can reduce the ranges iteratively and not at one step per node as in SRAP and AR-SC. Figure 5(b) shows the cover cost for all algorithms. With maximum sensing ranges, the energy consumed in the network can be computed as (R4 × R4 + 1) × Ecomm (which is 0.0234 Joule for N = 900). As expected, CentralizedApp gives the smallest cover cost. SRAP significantly reduces the cover cost over AR-SC, especially when distances are accurately estimated. SRAP-D and AR-SC show, respectively, about 10-20% and 30-70% increase in cover cost over SRAP-A.

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Network Operation. We now evaluate the network operation when sensing range assignment is employed. We focus on three metrics. The first metric is the duration while the coverage quality of the field is within a specified range. The second metric is the coverage quality over time as the network operates. Coverage quality is the fraction of field coverage at specific instances of time. The third metric is coverage redundancy, which is the number of sensors covering the least covered point within a sensor’s region. A coverage redundancy of 1 means that there is at least one point within any sensor’s region that is covered by only one sensor. This metric indicates how minimal the selected cover and ranges are. Figure 6(a) shows the coverage time during which the percentage of field coverage is within a specific range of coverage quality. CentralizedApp shows about 50% coverage time improvement over SRAP. SRAP-A and SRAP-D significantly improve coverage time over AR-SC, especially at the higher coverage quality ranges (60-80% and 80100%). This is a desirable effect for applications that try to maximize field coverage for the longest possible time. Figure 6(b) demonstrates the coverage quality of the field over time as the network is operating. We include results of the application when operated without sensing range adjustment (referred to as “No-Adjust”), i.e., all the sensors use their maximum sensing ranges (Rk ). The figure shows that under CentralizedApp and SRAP nodes die smoothly over time because of periodically refreshing the selected sensing ranges based on a dynamic parameter (battery level). We also study the redundancy in the selected covers under SRAP and AR-SC. CentralizedApp guarantees no

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redundancy in the selected cover and thus is not included in this experiment. Results (reported in [8]) indicate that for SRAP-A, the redundancy does not exceed 1 by more than 2-3%. We closely examined these redundancies and found that they occur at sensors which are assigned range R0 . For SRAP-D, redundancy may reach 9-10% due to the failure of VICON to place some neighbors for each node.

6 Conclusion We studied the problem of sensing range assignment in location-unaware networks. To handle location-unawareness, we proposed a novel localized algorithm (VICON) that each node uses to compute virtual coordinates of its neighbors. We then proposed a distributed protocol (SRAP) which periodically assigns sensing ranges to nodes based on their remaining battery powers. SRAP has negligible message overhead and computational complexity. Our simulation results indicate that SRAP significantly improves coverage time, even under inaccurate distance estimation. To extend the functionality of SRAP for different applications, we plan to study how to incorporate other parameters in the node weights, such as mobility, node degree, or potential coverage.

References [1] M. Cardei, J. Wu, M. Lu, and M. Pervaiz. Maximum network lifetime in wireless sensor networks with adjustable sensing ranges. In Proc. of the IEEE Intl. Conference on Wireless and Mobile Computing, Networking and Communications (WiMob), August 2005. [2] U. Feige. A threshold of ln n for approximating set cover. Journal of the ACM, 45(4): 634–652, July 1998. [3] J. L. Gross and T. Tucker. Topological Graph Theory. John Wiley and Sons, 2001. [4] P. Gupta and P. R. Kumar. Critical power for asymptotic connectivity in wireless networks. Stochastic Analysis, Control, Optimizations, and Applications: A Volume in Honor of W.H. Fleming, W.M. McEneaney, G. Yin, and Q. Zhang (Eds.), Birkhauser, 1998. [5] T. Moscibroda, R. O’Dell, M. Wattenhofer, and R. Wattenhofer. Virtual coordinates for ad hoc and sensor networks. In Proc. of DIALM-POMC, October 2004. [6] Osiris Photoelectric Sensors, http://schneider-electric.ca/www/en/products/sensors2000/ html/osiris.htm, 2007. [7] A. Rao, C. Papadimitriou, S. Ratnasamy, S. Shenker, and I. Stoica. Geographic routing without location information. In Proc. of the ACM MobiCom Conference, September 2003. [8] O. Younis, M. Krunz, and S. Ramasubramanian. Sensing range assignment in locationunaware networks. Technical report, University of Arizona, November 2006. [9] M. Youssef and A. Agrawala. The Horus WLAN location determination system. In Proc. of the ACM International Conference on Mobile Systems, Applications, and Services (ACM MobiSys), June 2005. [10] Z. Zhou, S. Das, and H. Gupta. Variable radii connected sensor cover in sensor networks. In Proc. of the IEEE Communications Society Conference on Sensors and Ad Hoc Comm. and Networks (SECON), September 2004.

A Distributed Energy-Efficient Topology Control Routing for Mobile Wireless Sensor Networks Yan Ren, Bo Wang, Sidong Zhang, and Hongke Zhang School of Electronics and Information Engineering, Beijing Jiaotong University, 100044 Beijing, China {yren,bwang,sdzhang,hkzhang}@center.njtu.edu.cn

Abstract. One of the fundamental issues in wireless sensor networks (WSNs) is the topology control (TC) problem, which reflects how well the energy consumption is reduced and the network capacity is enhanced. In this paper, by using computational geometry theoretic, we present a fully distributed routing protocol, Cooperative Energy-efficient Topology Control (Co-ETC), whose goal is to achieve energy efficiency in mobile wireless sensor networks. Based on underlying routing graph, the proposed scheme allows each node (with or without mobility) to locally select communication neighbors and dynamically adjust its transmission radius accordingly, such that all nodes together self-form a energy-efficient topology. The simulation results indicated that the proposed scheme was feasible. Compared with existing state-of-the-art algorithms and protocols, Co-ETC has better energy-efficiency. Moreover, it can adapt to mobile environment well. Keywords: topology control, energy efficiency, routing protocol, wireless sensor networks.

1 Introduction In recent years, extensive research has been conducted on wireless sensor networks (WSNs), considered one of the top research topics [1]. Such environments may have a large number of small sensor nodes, each capable of collecting, storing, processing observations and communicating over short-range wireless interfaces and multiple hops to central locations called sinks. Since sensors may be spread in an arbitrary manner, one of the fundamental issues that arise naturally in WSNs is topology control (TC) problem. Topology control technique is to let each wireless node locally adjust its transmission range and select certain neighbors for communication, while maintaining a structure that can support energy efficient routing and improve the overall network performance [2]. In general, it can be considered as a measure of the quality of service of a WSN. For instance, one may ask how well the network can maintain some global graph property (e.g., connectivity). Furthermore, TC formulations can reduce energy consumption and enhance network capacity. Due to mobility, sensor nodes (even sink) may change their locations after initial deployment in many scenarios. Mobility can result from environmental influences I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 132–142, 2007. © IFIP International Federation for Information Processing 2007

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(e.g., wind or water), available mobile platforms in the deployment area (e.g., robots in object tracking, soldiers in battlefield surveillance) or mobile devices can be incorporated into the design of the WSN architecture (e.g., airborne and vehicles) [3]. The impact of mobility on the effectiveness of TC is twofold: Increased message overhead (especially in the case of high mobility scenarios) and nonuniform node spatial distribution. Considering the impact above, deriving results regarding mobile WSNs is even more challenging. Several TC algorithms or routing protocols [3], [4] which use different underlying routing graphs with several good properties have been proposed in last few years. However, to our knowledge none of them has been defined to explicitly deal with all four key properties for unicast routing graph on WSNs simultaneously: power spanner, sparse, localized and degree-bounded. By using computational geometry theoretic techniques, we present a cooperative topology control routing protocol with following properties: 1.

2.

3. 4. 5.

Energy-efficient. It ensures that the routes calculated on given routing graph are at most a constant factor (defined as power stretch factor that will be specified later in this paper) away from the power-optimal routes. Sparse. There is linear number of edges in given network. It eases the task of finding path and maintaining the route path in the presence of node mobility, and it can reduce the communication overhead. Bounded node degree. Bounded node degree can reduce bottleneck and neighbor signal interference in network. Running in distributed fashion. Every node compute the scalable routing graph cooperatively using the information only provided by its neighbor. Adaptive to mobile environment. This ensures that topology requires little maintenance in the presence of mobility that could change routing graph to some extent.

The remainder of this article is organized as follows: In the next section, we first give some preliminaries and define the network model. The basic design of Co-ETC protocol is presented in Section 3. We then discuss several extensions in Section 4. Specifically, we consider how to find an energy-efficient-path and how to avoid “bottleneck” node in communication graph. Finally, we evaluate the performance of Co-ETC in Section 5, conclude the paper and discuss possible future research directions in Section 6.

2 Preliminaries and Network Model In our subsequent discussions, network topology is represented by an undirected simple graph G = (V, E) when all the nodes transmit at maximum power, where V = {v1, v2, …, vn} is the set of n wireless sensor nodes and E is the set of links in the WSN. For sake of simplicity, we will assume that every node has the same maximum transmission range Rmax. A node can reach all nodes (called neighbors) inside its transmission region. We also assume that each node is assigned a unique identifier, ID and knows its location.

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Before we design the Co-ETC protocol, we first give some computational geometry concepts, which will be used as the foundations of geometry for Co-ETC: Definition 1 (Voronoi Diagram and Delaunay Triangulation). The Voronoi diagram, denoted by VD(V) (real lines in Fig. 1), of a set of discrete nodes partitions the plane into a set of convex polygons (called voronoi regions) such that all sites inside a voronoi region are closest to only one node. This construction effectively produces polygons with edges that are equidistant from neighboring nodes. The Delaunay triangulation, denoted by DT(V) (dotted lines in Fig. 1), is the dual graph of the Voronoi Diagram. It is the unique triangulation such that the circumcircle of every triangle contains no nodes of V in its interior.

Fig. 1. Voronoi Diagram and Delaunary Triangulation

Definition 2 (Gabriel Graph). The Gabriel Graph, denoted by GG(V), consists of all edges uv such that the disk(a, b) does not contain any node from V, where disk(a, b) is the closed disk with diameter ab (see Fig. 2).

Fig. 2. Gabriel Graph

Definition 3 (Power Stretch Factor). The power stretch factor, denoted by ρp, respect to G is the maximum over all possible node pairs of the ratio between the cost of the minimum-power path in G’ (Any arbitrary subgraph of G, e.g., DT(V) and GG(V)) and in G, where is represented by pG’(u, v) and pG(u, v) respectively. In other words,

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ρ p = max u ,v∈V

p G ′ (u ,v ) pG (u ,v )

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(1)

Notice that, generally, we would like to use a subgraph G’ (also called a routing graph) which has a low-power stretch factor and which is sparser than the original graph G. Such a routing graph can be used to compute routes with guarantee that the energy needed to communicate along is almost minimal. In addition, computing optimal routes in G’ is easier and has less communication overhead than in G. Moreover, such a sparse routing graph requires little maintenance in the presence of node mobility. The power stretch factor and maximum node degree of the graphs defined previously have been analyzed in [5], and are reported in Table I. Table 1. Power Stretch Factor and Maximum Node Degree of DT and GG

Power Stretch Factor DT GG

⎛1 + 5 ⎞ ⎜ ⎟ ⎜ 2 π⎟ ⎝ ⎠ 1

Maximum Node Degree

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Θ(n) n-1

As shown, the Gabriel Graph is energy-optimal since it has a power stretch factor of 1. And neither DT(V) nor GG(V) has constant maximum node degree. We will utilize these attractive routing graphs for extensions of our Co-ETC protocol in Section 4.

3 Design of Co-ETC Protocol In this section, we consider base design of the Co-ETC protocol, which enables each node to maintain the relevant part of the Voronoi routing graph efficiently and consistently, with the knowledge only provided by its neighbors, and manage topology changes due to mobility, node joining/leaving. The motivation of the proposed protocol stems from the commonality encountered in the mobile WSNs. CoETC is composed of three main procedures: route graph setup, node joining and leaving, and node movement. 3.1 Routing Graph Setup Initially, when a node wants to communicate with another one, no prior knowledge of the routing graph is available. For sake of simplicity, we will assume that every node has the same initial transmission range R. This ensures routing graph is consistently for adjacency neighbors. To avoid message collision, every node waits for a random back-off time period Ti, then simply flood a query with its own ID and coordinates to neighbors. After every node has all its neighbors’ coordinates according to the definition of VD in Section 2, each node generate the local VD itself, and the union of local graphs corresponds to all the sensors in V (see Fig. 3). Notice that, each node has to have enough R to reach its neighbors at the beginning. Generally, we assign it equal to the maximum transmission range Rmax.

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Fig. 3. Voronoi Diagram in WSN

In above routing graph, each node maintains a Voronoi diagram of all neighbors and directly connects to them with minimal latency. As only a few neighbors are kept, the cost to maintain such a routing graph at each node is low. 3.2 Node Joining and Leaving A joining node (mark as ▲) first sends a Query message with its joining coordinates and ID to neighbors. Any acceptors (the node whose region contains the joining node’s coordinates) will respond by sending a list of joining node’s adjacency neighbors (the node whose Voronoi regions border the given node’s, e.g., we mark such nodes as ● in Fig. 4). Notice that, there must be only one acceptor except it on the Voronoi lines. The joining node first computes and organizes its local Voronoi diagram, and then connects to each adjacency neighbor of itself (affected by joining). Related neighbors also update their Voronoi diagram to account for the joining node. When a node will leave from WSN due to node failures or power duty cycling reasons etc., the leaving node simply disconnects. Its adjacency neighbors will update their Voronoi diagrams, replacements are learned via other still-connected adjacency neighbors. The procedure can be seen as the converse procedure of Fig. 4 (node ▲ leave the network).

Fig. 4. Node Joining Procedure. (Left) Before node joining. (Right) After node joining.

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3.3 Node Movement When a node moves, its position updates and transmission radius are sent to all connected neighbors. If the recipient is a periphery neighbors (the node whose adjacency neighbors may partially lie outside transmission range, we mark such nodes as ■. Notice that, some adjacency neighbors may be periphery neighbors at the same time.). it will check whether any of its adjacency neighbors tend to be visible to this moving node and send a Pre-register message with position update. In this way, new neighbors can estimate the connecting time and enhance the resilience of routing graph. When a new neighbor is detected, notifications are sent to the moving node for initiating communications. The moving node also disconnects any periphery neighbors that have left its transmission range. This procedure can be explained in Fig. 5.

Fig. 5. Node Movement. (Left) Before node movement. (Right) After node movement.

The three main procedures of Co-ETC protocol above illustrate that nodes communicate with each other efficiently and the changes to routing graph are localized. Besides, protocol is scalable and adaptive to mobile environment.

4 Extensions In this section, we consider two extensions of the Co-ETC protocol and present efficient distributed algorithms: 1) find an energy-efficient-path between nodes u and v in V; 2) adjust node degree of existing routing graph dynamically to avoid “bottleneck”. From section 2, we have known that the Gabriel Graph is energy-optimal since ρp(GG) = 1. However, we cannot use this graph directly in our extension because: 1) the Gabriel Graph may have long edges, while we are only allowed to connect points within limited transmission range and 2) the empty-disk rule is a global rule and is not suitable for local computation. To deal with those two problems, we consider the following algorithm to find an energy-efficient-path constructed by edges of Gabriel Graph according to existing Voronoi routing graph:

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Algorithm 1: Energy-Efficient-Path (V, u, v) 1. From the source point u, node u adds an edge uv1 if and only if the disk(u, v1) does not contain any node from V. 2. Continually add all such edges into new routing graph until there is no edge which is belonged to the Gabriel Graph GG(V). Notice that, because the original graph is a subgraph of G, so not every edge of GG(V) can be added into new routing graph. 3. Assign each constructed edge vivj the weight equal to ||dij||α. 4. Run the Bellman-Ford distributed shortest path algorithm [6] to compute the shortest path connecting u and v, which has the minimum weight among all paths between u and v. The correctness of the algorithm is based on the following observation: If there is a sensor node vk inside disk(vi, vj), then ||dik||α ≤ ||dij||α and ||djk||α ≤ ||dij||α. It is obvious that the path vivkvj is in the GG(V). Thus, the path by substituting edge vivj with edges vivk and vkvj consumes less energy, which is a contradiction. Consequently, edge vivj must be a Gabriel edge. For this reason, those extra long edges that are not belong to old Delaunay Triangulation also will not be added into our new routing graph. According to the analyses in Section 2, neither DT(V) nor GG(V) has constant maximum node degree. It means that there will be bottleneck nodes in our routing graph, and these nodes are forced to connect beyond their capacities. So we adjust node degree of existing routing graph dynamically as following: Algorithm 2: Dynamic-Node-Degree-Adjustments (V) 1. For all nodes whose neighbors exceed the upper bound value Nmax, decreases its transmission power by ∆P once a step, until it connects Nmax neighbors. At the same time, original node sends Hello message and attaches to it with current link neighborhood list and current transmission power, denoted by Poriginal-node. 2. Whenever another node, which so far does belong to the neighborhood list, hears the Hello message of the original node for the first time. For avoiding onedirected link, it first compares Poriginal-node and Pitself. z If Poriginal-node > Pitself, it leaves its transmission power as before, whichever is smaller. z Or else it set its transmission power to the original node equal to Poriginal-node (adopts directional antennas for transmission) and then begins the same procedure like original node. 3. Node answers Hello message with Reply message and attaches to it only with current transmission power. 4. Node will restores to the preferred transmission power if the number of neighbors falls below the lower bound Nmin.

5 Evaluation and Simulation Results To demonstrate the feasibility and effectiveness of our Co-ETC protocol, we have done an across-the-board performance evaluation of this protocol according to several

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vital criteria including network connectivity, network-lifetime, and robustness to mobility. We implement our Co-ETC protocol on the NS-2 simulator using an idealized MAC layer with fixed link error probability. The simulation environment is generated by using MATLAB. In simulation, the network nodes are uniformly distributed in a square area A of size 1000*1000. 5.1 Network Connectivity Perhaps, the most basic requirement of a topology is that it be connected. More precisely, to ensuring routing graph efficiently constructed, nodes in network must have enough initial transmission range R to reach its neighbors at the Route-GraphSetup stage (Section 3.1). In simulation, we assign it equal to the maximum transmission range Rmax. For every value of R considered in the simulations, we generated 100 random placements and, for every placement, we evaluated the percentage of nodes belong to the largest connected component. With different R, the average percentage of nodes which are in the largest strongly connected component related to the number of nodes is shown in Fig. 6.

Fig. 6. Percentage of nodes that belong to the largest connected component

As shown in Fig. 6, there are critical thresholds under different transmission range R. The sharpness of the threshold depends on the R. Based on these results; we can choose appropriate R for the initial scheme of different numbers of nodes. Fig.7 has shows the actual topologies for one simulated network with 100 nodes with maximum transmission range Rmax=250. Fig.7(a) and (b) are the topologies resulting from original graph G and our Co-ETC routing graph. As can be seen, Co-ETC maintains network connectivity in its routing graph.

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5.2 Network-Lifetime We compared the Co-ETC protocol (after adding extensions) presented in the previous sections to K-NEIGH protocol [3] and CBTC algorithm [4]. Notice that, the CBTC algorithm (with α=2/3π) and K-NEIGH protocol were all with pruning optimization in simulation. Since CBTC algorithm does not provide routing by itself, we used the AODV [7] routing protocol for it in simulation. The same network setup was used to compare the implementations of routing protocols. 100 sensor nodes were randomly placed in area with R=250. Each node had initial energy of 0.5 Joule. Five of them were source nodes, which produce CBR data traffic. The length of a data packet was 64 bytes. One node was assign as sink node. Nodes moved randomly with constant speeds 10/ time. Node bounced back once hitting the boundary. Original topology

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Fig. 7. Topology graph. (Left) Original topology. (Right) Co-ETC routing graph.

In WSNs, the metric of actual interest is not the energy-efficient of per packet, but the whole operational lifetime of WSN. So we use network lifetime as the metric to evaluate the energy-efficient performance of protocols. We consider the network to be down until there is no data packet can be received by sink node. Fig. 8 illustrates the normalized network lifetime simulation results of Co-ETC, and the reference K-NEIGH and CBTC+AODV (α=2/3π) under different network loads in both static and mobile scenarios. It is shown that Co-ETC extends the network-lifetime significantly in the mobile scenario. Lifetime at most a factor of 2.2 those of K-NEIGH and CBTC+AODV could be reached. Although Co-ETC is designed to be efficient in dynamic WSNs, it also prolongs the lifetime 10-45 percent in static scenario. Contrary to K-NEIGH and CBTC, our Co-ETC protocol is almost independent of the choice of scenario: static or mobile. This is due to the fact that the constructed routing graph of Co-ETC has good property adapt to mobile environment.

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Fig. 8. Network lifetimes of different schemes

6 Conclusion In this paper, we consider energy-efficient topology control routing in mobile wireless sensor networks. We present a distributed routing protocol, Co-ETC, and indicate that base on underlying routing graph, it has better energy-efficiency. Moreover, it can adapt to mobile environment well. Although Co-ETC outperforms other existing state-of-the-art algorithms and protocols in terms of network lifetime, and has desirable property including mobility, sparse, and localized. However, we have assumed that all nodes have circular communications ranges. In practice, this is often violated due to fading and multipath effects. It would be interesting to extend results of this paper to more realistic scenarios. Furthermore, we will further do research on using more complex mobility models such as group mobility. Acknowledgments. This work is supported by National Science Foundation of China. (No. 60473001, 60572037, 60573001), and the Innovation Foundation of Science and Technology for Excellent Doctorial Candidates of Beijing Jiaotong University (No. 48013).

References 1. Akyildiz, I.F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: Wireless sensor networks: a survey. Computer Networks, Vol. 38. (2002) 393-422 2. Rajaraman, R.: Topology control and routing in ad hoc network: A survey. SIGACT News, Vol. 33. (2002) 60-73 3. Blough, D.M., Leoncini, M., Resta, G., Santi, P.: The k-neighbors protocol for symmetric topology control in ad hoc networks. Proc. ACM Mobihoc’03, (2003) 141-152

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4. Li, L., Halpern, J.Y., Bahl, P., Wang, Y.M., Wattenhofer, R.: A cone-based distributed topology-control algorithm for wireless multi-hop networks. IEEE/ACM Transactions on Networking (TON), Vol. 13. (2005) 147-159 5. Wang, W., Li, X., Moaveninejad, K., Wang, Y., Song, W., The spanning ratio of β-skeletons. Proc. CCCG, (2003) 35-38 6. Cormen, T.J., Leiserson C.E., Rivest, R.L.: Introduction to Algorithms. Massachusetts: MIT Press/ New York: McGraw-Hill (1990) 7. Perkins, C.E., Royer, E.M.: Ad-hoc on-demand distance vector routing. Proc. IEEE WMCSA’99, (1999) 90-100

Integrated Clustering and Routing Strategies for Large Scale Sensor Networks Ataul Bari, Arunita Jaekel, and Subir Bandyopadhyay School of Computer Science, University of Windsor 401 Sunset Ave. Windsor, ON N9B 3P4, Canada {bari1,arunita,subir}@uwindsor.ca

Abstract. In two-tiered sensor networks using relay nodes, sensor nodes are arranged in clusters and the higher-powered relay nodes can be used as cluster heads. The lifetime of the networks is determined primarily by the lifetime of the relay nodes. Clustering techniques and routing schemes play a crucial role in determining the useful network lifetime. Traditionally, the clustering and the routing problems, for these networks, have been considered independently and solved separately. In this paper, we present a new integer linear program (ILP) formulation that jointly optimizes both clustering and routing to maximize the lifetime of such networks. We show that our integrated approach can lead to significant improvements over techniques that consider clustering and routing separately, particularly for the non-flow-splitting (single-path) routing model. We also propose a heuristic, based on LP-relaxation of the routing variables, which can be used for larger networks.

1

Introduction

A wireless sensor network (WSN) is a network of low-powered, multi-functional sensor nodes, each consisting, at a minimum, of a sensing circuit, a digital signal processor, and radio links [1], [2], [3]. It is extremely important to design routing protocols and algorithms that are energy efficient, so that the overall lifetime of the network can be extended as much as possible. In a two-tier hierarchical architecture, the network is organized as a number of clusters where each sensor node belongs to only one cluster. Some nodes are treated as cluster heads and have additional responsibilities (e.g. data gathering, data aggregation and routing) compared to the remaining nodes. Recently, relay nodes, acting as cluster heads, have been proposed in two-tier sensor networks [2], [4], [5], [6], [7], [8], [9] for energy-efficient data gathering, load-balancing and fault tolerance [2], [5], [7]. In relay-based networks, each relay node collects data from the sensor nodes in its cluster and forwards this data to the base station (or sink) using either single-hop or multi-hop communication model. The multi-hop data transmission model (MHDTM), [7], [8], [9], [10] is particularly suitable for larger networks and is the model used in this paper. A number of routing schemes for two-tiered networks have been proposed in the literature [2], [4], [5], [7], [8], [10]. Most of these adopt the flow-splitting (also I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 143–154, 2007. c IFIP International Federation for Information Processing 2007 

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called multi-path routing) model. In contrast, in a single-path routing model, a node is not allowed to split the traffic, and forwards all its data to a single neighbor. This model avoids many limitations of the flow splitting model [7]. An important factor affecting the lifetime of a two-tier network is the clustering scheme used to assign sensor nodes to the appropriate clusters [6], [11], particularly for single-path routing. Previous approaches to clustering and routing have considered the two problems independently. Typically, the assignment of sensor nodes to clusters is done first, and then a routing scheme to maximize the network lifetime is calculated. In this paper, we present a new integer linear program (ILP) formulation that jointly optimizes both clustering and routing to maximize the lifetime of the upper-tier relay node network. We have assumed a network model where a) the roles of the sensor nodes and the relay nodes are not interchangeable, b) the relay nodes do not perform sensing tasks and are provisioned with higher energy, c) the relay nodes can transmit over larger distances, compared to regular sensor nodes, d) each sensor node, is located close enough to some relay node so that the sensor node can transmit directly to the relay node, e) sensor nodes only communicate to their respective cluster heads and do not take part in the routing, and f) both the sensor nodes and the relay nodes communicate through an ideal shared medium where communication between nodes is handled by appropriate MAC protocols (as in [2], [5]). We focus on the non-flow-splitting (single-path) routing model and show that our integrated approach can lead to significant improvements over techniques that consider clustering and routing separately. To the best of our knowledge, this is the first technique that combines the clustering and the routing problem to maximize the network lifetime. We assume that the clustering and the routing scheme is computed at the base station (or at some centralized entity where such computation may be carried out). There are two possible scenarios for determining the positions of the relay nodes and the sensor nodes as follows: Case i) We place the sensor and the relay nodes at predetermined locations. Before the deployment of the network, we can compute the clustering and the routing decisions at some centralized location. The sensor nodes and the relay nodes may be pre-configured with this information. Case ii) We can find the locations of the nodes using a GPS system. GPS equipped nodes has been widely proposed in the literature [1], [2], [5], [6]. The GPS system needs to be operated for a very short period of time, to know the locations of the sensor and the relay nodes. We also assume that the nodes are stationary after deployment. We can then compute, at some central location, the clustering and the routing decisions and broadcast the result to the entire network. Since the communication from each sensor or relay node as well as the communication broadcast from the base station to the sensor and relay nodes will be a single, small packet, the energy

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dissipated for sending/receiving these two packets is insignificant, compared to the subsequent transmissions, and will not have any substantial impact on the lifetime of the network. In this paper we have i) presented an integrated ILP for optimal clustering and single-path routing to maximize network lifetime, giving a significant increase in network lifetime compared to solving the two problems separately. ii) proposed a LP-relaxation of the routing variables so that our approach can be used for multi-path routing as well. iii) extended the above ILP to develop a new heuristic for single-path routing capable of handling large networks, and have shown, through simulations, that the network lifetimes that may be achieved by the heuristic solutions is close to the theoretical upper bound.

2 2.1

Review Load Balanced Clustering

Many researchers have investigated clustering of nodes in a wireless network [2], [3], [5]. In [2], the problem of forming clusters around a few high-energy gateway nodes has been investigated. In Fig. 1, the sensor nodes in the shaded region can be assigned to any one of clusters A, B or C. The routing scheme and/or the energy dissipation of relay nodes A, B and C, may favor one assignment over the others. A load balanced clustering algorithm assigns each sensor node to an appropriate cluster to maximize the lifetime of the network. In [9], a minimum number relay nodes have been used as cluster heads to cover all sensor nodes. However, [9] does not address the issue of clustering after the placement of the relay nodes. In [2], the “cardinality” of a cluster (the number of sensor nodes associated with the cluster) is used in a heuristic to minimize the variance of the cardinality of each cluster in the network. In [6], it is demonstrated that suitable clustering techniques can be used to increase the lifetime of the network. 2.2

Routing in Sensor Networks Using Relay Nodes

The problem of routing in wireless sensor networks, under the “flow-splitting” model, has been extensively covered in the literature. In [8], Hou et al. have attempted to maximize the lifetime of a sensor network by provisioning relay and sensor nodes with additional energy using a mixed-integer non-linear program and have proposed a heuristic. In [10], the authors have formulated the lifetime optimization problem, under the flow-splitting model. In [12], Falck et al. have addressed the issue of balanced data gathering in sensor networks and have proposed a LP formulation that enforces some balancing constraints in the data gathering schedule. In [2], Gupta and Younis have focused on load balanced

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clustering and have proposed a heuristic solution for the optimization problem. Routing without flow splitting (i.e., single-path routing) has been studied in [7], [13], and [14]. In [7], the authors have presented a transformation algorithm to convert a multiple outgoing flow routing model to a single outgoing flow routing model. In [14], the authors have investigated the problem of maximizing network lifetime by appropriately placing nodes which are not energy constrained (e.g., connected to a wall outlet). In [13], the authors propose a formulation for constructing minimum-energy data-aggregation trees, for a flat architecture.

3 3.1

ILP Formulations for Optimal Clustering and Routing Network Model

In this paper, we have assumed that the communication energy dissipation is based on the first order radio model [3], where the energy required to transmit (receive) b bits, at a distance d, is given by ETx (b, d) = α1 b + βbdm (ERx (b) = α2 b), where α1 (α2 ) is the energy coefficient for transmitter (receiver), β is the energy coefficient for the transmit amplifier and q is the path loss exponent. For our network model, we consider a two-tiered wireless sensor network with n sensor nodes, m relay nodes and one base station. Each sensor node belongs to only one cluster and each relay node acts as the cluster head of exactly one cluster. We assign each node a unique label as follows: i) for each sensor node, a label i, 1 ≤ i ≤ n, ii) for each relay node, a label j, n < j ≤ n + m, and iii) for the base station, a label n + m + 1. Let S be the set of all sensor nodes. Each sensor node belongs to only one cluster and each relay node acts as the cluster head of exactly one cluster. In

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other words, if S j , n + 1 ≤ j ≤ m + n, is the set of sensor nodes belonging to the j th cluster, then S = S n+1 ∪ S n+2 ∪ . . . ∪S m+n and S j ∩ S k = ∅, ∀j = k, n + 1 ≤ j, k ≤ m + n. The set S j will constitute the cluster with the relay node having label j as the cluster head. As mentioned in the introduction, we assume that the locations of all the sensor nodes and the relay nodes are known (or can be determined), and the average amount of data generated by each sensor node is also known a priori. The data rate for all sensor nodes need not be uniform, but can vary from node to node. We also assume that the placement strategy, applied during the deployment phase of the network, ensures proper coverage of each sensor node and the connectivity of the relay node network. In our model, data gathering is proactive, i.e., data are collected and forwarded to the base station periodically, following a predefined schedule. We refer to each period of data gathering as a round [10]. In each round of data gathering, each relay node gathers the data it receives from its own cluster and transmits that data, either directly to the base station (single hop model) or forwards the data towards the base station using a multi-hop path (multi-hop model). In the case of multi-hop routing, in addition to the data generated by its own cluster, each relay node also relays any data it receives from neighboring relay nodes. We will measure the lifetime of the network by the number of rounds the network operates from the start, until a relay node depletes its energy completely and ceases to function. 3.2

Notation Used

In our formulation we are given the following data as input: • • • • • • • • •

α1 (α2 ): Energy coefficient for transmitter (receiver). β: Energy coefficient for amplifier. q: Path loss exponent. bi : Number of bits generated by sensor node i per round. n (m): Total number of sensor (relay) nodes, with each sensor (relay) node having a unique index lying between 1 and n (n + 1 and n + m). n + m + 1: Index of the base station.  C: A large constant, greater than bi , the total number of bits received by the base station in a round. rmax (dmax ): Transmission range of each sensor (relay) node. di,j : Euclidean distance from node i to node j.

We also define the following variables: • Xi,j : Binary variable defined as follows: ⎧ 1 if sensor node i belongs to the cluster ⎪ ⎪ ⎨ of relay node j, Xi,j = ∀i, j : 1 ≤ i ≤ n, n + 1 ≤ j ≤ n + m, ⎪ ⎪ ⎩ 0 otherwise.

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• Yj,k : Binary variable defined as follows:  1 if relay node j transmits to relay node k, Yj,k = 0 otherwise. • Bj : Total number of bits generated by the sensor nodes belonging to cluster j in one round. • fj,k : Number of bits sent by relay node j to relay node k in one round. • Rj : Number of bits received by relay node j from other relay nodes in one round. • Tj : Number of bits transmitted by relay node j in one round. • Fmax : The total energy spent per round by the relay node which is being depleted at the fastest rate. 3.3

ILP Formulation for Non Flow-Splitting Model (ILP-NFS)

Given the network as described in Section 3.1, the objective of this formulation is to maximize the lifetime of the network by finding an optimal clustering and routing scheme. Minimize Fmax

(1)

Subject to: a) A sensor node i can transmit to a cluster-head j, only if the distance between i and j is less than the range rmax of the sensor node. Xi,j · di,j ≤ rmax ,

∀i, 1 ≤ i ≤ n,

(2)

∀j, n < j ≤ n + m b) A sensor node must belong to exactly one cluster. n+m 

Xi,j = 1,

∀i, 1 ≤ i ≤ n

(3)

j=n+1

c) Compute the total number of bits Bj received at relay node j from its own cluster in one round of data gathering. n 

bi · Xi,j = Bj ,

∀j, n < j ≤ n + m

(4)

i=1

d) Relay node j can only transmit to one relay node or to the base station (non-flow-splitting constraint). n+m+1  k=n+1

Yj,k = 1,

∀j, n < j ≤ n + m

(5)

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e) Compute the total number of bits Tj transmitted by relay node j in one round of data gathering. Tj =

n+m+1 

fj,k ,

∀j, n < j ≤ n + m

(6)

k=n+1

f) Compute the total number of bits Rj received at node j (a relay node or the base station) from other relay nodes in one round of data gathering. Rj =

n+m 

fk,j ,

∀j, n < j ≤ n + m + 1

(7)

k=n+1

g) Ensure that relay node j is transmitting to relay node k, only if relay node k is the next node in the multi-hop path from j to the base station (or k is the base station). fj,k ≤ C · Yj,k ,

∀j, k, n < j ≤ n + m,

(8)

n
∀j, n < j ≤ n + m

(9)

i) A source relay node can transmit to a destination relay node (or base station) if the destination node is within the transmission range of the source node. (10) Yj,k · dj,k ≤ dmax , ∀j, k, n < j ≤ n + m, n
n+m+1  k=n+1

fj,k · dqj,k ≤ Fmax ,

(11)

∀j, n < j ≤ n + m

In evaluating ILP-NFS, we have computed the lifetime as the number of rounds until one relay node becomes completely depleted. Although ILP-NFS minimizes the maximum load in any relay node in a round, it is possible that, after the first relay node is depleted, other relay nodes might still have some residual power. We could have used the surviving relay nodes to further extend the lifetime of the network. The rescheduling strategy we have proposed in [4] may be used, where the routes are recomputed at periodic intervals1 , taking into consideration the available residual energy of each relay node. We have shown in [4] that it is possible to increase significantly the lifetime of the network by this technique. We may apply the same technique to this formulation as well. We omit the details since the technique is essentially the same. 1

Clustering was not considered in that paper.

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LP-Relaxation Based Heuristic

The ILP formulation presented in the previous section guarantees an optimal solution that maximizes the lifetime of the upper-tier relay node network. However, this formulation becomes computationally intractable for larger networks. In this section, we propose a heuristic approach based on a LP-relaxation of the routing variables Yj,k . In this approach, we first solve the ILP (ILP-FS) for the combined clustering and routing problem under the flow-splitting model. This means that we allow the traffic to be split among different nodes, and no longer require the integer variables Yj,k . The solution obtained for the flow-splitting model is then used to guide the ILP for the non-flow-splitting model. The idea is that, we define a small set P j of “promising” relay nodes, for node j, for all j, n < j ≤ n + m. The nodes in P j are selected, based on the nodes that j transmits to, in the solution generated by ILP-FS. When looking for the next node, in the path from relay node j to the base station, the new formulation only considers the nodes in P j . 4.1

ILP for Flow-Splitting Model (ILP-FS)

The formulation for the flow-splitting model is similar to ILP-NFS presented in the previous section, with the following modifications. 1. The variables Yj,k are eliminated. Since, we are allowed to arbitrarily split the traffic, the integer routing variables Yj,k are no longer needed and traffic flows can be determined by the continuous flow variables fj,k . 2. Since a relay node can transmit to any number of other nodes, constraint (5) is no longer needed, and is removed. 3. Since there can be non-zero flow to more than one node, constraint (8) is not needed, and is removed. 4. Constraint (10) is modified as follows: fj,k = 0,

∀j, k,  dj,k > dmax

(12)

All other variables and constraints, as well as the objective function are identical to ILP-NFS. 4.2

Non Flow Splitting-Heuristic (NFS-H)

In the heuristic, we find the routing scheme in three steps. The first step in the heuristic is to run ILP-FS to identify the set, P j , of promising relay nodes for the j th relay node. In the second step, we set Yj,k = 0, for all relay nodes not in P j . Finally, we run ILP-NFS to generate a solution for combined clustering and routing, under non-flow splitting model. By setting Yj,k = 0, in step 2, for all relay nodes not in P j , ILP-NFS is forced to select one of the nodes in P j as the next node in the path from node j to the base station. By extensive simulation, we have observed that the size of P j , for each node j, is typically from 1 to 4. This considerably reduces the complexity for ILP-NFS and we find that ILP-NFS quickly converges to a solution.

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151

Experimental Results Experimental Setup

We have carried out a number of experiments to test the effectiveness of our formulations, with different sensor and relay node distributions. We have measured the achieved lifetime of a network by the number of rounds until the first relay node runs out of battery power. The ILP formulations were solved using CPLEX version 9.1 [15]. In the first set of experiments, we consider networks with up to 15 relay nodes, and sensor nodes randomly distributed over the region. We varied the number of sensor nodes from 100 to 500 nodes. To evaluate the performance of our approach, we compared the achieved lifetime with standard multi-hop routing schemes such as the minimum hop (MH) routing and the minimum transmission energy (MTE) routing. We also considered an optimal single-path routing scheme (ILP-R) [4], which maximizes the network lifetime for a specified clustering strategy. For each routing scheme, we experimented with a number of standard clustering techniques [11] such as: i. Greedy Clustering (GC): Each relay node greedily selects all sensor nodes which can communicate with it, and has not yet been assigned to a cluster. ii. Least Distance Clustering (LDC): Each sensor node transmits to the closest relay node. iii. Minimum Variance Clustering (MVC): The clustering algorithm attempts to distribute sensor nodes uniformly over the relay nodes, such that the variation in cluster size is minimized. In the following sections, we have shown the results corresponding to the MVC clustering algorithm, which is the best performing algorithm as reported in [6]. The improvements obtained with respect to GC and LDC are comparable to MVC, or even higher. The first set of experiments was used to calibrate the performance of the heuristic with respect to the optimal. In the second set of experiments, we considered much larger networks with up to 44 relay nodes and 5000 sensor nodes. For such networks, it was not possible to obtain optimal solutions using the ILP for the non-flow-splitting model. So, we compared our heuristic with MTE and MH routing. We have assumed that the communication energy dissipation is based on the first order radio model, described in Section 3.1. The values for the constants are taken as α1 = α2 = 50nJ/bit, β = 100pJ/bit/m2 and the path-loss exponent, q = 2, which are similar to [3]. The range of each sensor (relay) node is set to 40m (200m) and the initial energy of each relay node is set to 5J, as in [9]. 5.2

Performance Evaluation for Moderate Sized Networks

In this section, we present the results for a 160m × 160m area network with 12 relay nodes. Figure 2 shows the network lifetime obtained by using our integrated approach versus the MH, MTE, and ILP-R routing strategies combined with MVC clustering scheme, for the non-flow-splitting model. For each data set, we

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represent the lifetimes achieved by the different strategies in the following order: minimum-hop routing (MH), minimum transmission energy routing (MTE), optimal routing performed separately after clustering (ILP-R), LP-relaxation based heuristic for combined clustering and routing (NFS-H), and optimal solution for combined clustering and routing (ILP-NFS). 4

5

x 10

MH MTE ILP−R NFS−H ILP−NFS

4.5

4

Lifetime in rounds

3.5

3

2.5

2

1.5

1

0.5

0

100

200

300

400

500

Number of sensor nodes

Fig. 2. Comparison of achieved lifetimes with MVC scheme

The data clearly indicate that an integrated approach performs significantly better than traditional routing schemes. The average achieved lifetime obtained by ILP-NFS increased by over 300% (over 200%) compared to traditional routing schemes such as MH (MTE). Even when compared to the optimal routing generated by ILP-R, ILP-NFS produced an average improvement of 23%. The results also show that the performance of our heuristic (NFS-H) is quite close to the optimal (within 10% - 15%) in all cases. 5.3

Performance Evaluation for Large Scale Networks

In the previous sections we compared our heuristic (NFS-H), with the optimal solution and have shown that its performance is close to optimal for small networks. For large networks, it was not possible to generate optimal solutions for the non-flow-splitting model, using ILP-NFS. The optimal routing formulation (ILP-R) in [4] was also unable to generate solutions for larger networks. Therefore, in this section, we compare the performance of our heuristic with traditional MH and MTE routing schemes. We also report the achieved lifetime obtained using ILP-FS. This provides an upper bound on the maximum achievable lifetime for each experimental run.

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4

3

x 10

MH MTE NFS−H ILP−FS

Lifetime in rounds

2.5

2

1.5

1

0.5

0

12

15

24

36

44

Number of relay nodes

Fig. 3. Comparison of achieved lifetimes for moderate to large networks

Figure 3 shows how the achieved lifetime varies with the size of the network. For a specific size of relay node network, we selected the number of sensor nodes so that the average cluster size remains the same for all networks. The sensing area varied from 160m × 160m for a network with 12 relay nodes to 400m × 280m for a network with 44 relay nodes. As before, Figure 3 confirms that the combined approach clearly performs better than both MH and MTE for large networks. The average improvement of our combined approach is 300% and 200% over MH and MTE respectively. The overall lifetime decreases with network size, since the sensing area as well as the total amount of data to be transmitted increases, which in turn increases the load on critical nodes close to the base station.

6

Conclusion

In this paper we have proposed an integrated approach that jointly optimizes clustering and routing in large scale two-tier sensor networks. We have presented an ILP formulation that maximizes the lifetime of the upper-tier relay node network, as well as a LP-relaxation based heuristic that can be used for large networks with thousands of nodes. We have calibrated the performance of the heuristic, by comparing with optimal solutions for smaller networks. We have demonstrated that our combined approach significantly increases network lifetime for non-flow-splitting (single-path) routing. Our proposed heuristic clearly outperforms traditional routing schemes such as minimum-hop routing and minimum-transmission-energy routing, for large scale networks.

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Acknowledgment The work of A. Jaekel and S. Bandyopadhyay have been supported by research grants from the Natural Sciences and Engineering Research Council of Canada (NSERC).

References 1. I.F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci. Wireless sensor networks: a survey. Computer Networks, vol. 38, pp. 393-422, 2002. 2. G. Gupta and M. Younis. Load-balanced clustering of wireless sensor networks. In IEEE Intl. Conf. on Comm., vol. 3, pp. 1848-1852, 2003. 3. W. Heinzelman, A. Chandrakasan, and H. Balakrishnan. Energy effcient communication protocol for wireless micro-sensor networks. In Proc. of the 33rd HICSS, pp. 3005-3014, 2000. 4. A. Bari, A. Jaekel and S. Bandyopadhyay. Maximizing the Lifetime of Two-Tiered Sensor Networks. In IEEE EIT, pp. 222–226, 2006. 5. G. Gupta and M. Younis. Fault-tolerant clustering of wireless sensor networks. Proceedings of IEEE WCNC. pp. 1579–1584, 2003. 6. G. Gupta and M. Younis. Performance evaluation of load-balanced clustering of wireless sensor networks. 10th Inter. Conf. on Telecomm., vol. 2, pp. 1577–1583, 2003. 7. Y. T. Hou, Y. Shi, J. Pan, and S. F. Midkiff. Lifetime-optimal data routing in wireless sensor networks without flow splitting. In Workshop on Broadband Adv. Sensor Networks, San Jose, CA, 2004. 8. Y. T. Hou, Y. Shi, H. D. Sherali, and S. F. Midkiff. On Energy Provisioning and Relay Node Placement for Wireless Sensor Networks. In IEEE SECON, vol. 32, 2005. 9. J. Tang, B. Hao, and A. Sen. Relay node placement in large scale wireless sensor networks. Comp. Comm., vol. 29(4), pp. 490–501, 2006. 10. K. Kalpakis, K. Dasgupta, and P. Namjoshi. Maximum Lifetime Data Gathering and Aggregation in Wireless Sensor Networks. IEEE Inter. Conf. on Network., 2002. 11. A. Bari, A. Jaekel and S. Bandyopadhyay. Optimal load balanced clustering in two-tiered sensor networks. In IEEE BaseNets, 2006. 12. E. Falck, P. Floren, P. Kaski, J. Kohonen, and P. Orponen. Balanced data gathering in energy-constrained sensor networks, vol. 3121 LNCS, pp. 59-70, Berlin Heidelberg, 2004. Springer-Verlag. 13. M. Borghini, F. Cuomo, T. Melodia, U. Monaco and F. Ricciato. Optimal data delivery in wireless sensor networks in the energy and latency domains. WICON, pp. 138–145, 2005. 14. M. Yarvis, N. Kushalnagar, H. Singh, A. Rangarajan, Y. Liu nad S. Singh. Exploiting heterogeneity in sensor networks. INFOCOM 2005, vol. 2, pp. 878–890, 2005. 15. ILOG CPLEX 9.1 Documentation. Available at the website http://www.columbia. edu/˜dano/resources/cplex91 man/index.html

On-Demand Routing in Disrupted Environments Jay Boice, J.J. Garcia-Luna-Aceves, and Katia Obraczka Department of Computer Engineering University of California at Santa Cruz

Abstract. While current on-demand routing protocols are optimized to take into account unique features of mobile ad hoc networks (MANETs) such as frequent topology changes and limited battery life, they often do not consider the possibility of intermittent connectivity that may lead to temporary partitions. In this work, we introduce the Space-Contentadaptive-Time Routing (SCaTR) framework, which enables data delivery in the face of both temporary and long-lived MANET partitions. SCaTR takes advantage of past connectivity information to effectively route traffic towards destinations when no direct route from the source exists. We show through simulations that, when compared to traditional on-demand protocols, as well as Epidemic routing, SCaTR increases delivery ratio with lower signaling overhead in a variety of network scenarios with intermittent connectivity. We also show that SCaTR performs as well as on-demand routing in scenarios that are well-connected, and/or have no mobility predictability (e.g., scenarios with random mobility).

1

Introduction

The price, performance, and form factors of sensors, processors, storage elements, and radios today are enabling the development of network-supported applications in very disrupted environments, i.e., environments where end-to-end connectivity is not guaranteed at all times because of either the characteristics of the environment or the normal operation of the network nodes. Examples of such applications and environments include monitoring of disrupted phenomena (e.g., wild fires), object tracking, establishment of on-demand network infrastructure for disaster relief or military purposes (in which case, the ad hoc network can be disrupted by terrain, weather, and other natural phenomena, as well as jamming, interference, etc.), peer-to-peer vehicular or interpersonal networks [1] with very sparse connectivity, and mobile ad hoc networks (MANETs) that need not be connected at all times in order to limit interference and contention. In these scenarios, network disconnection is the normal state of operation rather than an exception. The demand for networking in environments prone to intermittent connectivity poses a challenge because the architects of the IP Internet and MANETs have assumed that physical connectivity exists on an end-to-end basis between sources and destinations for extended periods of time, or at least for the duration of a transaction among communicating parties. This assumption has had I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 155–166, 2007. c IFIP International Federation for Information Processing 2007 

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profound implications on how communication bandwidth is shared, how routing is accomplished, and how messages are disseminated across computer networks. In particular, routing in packet-switching networks has been based on routing tables that specify the next hop to one or more destinations. Such routing information is derived entirely from topology (or connectivity) information that represents only a snapshot of the state and characteristics of network links at particular instants. Regardless of the specific mechanisms used in a routing protocol today (e.g., proactive or on-demand routing), computing the routing table entry for a given destination can be viewed as a particular form of searching a database. The routing database can be replicated (as it is done in such topology broadcast approaches as TBRPF [2] and OLSR [3]) or distributed, as in AODV [4] or DSR [5]. Depending on whether the routing database is replicated or distributed, the search algorithm can be centralized (e.g., using Dijkstra’s shortest path first algorithm) or distributed (e.g., using a flood search based on route requests and route replies). The routing databases constructed by traditional routing algorithms specify the instantaneous status of a link (up or down), and the value of its parameters such as delay and bandwidth at some specific point in time. The search for routes in such databases produces snapshot paths that have no temporal dimension. Hence, if the network connectivity or link parameters change, multiple paths to destinations may be affected; the only way most current routing protocol can recover is to search for new paths. This time-independent, reactive approach to changes in network connectivity and link parameters works well as long as the disruptions in network connectivity due to environmental or operational reasons are not so frequent and/or long-lived that they prevent the routing protocol from obtaining time-independent paths to intended destinations. Starting with the work in the Interplanetary Internet Research Group (IPNRG) [6] of the IRTF (Internet Research Task Force), considerable effort has recently been devoted to the study of networks with intermittent connectivity or very long latencies. Perhaps most prominent in this area is the work by the DTNRG (Delay Tolerant Networking Research Group) [7], which started in 2002 under the IRTF. Section 2 summarizes prior related work on routing in disrupted environments. From our summary of related work, it becomes apparent that no complete solution exists for on-demand routing that incorporates the network topology’s time dependency. In this paper we describe the SCaTR (Space Content adaptive Time Routing) framework to enable on-demand routing in MANETs with intermittent connectivity. Section 3 describes SCaTR which we currently implement by extending the On Demand Ad Hoc Distance Vector Routing Protocol [4] (AODV). Our current instantiation of SCaTR is such that, if the network is connected, it operates exactly as regular on-demand routing, in this case AODV. However, if no direct route is available from source to destination, a node that is deemed closer to the destination than the source will advertise itself as a proxy. In this manner, we are assured that the resulting protocol will do no worse than standard AODV in well-connected environments, and better in partitioned networks.

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Section 5 addresses the performance of SCaTR compared to on-demand and Epidemic routing. Scenarios involving both random and predictable node mobility are investigated. In predictable mobility scenarios, node schedules or trajectories are not assumed to be global knowledge. Instead, the routing algorithm in SCaTR uses mobility histories to improve performance. Our simulation results show that the added functionality of proxies in SCaTR improves delivery rates in both predictable and random mobility situations, while incurring lower signalling overhead. Given enough time, the protocol delivers all possible packets to their intended destinations, achieving optimal reliability. Section 6 summarizes our contributions and discusses ideas for future work.

2

Related Work

Recently, Message Ferrying [8] has been investigated for use in highly partitioned networks. The approach utilizes special nodes called ferries whose mobility can be controlled to maintain communication between partitions. Much of the work has focused on route scheduling of the ferries, and synchronization between their routes, since a well-chosen schedule will have a great impact on timely and reliable message delivery. It has also been shown that the ferries can be used as an energy saving device for other nodes in the network; if there are no ferries nearby, nodes can be turned off to conserve energy. This work makes the assumption that controllable nodes exist in the network, however, there are situations in which these nodes are not available. Our work addresses these situations. In the Epidemic routing [9] approach, data are transmitted through message exchanges between neighboring nodes. The premise behind the work is that by duplicating a message and sending it to all neighbors, it can quickly and reliably reach its destination. Similar work [10] has been done to improve Epidemic routing by limiting the number of nodes to which messages are sent. Epidemic routing, however, relies on data duplication to deliver messages which can be prohibitively expensive in terms of energy consumption. Delay Tolerant Networking [7] has attracted considerable interest from the network research community for several years now. Additional layers atop the routing and transport layers have been proposed to provide store and forward capabilities, as well as interoperability services to partitioned networks. This work has also examined the idea of custody [11], which is a hop-by-hop method of reliability for disconnected networks. This is a much-needed approach to the issue of reliability, as end-to-end reliability is unmanageable in these scenarios. A more general framework for routing using knowledge of network mobility has also been proposed [12]. This approach adds the time dimension to routing tables, and selects routes based on a combination of the data’s destination and the time of message arrival. It uses global knowledge of node mobility schedules to construct these routing tables. In some scenarios, these schedules may not be available, or too expensive to maintain. Spray and Wait [13] is a recent improvement over a pure flooding protocol such as Epidemic routing. In this work, only the source can replicate a message, and

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the amount of replication is proportional to the number of nodes in the network. It is shown that the method can bound delay proportional to the optimal delay. After ’spraying’ several copies of a message, the host ’waits’ until one is delivered. Location information is a useful tool for routing in disrupted networks. Both MobySpace [14] and MV routing [15] are methods that use location information to aid routing decisions. They assume that a node who has visited a particular location is likely to revisit it, and therefore is a good candidate to carry messages to that location. MV routing uses location information to facilitate buffer management, while MobySpace is a framework for generating probabilities that a nodes will move to specific locations in the future. Both methods require some sort of localization method such as GPS. While there has been significant prior work on the topic of partitioned networks, most of the approaches have made one of three assumptions. One assumption is global topology knowledge, which has proved to be useful in determining future connectivity. Another assumption is the existence of controllable nodes, which can be extremely useful in aiding delivery in sparse networks. The third assumption is that data can be duplicated freely among nodes, which can lead to excellent delivery ratios. Our work is an attempt to do away with these assumptions, yielding a more general framework applicable to any network scenario where any such assumption may be unrealistic.

3

SCaTR

The SCaTR framework extends on-demand routing, taking action only when direct routes cannot be established by the underlying protocol. In the case of a route discovery failure, i.e., the source and destination are in separate partitions, SCaTR tries to route data to the node or nodes in the source’s partition that are likely to have a route to the destination in the near future. These nodes act as proxies for the destination and buffer messages until either the destination is discovered, or another node is selected as a better proxy for those messages. Messages are replicated at most one time, resulting in minimal data replication and duplicate message filtering overhead. Proxies are selected based on past connectivity information which nodes keep in content-adaptive contact tables. As it will become clear, contact tables, which are the equivalent of traditional routing tables, use time-dependent and spacedependent routing metrics. These metrics differ for different types of content or local constraints such as buffer size. For instance, if a proxy is running low on buffer space, it may decide to select as the next proxy for that destination the first node it hears from that has been in contact with the destination; this is done even if the node’s contact value is lower that its own; however, if the node has higher buffer availability, it can carry the data for a longer interval. Because SCaTR takes no action if routes are successfully established, we are guaranteed that it will perform no worse than the underlying on-demand routing protocol in any situation. This diversity makes it well suited for adoption in any network scenario. SCaTR consists of several phases: contact table maintenance,

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route discovery, route selection, and proxy rediscovery. Each phase is described in detail below. Each node in the network maintains a contact table containing a measure of time-dependent distances to other nodes in the network. Each entry in the table consists of a destination address and its current contact value. Nodes maintain these tables with information that is piggybacked onto hello messages; when a node receives a hello message from a neighbor, it also receives that node’s contact table. It uses this table to make changes to its own contact table. Because it can be very expensive to maintain contact information about all nodes in a network, SCaTR initializes its contact tables on-demand. Each node starts with an empty table, and adds destinations only when it receives a request for that destination, or meets another node who has an entry in its table for that destination. This method of initialization results in a delay for the first messages introduced into the network because the contact table request must propagate to the destination and then back to the source before proxies are advertised. In large networks with predefined sinks or a limited number of destinations, however, this method saves significant computational and communication overhead. The mechanisms used to maintain and update contact values have several important characteristics that must be addressed: – Ordering: The highest contact value advertised for any node must be advertised by the node itself. A node that will reach a destination sooner than another node should have a higher contact value for that destination. – Stability: Contact values should not fluctuate greatly over time in order to minimize ’leapfrogging’ of contact values (the case in which nodes alternately select each other as proxies due to asynchronous contact value updates). – Simplicity: Contact value calculation should not be computationally complex, as it must be frequently invoked. To address these issues, we propose an algorithm that is initiated with a maximum contact value advertised by destinations themselves. Time is broken into hello intervals. During a hello interval, nodes maximize their neighbors’ advertised contact values for each destination. These values are averaged over a hello period, and each node maintain a window of periods, used to generate the next interval’s contact value for each destination. A more detailed description of contact value maintenance follows. The length of a hello interval is the amount of time between hello message advertisements. During each hello interval, a node maintains the maximum contact value it receives from its neighbors for each destination. The hello period consists of a sequential group of hello intervals as defined by the parameter τ . At the end of a hello period, a node averages the values obtained during each hello interval to obtain a single value for the entire period for each destination. The length of time for which a node retains contact information is specified by the period window κ. At the end of each hello period, the value obtained during the most recent period is added to a queue, and the oldest value is removed. Each node’s contact values are recalculated at the end of each period by averaging the

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most recent κ periods. Until the node’s contact value is updated again, it will advertise this value to its neighbors. The main mechanisms for route discovery in the SCaTR framework are the Proxy Request (PREQ) and Proxy Reply (PREP) messages. When the underlying routing protocol is unable to establish a route to a destination, the source node will issue a PREQ to its current partition. This is a request for a candidate node or nodes in the source’s partition to buffer messages and carry them towards their destination. The PREQ can request one or more destinations to reduce signaling overhead. Instead of sending out an individual PREQ for each destination, the node will send a single PREQ with all destinations for which it has buffered data. The PREQ also contains the source node’s contact value for each destination that is being requested. The contact value is included so that only nodes with a significantly better value reply to the request. In our implementation, we have used a threshold of 5% to determine whether or not a proxy is better; a proxy is only selected if its contact value is 5% higher than the node at which the messages currently reside. Different threshold values could be used and will determine how selective a node is in choosing proxies. In preliminary experiments, we found 5% to be an effective threshold to balance overhead and delivery ratios. The PREP is a message that advertises the responding node as a possible proxy for one or more of the destinations in the PREQ. The source can then decide which proxy or proxies to use for each destination. The PREP contains the proxy’s contact value for the destination, as well as its remaining buffer space, and the number of messages it has already buffered for the source-destination pair. It is important to note that the PREP specifies the destination, not the proxy itself. The source need not know the address of the proxy; it must only know the next hop towards the destination. The source-destination pair obtained from the PREQ packet is entered into a buffering table at the proxy, and any packets that are later received by the proxy with this source-destination pair are buffered. As the source collects PREPs from the nodes in its partition, it compares contact values for each of the destinations. If a new PREP has a higher contact value than the one currently in its routing table, it replaces the entry. Routing tables may now contain two types of routes. One is an active, connected route, while the other is a route to a destination that was advertised by a proxy. These are distinguished only because a reply that advertises a direct route will always take precedence over a proxy route. After a proxy buffers packets, it must ensure that those packets reach their destination. Proxies have several methods of initiating the route discovery process for buffered messages. One method is ’listening’ as updates to its contact table are received. If it receives an improved contact value for a destination for whom it has buffered packets, the node assumes that a better route to the destination is available in its partition, or that the destination itself is nearby. This information initiates route discovery behavior in the proxy. The proxy sends out a single PREQ for all nodes for which it has buffered packets. In the same

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manner as the route discovery process described above, nodes reply to this request, and the proxy selects the best next destination for the data. The proxy also listens to any relevant RREPs or PREPs that it relays, and if route information for destinations in its buffer is relayed, a route is established along the advertised path. In the case that a proxy does not make any updates to the contact value for a buffered destination, or relay a reply for that destination, it sends a PREQ periodically. There are many approaches to message replication, ranging from the minimal approach of a single copy of each message, to the unlimited duplication (up to the number of nodes in the network) of Epidemic routing. More message redundancy requires increased overhead in the form of replicated data, as well as the computational and memory requirements required to maintain buffers and detect duplicate messages. One approach to the problem is to allow each proxy to replicate a message a certain number of times. However, as the network scales, it is clear that this number will grow exponentially. In addition, a proxy holding a message has no indication of whether another proxy has successfully delivered the message already. Thus, any replicas made by this proxy are in waste. This clearly is not a feasible solution. It is also possible to control replication in a tree fashion with the message source as the root of the tree. There can be a defined branching factor or replication degree that each level of the tree is permitted to use. Using the depth of a message in the tree and the branching factor, one can specify an exact number of duplications for each message. This reduces message duplication, but has the same problem of communicating message deliveries as mentioned above. In SCaTR, we have decided to minimize the amount of message replication. Prior work by one of the authors [16] has indicated analytically that under constrained conditions, the optimal number of message duplications is one. The overhead resulting in any further duplication is not justified by the increase in delivery ratio. For these reasons, the source can select at most two initial proxies for message transmission, and proxies may not duplicate messages.

4

Simulation Setup and Mobility Models

The SCaTR framework is implemented as an extension to the AODV routing protocol and simulated in GloMoSim [17] with several mobility scenarios and connectivity models. Epidemic routing was implemented for comparison to SCaTR, in which messages are passed to all neighbors. Throughout the experiments, 18 CBR data flows generate messages at ten second intervals for the first 400 seconds of the simulation. The experiments run for 2000 seconds to give messages time to propagate to their destination, and use an 802.11 MAC layer. All experiments were run with 5 seed values and the results averaged. The two mobility scenarios described below, in addition to the random waypoint model, show the effectiveness of the protocol over varied topologies and connectivity models. In the gridded random waypoint setup, nodes are arranged in a square field with a 377m radio propagation range. Within each square, a fixed number of

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nodes move according to the random waypoint mobility model; random locations are selected within the square, and a node moves there at a rate of between 5m/s and 10m/s. After reaching its destination, a node pauses for 20s. The flows exist between nodes on opposite ends of the grid to provide maximum route lengths. Throughout the experiments with this mobility model, the number of nodes and flows are fixed, while the dimensions of the scenario are varied to provide more or less connectivity in the network. In the scheduled routes setup, 50 nodes are arranged in a square field with a radio propagation range of 377m. Ten nodes are positioned around the perimeter of the network, and act as sources and destinations. All other nodes are assigned a randomly sized and positioned rectangle over which to travel at a random speed of between 5m/s and 20m/s. Using these parameters, links will be somewhat predictable, although they will not always occur at the same interval. Throughout the experiments, the size of the scenario is increased to provide less connectivity in the network. We also run simulations with the random waypoint mobility model to illustrate the performance of SCaTR in a purely random network; in this case, past mobility information gives no indication of future topologies. This scenario is especially interesting as it is not favorable to SCaTR. 40 nodes move according to the random waypoint mobility model within a square area 3000m x 3000m. Due to the sparseness of the network, the connectivity is poor. The experiments vary the speed of each node to change the duration of connected paths in the network. Pause time remains a constant 30s throughout the simulations.

5

Performance Comparison

In this section we show that the addition of SCaTR to an on-demand routing protocol results in significantly improved performance in terms of delivery ratio and signaling overhead in all mobility scenarios that were tested. In these experiments, signaling overhead includes control messages such as route requests and replies, as well as data packet replicas. Because the networks simulated are sparse, it is often not possible to deliver all messages in the allotted time. All simulations were run for 2000 seconds, and it should be noted that undelivered packets after this time were not lost; they have not yet reached their destination. It would be possible to run much longer simulations, and have much higher delivery ratios, but the time selected gives a good indication of the relative performance between protocols. In a subsequent experiment, we show how lengthening simulation time affects performance. We first compare routing methods in the scheduled routes mobility scenario. Connectivity is varied by increasing the size of the scenario; clearly a larger scenario size results in less connectivity. Experiments with scheduled routes show that SCaTR takes advantage of predictability to provide high delivery ratios with low signaling overhead. Figure 1 illustrates delivery rates and overheads for the various protocols. At small scenario sizes with good network connectivity, all protocols successfully deliver some messages. Epidemic routing delivers, as

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expected, 100% of messages, while SCaTR delivers approximately 96%. AODV, due to frequent route disruptions, delivers only 6% of messages. Epidemic routing maintains a 100% delivery ratio until the scenario size reaches 2500m x 2500m. Most notably, SCaTR sustains similar delivery ratio to Epidemic routing throughout the experiment. At 4500m x 4500m, connectivity is extremely poor, and none of the protocols deliver more than 40% of messages. The plot of signaling overhead in Figure 1 shows that SCaTR maintains its high delivery rates with little overhead. Since those packets that reach their destination with Epidemic routing likely reach all nodes in the network, overhead remains at nearly 50 messages per delivery. The addition of SCaTR enables AODV to maintain fairly constant overhead, much lower than that of Epidemic routing. The ’hump’ in the plot for AODV occurred because partitions at the start of the simulations surrounding the sources were large. Thus, as AODV tried its route establishment attempts, they reached a high number of nodes (but not the destination). This behavior had a large impact on overhead since so few packets were delivered.

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Fig. 1. Delivery ratio (left) and signaling overhead (right) for the scheduled routes mobility model with varied network connectivity

The results for the gridded random waypoint model, shown in Figure 2, are similar to that of the scheduled routes scenario. AODV’s performance decreases sharply as connectivity diminishes, while SCaTR maintains delivery ratios similar to Epidemic routing. In addition, Epidemic routing and SCaTR both show very high delivery ratios until the network is extremely disconnected. Notably, in both scenarios, the results show that adding a second proxy to SCaTR does not have a significant impact on its delivery ratio, although it does incur additional overhead. It is likely that a network with many more nodes would show the benefit of the second proxy more clearly, however these results indicate that it is not a significant factor. When buffer limitations are introduced, SCaTR’s performance significantly improves compared to that of Epidemic routing. All protocols employed a FIFO drop strategy for buffered messages. As shown in Figure 2, the duplicate messages in Epidemic routing have a detrimental effect with a small buffer. Only once

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the size of the buffer reaches approximately 25% of the number of messages originated in the network does Epidemic routing’s delivery ratio surpass that of SCaTR. This improvement, however, is still offset by the high overhead of Epidemic routing. We can also see that with a very constrained buffer of 5% to 10%, it is beneficial to select only one proxy for each message.

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Fig. 2. Left, delivery ratio for the gridded random waypoint mobility model with varied network connectivity. Right, delivery ratio for scheduled routes mobility model with limited buffer space.

SCaTR, because it utilizes mobility predictability, was not designed with random mobility in mind, but we include this scenario to illustrate that it will perform at least as well as the underlying on-demand protocol in any situation. Figure 3 illustrates performance when node speeds were varied to provide more or less connectivity in the network. SCaTR shows a higher delivery ratio than standard AODV despite the fact that it is unable to take advantage of historical information to predict future topologies. In addition, this experiment shows the benefit of additional message replication that can be provided with SCaTR. Epidemic routing has excellent delivery ratios at the expense of very high overhead. In power constrained environments, this would likely not be acceptable. It should be noted that the overhead of AODV is extremely high because it delivers so few messages. Figure 4 shows that SCaTR’s performance improves as the length of simulation increases. As the scenario time increases, delivery rates increase and signaling overhead remains constant after an initial drop. Epidemic routing quickly achieves nearly a 100% delivery rate, while SCaTR is able to achieve better than 80% after approximately 2000 seconds. Despite the fact that SCaTR takes longer than Epidemic routing to deliver messages, it does so with far less signaling. After an initial drop in signaling overhead due to low delivery rates (most packets are en route to their destination at this point), SCaTR settles at approximately 10-20 messages per delivered packet. Epidemic routing settles at approximately 38 messages per delivered packet, since each message reaches a large portion of the network.

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6

Discussion and Future Work

We have introduced the Space-Content-adaptive-Time Routing (SCaTR) framework to efficiently and effectively route data in networked environments where connectivity is intermittent. SCaTR extends on-demand routing to operate in environments where, often times, there may not be a direct route between source and destination. Thus, if the network is connected, SCaTR operates exactly as regular on-demand routing. However, if source and destination do not have a connected route, SCaTR chooses a node that is deemed closer to the destination than the source as a proxy for that destination. The proxy will either deliver the data to the destination directly, or choose another proxy closer to the destination than itself. In summary, the resulting protocol will do no worse than standard AODV in well-connected environments, and far better in partitioned networks. Through extensive simulations in environments with varying connectivity and mobility patterns, we showed that SCaTR can yield considerably higher delivery ratio with lower signaling overhead than traditional on-demand routing.

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References 1. Davis, J., Fagg, A., Levine, B.: Wearable computers as packet transport mechanisms in highly-partitioned ad-hoc networks. In: Proceedings of the International Symposium on Wearable Computing, Zurich, Switzerland, October 2001. (2001) 141–148 2. Ogier, R., Templin, F., Lewis, M.: Rfc 3684: Topology dissemination based on reverse-path forwarding (tbrpf) (2004) 3. Clausen, T., Jacquet, P.: Rfc 3626: Optimized link state routing protocol (olsr) (2003) 4. Perkins, C., Belding-Royer, E.: Rfc 3561: Ad hoc on-demand distance vector (aodv) routing (2003) 5. Johnson, D.B., Maltz, D.A.: Dynamic source routing in ad hoc wireless networks. In Imielinski, Korth, eds.: Mobile Computing. Volume 353. Kluwer Academic Publishers (1996) 6. Cerf, V., Burleigh, S., Hooke, A., Torgerson, L., Durst, R., Scott, K., Fall, K., Weiss, H.: Delay-tolerant network architecture (2004) 7. dtnrg: Delay tolerant networking research group (2006) 8. Zhao, W., Ammar, M., Zegura, E.: A message ferrying approach for data delivery in sparse mobile ad hoc networks. In: Proceedings of ACM Mobihoc 2004. (2004) 9. Mitchener, W., Vahdat, A.: Epidemic routing for partially connected ad-hoc networks (2000) 10. Lindgren, A., Doria, A., Schelen, O.: Probabilistic routing in intermittently connected networks. In: The First International Workshop on Service Assurance with Partial and Intermittent Resources (SAPIR 2004). (2004) 11. Fall, K., Hong, W., Madden, S.: Custody transfer for reliable delivery in delay tolerant networks (2003) 12. Merugu, S., Ammar, M., Zegura, E.: Routing in space and time in networks with predictable mobility (2004) 13. Spyropoulos, T., Psounis, K., Raghavendra, C.: Spray and wait: An efficient routing scheme for intermittently connected mobile networks. In: Proc. SIGCOMM 2005. (2005) 14. Leguay, J., Friedman, T., Conan, V.: Dtn routing in a mobility pattern space. In: Proc. SIGCOMM 2005. (2005) 15. Burns, B., Brock, O., Levine, B.N.: Mv routing and capacity building in disruption tolerant networks. In: IEEE INFOCOM 2005. (2005) 16. de Moraes, R., Sadjadpour, H., Garcia-Luna-Aceves, J.: Throughput-delay analysis of mobile ad-hoc networks with a multi-copy relaying strategy. In: Proc. IEEE SECON 2004: The First IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks. (2004) 17. glomosim: Global mobile information systems simulation library (2001)

Delivery Guarantees in Predictable Disruption Tolerant Networks Jean-Marc Fran¸cois and Guy Leduc Research Unit in Networking (RUN) DEECS — Institut Montefiore, B28 — Sart-Tilman University of Li`ege 4000 Li`ege, Belgium {francois,leduc}@run.montefiore.ulg.ac.be

Abstract. This article studies disruption tolerant networks (DTNs) where each node knows the probabilistic distribution of contacts with other nodes. It proposes a framework that allows one to formalize the behaviour of such a network. It generalizes extreme cases that have been studied before where either (a) nodes only know their contact frequency with each other or (b) they have a perfect knowledge of who meets who and when. This paper then gives an example of how this framework can be used; it shows how one can find a packet forwarding algorithm optimized to meet the delay/bandwidth consumption trade-off: packets are duplicated so as to (statistically) guarantee a given delay or delivery probability, but not too much so as to reduce the bandwidth, energy, and memory consumption.

1

Introduction

Disruption (or Delay) Tolerant Networks (DTNs, [1]) have been the subject of much research activity in the last few years, pushing further the concept of Ad Hoc networks. Like Ad Hoc networks, DTNs are infrastructureless, thus the packets are relayed from one node to the next until they reach their destination. However, in DTNs, node clusters can be completely disconnected from the rest of the network. In this case, nodes must buffer the packets and wait until node mobility changes the network’s topology, allowing the packets to be finally delivered. A network of Bluetooth-enabled PDAs, a village intermittently connected via low Earth orbiting satellites, or even an interplanetary Internet ([2]) are examples of disruption tolerant networks. The atomic data unit is a group of packets to be delivered together. In DTN parlance, it is called a message or a bundle; we use the latter in the following. Routing in such networks is particularly challenging since it requires to take into account the uncertainty of mobiles movements. The first method that has 

This work has been supported by the Belgian Science Policy in the framework of the IAP program (Motion P5/11 project) and by the IST-FET ANA project.

I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 167–178, 2007. c IFIP International Federation for Information Processing 2007 

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been proposed in the literature is pretty radical and proposes to forward bundles in an “epidemic” way ([3,4]), i.e., to copy them each time a new node is encountered. This method of course results in optimum delays and delivery probabilities, at the expense of an extremely high consumption of bandwidth (and, thus, energy) and memory. To mitigate those shortcomings, the epidemic routing has been enhanced using heuristics that allow the propagation of bundles to a subset of all the nodes ([5,6]). More advance heuristics have been introduced to cope with the nodes limited memory. Cache mechanisms have been proposed, where the most interesting bundles are kept (i.e. those that are likely to reach their destination soon) and the others are discarded when the cache is full ([7,8,9,10]). Few papers explore how the expected delay could be more precisely estimated (notable exceptions are [11,12]). It has been proved ([13]) that a perfect knowledge of the future node meetings allows the computation of an optimal bundle routing. This short introduction emphasizes two shortcomings: – Previous works suppose either that nodes contacts are perfectly deterministic, or that only the contact frequency is known for each pair of nodes. In this paper, we introduce a framework which generalizes those extreme cases and formalizes the nodes contact predictability. It allows one to compute the expected impact of a particular bundle forwarding strategy; – Previous works only propose bundle forwarding heuristics. In what follows, we give an example of how the above-mentioned framework can be used to find a bundle routing strategy that fulfills delivery guarantees while limiting bandwidth/energy consumption.

2

Predictable Future Contacts

The network is composed of a finite set of wireless nodes N that can move and thus, from time to time, come into contact. In the sequel, a contact between two nodes happens when those nodes have setup a bi-directional wireless link between them. A contact is always considered long enough to allow all the required data exchanges to take place1 . 2.1

Contact Profiles

We expect the mobiles motion to be predictable, yet obviously the degree of predictability varies from one network to another. Sometimes nodes motion is known in advance because they must stick to a given schedule (e.g. a network of buses) or because their trajectory can easily be modelled (e.g. nodes embedded in a satellite). Other networks are less predictable, yet not totally random: colleagues could be pretty sure to meet every day during working hours, without 1

This is a major difference with [13] which does not neglect bundle transmission times.

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Fig. 1. Contact profile and first contact distribution: example. Top: A contact profile: the height of a bar gives the probability that two nodes meet (at least once) during the corresponding 12-hour time period. Bottom: The corresponding first contact distribution; each bar corresponds to a 12-hour period.

any other time guarantee. Mobile nodes behaviour could also be learnt automatically so as to extract cyclical contact patterns. We therefore suppose that each node pair {a, b} ⊂ N can estimate its contact probability for (discrete) each time step in the near future. We call it a contact profile and denote it Cab : N → [0, 1]. In the following, we suppose the profile known for each node pair. Contact profiles can easily represent situations usually depicted in the literature: – A constant profile Cab (t) = k describes a node pair that only knows its contact frequency. For example, the profile Cab (t) = 1/30 (contact probability per day) corresponds to two nodes a and b meeting once a month on average. – Perfect knowledge of meeting times results in a profile made of peaks: ∀t ∈ N : Cab (t) ∈ {0, 1}. In practice, unknown contact profiles could be replaced by a constant function equal to zero on its domain to get a defensive approximation of their behaviour. The following sections aim at studying how bundles propagate from one node to another in a network whose nodes’ contact profiles are known. 2.2

First Contact Distribution

It is easy to deduce the probability distribution of a (first) contact at time t between nodes a and b ∈ N given their profile Cab ; we denote this distribution

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dab . Since the probability of a first contact at time t is the probability of meeting at time step t times the probability not to meet at time steps 0, 1, . . . , t − 1. We have (∀a, b ∈ N ): dab (t) = Cab (t)

t−1 

  1 − Cab (i)

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(1)

i=0

The distributions domain is N since contact profiles have been defined using discrete time steps. We extend the distributions to R to get rid of this artifact. Notice that dab is not a well-defined probability distribution since its integral over its domain is not equal to 1: two nodes might never meet. Definition 1. The first contact distribution set, C, is the set of functions2 ∞ f : R+ → R+ such that 0 f (x) dx ≤ 1. Contact profiles do not allow us to express contact interdependencies; for example, they cannot model that two nodes are certain to meet exactly once during the weekend without knowing exactly which day (if a probability of .5 is assignated to Saturday and Sunday, there is a .25 probability that the nodes will meet twice). First contact distributions have no such limitations. Therefore, when it is possible, one could find preferable to generate them directly without relying on contact profiles. Figure 1 gives an example contact profile Cab (top) and the corresponding first contact distribution dab (bottom). Notice that if a bundle is delivered directly from a to b, knowing the first contact distribution allows an easy verification of a large spectrum of guarantees, such as the average delay or the probability of delivery before a certain date.

3

Delivery Distributions

3.1

Definition

First contact distributions can be generalized to take into account the knowledge that no contact were made before a certain date. Let Dab (T, t) be the probability distribution that a and b require a delay of t time steps to meet for the first time after time step T . Since these distributions will be the building blocks that allow us to compute when a bundle can be delivered to its destination, we call them delivery distributions. Dab can directly be derived from the contact profile Cab (∀a, b ∈ N ): Dab (T, t) = Cab (T + t)

T +t−1 

  1 − Cab (i)

∀T, t ∈ N

i=T 2

As before, the domain of these functions can be extended to R+ . 2

R+ denotes the set of positive reals.

(2)

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Definition 2. The delivery distribution set, D, holds all the functions ∞ 2 f : R+ → R+ such that ∀T ∈ R+ : 0 f (T, x) dx ≤ 1. Notice the inequality. D (%/day) 60 50 40 30 25

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Figure 2 draws the Dab (T, t) distribution corresponding to the contact profile given in figure 1. Notice that the D(T, ·) functions of course belong to C (∀T ≥ 0). Notice that Dab (T, ·) is the expected delivery delay distribution for a bundle sent directly from a source a to a destination b if a decides to send it at time T . 3.2

Order Relation on Distributions

We define an order relation between first contact distributions. Intuitively, this relation allows one to compare two distributions to find which one represents more frequent or predictable contacts. A rigorous definition is given below. Definition 3. The first contact distributions d1 ∈ C is greater (or equal) than d2 ∈ C (denoted d1  d2 ) if and only if:  x  x ∀x ≥ 0 : d1 (t) dt ≥ d2 (t) dt (3) 0

0

This relation is a partial order (but not a total order as there exist d1 , d2 ∈ C such that neither d1  d2 nor d1 d2 ; see [14] for more details). It appears difficult to define a total order on C: comparing two distributions that cannot be ordered using the  relation is a matter of choice and depends on the bundle delivery guarantees one wants to enforce. The  relation is thus a least common denominator, and could be replaced in what follows with a more restrictive order definition. The worst (smallest) element of C is the ⊥ (bottom) distribution: ⊥(t) = 0 (∀t ≥ 0). The best (greatest) first contact distribution is denoted  (top): (t) = δ(t) (∀t ≥ 0); the δ symbol denotes the Dirac distribution.

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The  relation can be extended to D. For all D1 , D2 ∈ D: D1  D2 ⇐⇒ ∀T ≥ 0 : D1 (T, ·)  D2 (T, ·) The D⊥ delivery distribution is such that ∀T ≥ 0 : D⊥ (T, ·) ≡ ⊥. The definition of D follows immediately.

4 4.1

Delivery Distribution Operators The Forwarding Operator

Let Dsbd be the delivery distribution associated with the delivery of a bundle from a source node s to a destination d via node b. More precisely, if s decides to send a bundle at time T , it will reach d after a delay described by the Dsbd (T, ·) distribution. Dsbd can be computed thanks to Dsb and Dbd : Dsbd ≡ Dsb ⊗ Dbd

(4)

The ⊗ (or forwarding) operator is a function defined for all distribution pair. We have ⊗ : D2 → D:  t   D1 ⊗ D2 (T, t) = D1 (T, x) D2 (T + x, t − x) dx (5) 0

It is easy to see that this operator is associative but not commutative. Equation (5) simply states that since the total delivery delay is equal to t, if the delay to reach b is equal to x, then the delay from b to d is t − x. Equation (4) can be generalized: a bundle could be forwarded through several intermediate hops before reaching its destination. We denote Ds−d (notice the dash) the delivery delay distribution for a bundle sent from a source s to a destination d at time T ; from now on, ⊗ will thus be applied to any kind of delivery distributions. For example, the graph below depicts a simple delivery path, i.e. a sequence of forwarding nodes; the corresponding delivery distribution is also given. s

/a

/b

/d :

Ds−d ≡ Dsa ⊗ Dab ⊗ Dbd

We say that two delivery paths with a common source s and destination d are disjoint if the intersection of the set of nodes they involve is {s, d}. 4.2

The Duplication Operator

Let D s Ed be the delivery distribution associated with the delivery of a bundle d

from s to d if it is duplicated so as to follow the disjoint delivery paths described  by the distributions Ds−d and Ds−d . We have:  D s Ed ≡ Ds−d ⊕ Ds−d d

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The ⊕ (or duplication) operator is a function ⊕ : D2 → D, defined as follows:   D1 ⊕ D2 (T, t) =

   t D1 (T, x) dx D2 (T, t)+ 1− 0    t 1− D2 (T, x) dx D1 (T, t) (7) 0

The expected delay computed is that of the first bundle to reach the destination d. It is easy to see that ⊕ is associative and commutative. Operators ⊗ and ⊕ can be combined to consider more complex forwarding strategies, assigning a higher precedence to ⊗. Equation (7) is the sum of two terms. Each term is the probability that the bundle reaches the destination after a delay t using one path and that the bundle following the other path is not arrived yet. It can be proven that we have both D1 ⊕ D2  D1 and D1 ⊕ D2  D2 . This means that, contrary to what happens in deterministic networks, duplicating a bundle to send it along two paths can improve performance: it is not the case that the best path always delivers the bundle first. Figure 3 shows an example of the distributions obtained using the “duplication” operator. As expected, duplicating bundles shortens the delays and increases the delivery probability. D (%/day) 250 200 150 100 25 50 0

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Fig. 3. Duplication (⊕) operator: example. We denote D1 the delivery distribution depicted in figure 2. Let D2 be a distribution that corresponds to nodes that are certain to meet on day 9, 16 and 25. This plot depicts D1 ⊕ D2 .

4.3

The Scheduling Operator

Let D s

d d

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 . We have: chooses the best delivery strategy out of Ds−d and Ds−d

Ds

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The definition of  is straightforward. It is a function  : D2 → D such that:   D1 (T, t) if D2 (T, ·)  D1 (T, ·) D1  D2 (T, t) = (9) D2 (T, t) otherwise If s sends a bundle at time T , it is delivered using D2 (T, ·) if and only if D2 (T, ·)  D1 (T, ·). This operator is not commutative since  is not a total order: when D1 (T, ·) and D2 (T, ·) cannot be compared, D1 (T, ·) is chosen. This new operator can be combined with the other two (⊗ and ⊕) assigning it a lower precedence. The following example involves all the operators defined above. Two plain arrows leaving a node depict a duplication. Two arrows leaving a node, one of them dotted, depict a scheduling operation. The dotted arrow leads to the second argument of , emphasizing the operator’s non-commutativity. ;e s GG / b G# c 4.4

/f

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Delivery Schemes

We have defined a delivery path as a delivery strategy that only involves forwarding. A delivery scheme with source s and destination d is a general delivery strategy that allows a bundle to be delivered from s to d. It can use an arbitrary number of forwarding, duplication and scheduling operations.

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Knowing the delay distribution d ∈ C associated with the delivery of a bundle allows us to verify a large range of conditions on permissible delays or on delivery probabilities. For example, the condition  ∞ d(t) t dt ≤ dmax 0

imposes a maximum expected delay dmax , while 



1h

d(t) dt ≥ .9 0

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and 0

matches distributions delivering a bundle in less than one hour nine times out of ten, and in less than a day with a probability of 99%. We naturally impose that a condition fulfilled for a certain delivery scheme must be fulfilled for better schemes.

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Definition 4. A delivery condition C is a predicate: C : C → {true, false} iff ∀d1 , d2 ∈ C such that d1  d2 , we have C(d2 ) =⇒ C(d1 ). A condition C can be extended to a delivery distribution D ∈ D:   C(D) ⇐⇒ ∀T ≥ 0 : C D(T, ·)

6 6.1

Delivering Bundles with Guarantees Probabilistic Bellman-Ford

Algorithm 1 adapts the Bellman-Ford algorithm to predictable disruption tolerant networks. In this section, we do not allow bundle duplication. Notice that, in general, the concept of “shortest path” is meaningless since the relation is a partial order.

Algorithm 1. Probabilistic Bellman-Ford Data: d is the destination node 1 2

∀ x ∈ N \ {d} : Bx ← D⊥ ; Bd ← D ;

10

repeat stabilized ← true; forall x ∈ N do forall y ∈ N do Dxy−d ← Dxy ⊗ By ; if Bx = Bx  Dxy−d then stabilized ← false; Bx ← Bx  Dxy−d ;

11

until stabilized ;

3 4 5 6 7 8 9

Similarly to the Bellman-Ford algorithm, algorithm 1 computes, for every node n ∈ N , the best distribution leading to the destinations found so far (Bn ). This distribution is propagated to its neighbours (i.e. all the other nodes since the network is infrastructureless). Once node x receives the best delivery distribution By found by y, it computes the delivery distribution obtained if it would send the bundle directly to y, and if y would forward it according to By . The resulting distribution is denoted Dxy−d (line 6). Dxy−d is compared to the best known distribution to the destination (Bx ) by means of the  operator. If Dxy−d is better than Bx on some time intervals, Bx is updated (line 9). The algorithm terminates once no more Bx distribution is updated.

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As mentioned before, this algorithm generalizes both [15] (i.e. converges to the “shortest expected path”) and [13]3 (i.e. finds the exact shortest path in the case of perfectly predictable networks). The delivery computed by this algorithm depends on the order at which the elements of N are picked up (lines 5 and 6). In practice, it might be preferable to rely on a heuristic to choose the preferred elements first. 6.2

Guarantees

Our aim is now to find a way to deliver bundles that fulfills a given condition C as specified in definition 4, while trying to minimize the network’s bandwidth/energy/memory consumption. Ideally, the DTN is predictable enough to enforce condition C without duplicating any bundle. We thus propose to rely on algorithm 1 to find a first delivery scheme (and, thus, a first delivery distribution D1 ). If C is not fulfilled by D1 , we search for another fast bundle forwarding scheme using algorithm 1; let D2 be its delivery distribution. We then duplicate the bundle on both delivery schemes, yielding a distribution D1 ⊕ D2 . We have already pointed out that D1 ⊕ D2  D1 , thus C(D1 ⊕ D2 ) is more likely to be true then C(D1 ). This process is iterated until C is finally fulfilled; see algorithm 2. As mentioned in section 4.2, the distribution computed by the “duplication” (⊕) operator is biased if its operands are not independent distributions. To avoid this bias, we ensure that D1 and D2 are independent by forbidding D2 to rely on the nodes involved in D1 (source and destination nodes excluded, line 5). More details can be found in [14].

Algorithm 2. Constrained probabilistic delivery Data: Delivery condition C Data: Bundle source s and destination d 1 2 3 4 5 6

B ← D⊥ repeat Using nodes in N , compute D ∈ D via algorithm 1 B ←B⊕D   N ← N \ {nodes involved in D} ∪ {s, d} until C(B) or N = {s, d}

Nothing guarantees of course that there exists a way to deliver bundles that satisfies C: even an epidemic broadcasting might not suffice. 3

To be fair, this work also deals with message transmission delays, which are not considered here.

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Conclusion and Future Works

We propose to model contacts between a disruption tolerant network’s mobile nodes as a random process, characterized by contact distributions. Such a description is more general than those generally encountered in the literature. We have setup a framework that shows how such contact distributions can be combined to compute the bundle delivery delay distribution corresponding to a given delivery strategy (i.e. a description of the nodes forwarding decisions). This framework is formally defined and quite generic; it can be used to evaluate quantitatively the performance of new routing protocols. It could be expanded with new operators describing other (more subtle) forwarding schemes. A significant improvement would be to modify the framework so as to deal with bundles transmission delays. As a future work, real network traces can be analysed so as to quantify their predictability; the delivery strategies elaborated using this framework could then be compared with the heuristics proposed in the literature. To demonstrate the applicability of the framework, we have used it to build a new routing algorithm. It uses a modified Bellman-Ford algorithm adapted to DTNs and asks the source to duplicate bundles. It tries to compute a routing strategy that fulfills a given delivery condition without consuming too many resources.

References 1. Zhang, Z.: Routing in intermittently connected mobile ad hoc networks and delay tolerant networks. In: IEEE Surveys and Tutorials. Volume 8-1. (2006) 24–37 2. Burleigh, S., Hooke, A., et al.: Delay-tolerant networking — an approach to interplanetary internet. IEEE Communications Magazine 41(6) (2003) 128–136 3. Vahdat, A., Becker, D.: Epidemic routing for partially connected ad hoc networks. Technical Report TR CS-200006, Duke University (April 2000) 4. Juang, P., Oki, H., et al.: Energy-efficient computing for wildlife tracking: Design tradeoffs and early experiences with zebranet. In: ASPLOS, San Jose, CA. (October 2002) 5. Spuropoulos, A., Psounis, K., Raghavendra, C.: Single-copy routing in intermittently connected mobile networks. In: Proceedings of IEEE SECON. (October 2004) 6. Spyropoulos, T., Psounis, K., et al.: Spray and wait: An efficient routing scheme for intermittently connected mobile networks. In: Proc. of SIGCOMM’05. (2005) 7. Wang, Y., Jain, S., Martonosi, M., Fall, K.: Erasure-coding based routing for opportunistic networks. In: WDTN ’05: Proceeding of the 2005 ACM SIGCOMM workshop on Delay-tolerant networking, New York, NY, USA, ACM Press (2005) 229–236 8. Lindgren, A., Doria, A., Schel`en, O.: Probabilistic routing in intermittently connected networks. SIGMOBILE Mob. Comput. Commun. Rev. 7(3) (2003) 19–20 9. Jones, E., Li, L., Ward, P.: Practical routing in delay-tolerant networks. In: Proc. of WDTN’05, New York, NY, USA, ACM Press (2005) 237–243 10. Leguay, J., Friedman, T., Conan, V.: DTN routing in a mobility pattern space. In: Proc. of WDTN’05, New York, NY, USA, ACM Press (2005) 276–283

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11. Shen, C., Borkar, G., Rajagopalan, S., Jaikaeo, C.: Interrogation-based relay routing for ad hoc satellite networks. In: IEEE Globecom, Taipei, Taiwan (November 17-21 2002) 12. Musolesi, M., Hailes, S., Mascolo, C.: Adaptive routing for intermittently connected mobile ad hoc networks. In: Proc. of WoWMoM’05. (2005) 183–189 13. Merugu, S., Ammar, M., Zegura, E.: Routing in space and time in networks with predictable mobility. Technical Report GIT-CC-04-7, Georgia Tech. Inst. (2004) 14. Fran¸cois, J.M., Leduc, G.: Predictable disruption tolerant networks and delivery guarantees. Technical Report (arXiv:cs.NI/0612034 v1) (2006) 15. Tan, K., Zhang, Q., Zhu, W.: Shortest path routing in partially connected Ad Hoc networks. In: Proc. of IEEE GLOBECOM’03. Volume 2. (December 2003) 1038– 1042

PWave: A Multi-source Multi-sink Anycast Routing Framework for Wireless Sensor Networks Haiyang Liu1 , Zhi-Li Zhang1, , Jaideep Srivastava1 , and Victor Firoiu2 1 2

Dept. of Comp. Sci. and Eng., Univ. of Minnesota, Minneapolis, MN 55414 Advanced Information Technologies, BAE Systems, Burlington, MA 01803

Abstract. We propose a novel routing framework called PWave that supports multi-source multi-sink anycast routing for wireless sensor networks. A distributed and scalable potential field estimation algorithm and a probabilistic forwarding scheme are proposed to ensure low overhead and high resilience to network dynamics. Key properties of this framework are proved through theoretical analysis and verified through simulations.Using network lifetime maximization problem as one example, we illustrated the power of this framework by showing a 2.7 to 8 times lifetime extension over Directed Diffusion and up to 5 times lifetime extension over the energy-aware multipath routing.

1 Introduction Wireless sensor networks (WSNs) are generally deployed to support specific missions or applications such as habitat monitoring, object tracking. Traffic are generated from a number of sensing sources and collected by (any one of) a few sinks [1]. Hence data communications in WSNs exhibit multi-source, a multi-sink anycast pattern, which is fundamentally different from that in general-purpose communication networks (whether wired or wireless), where any two nodes may serve as the two ends of an end-to-end communication. In addition, WSNs often operate in challenging environments and are subject to frequent disruptions and node failures. These unique settings and constraints call for a robust routing framework for WSNs that can quickly adapt to changes in traffic pattern, network conditions and environments. Existing routing schemes (e.g., [2]) used in WSNs are either variations, or even direct adoption, of routing algorithms for general-purpose wired networks, or mobile wireless ad hoc networks (MANETs), which are typically designed using the single shortest path unicast routing paradigm1. While several multi-path routing schemes (see, e.g., [3,4,5]) have been proposed, they tend to be extension of the single shortest-path routing paradigm with use of additional paths – choice of these alternative paths is often decided based on somewhat ad hoc mechanisms. More importantly, these techniques 

1

This work was supported in part by the NSF grant CNS-0435444 and a DoD Army High Performance Computing Research Center grant. While offering some desirable local properties, the more recent geographic or trajectory-based routing paradigm is still unicast based, using “shortest distance” paths in an Euclidean or metric space. In addition, it requires some type of location information, which may not be easy to obtain.

I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 179–190, 2007. c IFIP International Federation for Information Processing 2007 

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only support single-sink configuration (i.e., unicast routing) with no direct and easy extension to support multi-source, multi-sink anycast routing. In this paper we propose a novel framework – referred to as PWave to support multisource, multi-sink anycast routing that is inherent in WSNs. Inspired by the analogy between WSNs and electric networks, PWave constructs a potential field by assigning a “potential” (analogous to “voltage” in an electric network) to each node: a source or an intermediate node routes traffic (proportionally) to neighboring nodes with lower potentials towards the sinks, which have the lowest (zero) potentials. The PWave framework is designed with strong theoretical underpinnings. First of all, the constructed potential field realizes scalable, robust, proportional multi-source, multi-sink traffic allocation that optimizes a customizable quadratic function (based on appropriate definition of “link costs”). Furthermore, it guarantees that there is no local minima (i.e. packets are never stuck in a local dead-end) and thus ensures loop-free routing. It adapts to local changes rapidly, while dampening their global impact. These features enable compact and efficient protocol design with low execution overhead. We develop a fully distributed algorithm for constructing the potential field and implement PWave using probabilistic forwarding to achieve the properties described above. PWave scales to the density of the network because only one-hop neighborhood information exchange is needed. In addition this algorithm is resilient to network dynamics in that local perturbations only have local effect. These features make PWave a suitable routing framework for WSNs. In a nutshell, the research contribution of this paper lies in the proposal of a novel routing framework that supports global optimization of custom objectives in a multi-source multi-sink anycast routing settings via fully localized computations. To the best of our knowledge, this is the first systematic routing framework for WSN with this capability. The remainder of this paper is organized as follows. We detail the PWave framework design in section 2. The potential field estimation algorithm is described in section 3, followed by the experimental evaluations in section 4. We describe related work in section 5 and conclude in section 6.

2 The PWave Routing Framework 2.1 System Model and Problem Formulation In order to formally define the PWave routing framework, we first introduce the system model, notations and assumptions. We assume that a WSN can be represented as a weighted (undirected) graph G = (N, E), where N is the set of nodes and E the edges (i.e., links) between nodes which are assumed to be symmetric. Asymmetric links are blacklisted as suggested in literatures. We use Rx,y denote the weight of an edge e connecting nodes x and y, which is strictly positive, i.e., Rx,y > 0. This weight represents some measure of unit cost for transmitting one bit of information between x and y defined in certain manners depending on the applications and routing design objectives. (We will provide some examples of Rx,y later.) Hence if Ix,y amount of data is transmitted from x to y, the total cost would be Ix,y Rx,y . For simplicity, we assume that data traffic only flow along one direction of an edge. The cost for acknowledgements is implicitly accounted for in Rx,y . Under this assumption, Ix,y denote the data rate

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flowing from x to y, we define Iy,x = −Ix,y . The same relation also holds if Iy,x is the data rate flowing from y to x. Let S ⊂ N denote the set of source nodes, and D ⊂ N be the set of sink nodes. For each s ∈ S, Is denote the data rate that may be generated by source node s. More generally, to account for potential in-network processing at intermediate nodes in a WSN that may increase or decrease the data rate flowing through them, for each x ∈ (N − D), we use Ix to denote the (internal) data generation/consumption rate at node x. Note here Ix > 0 means that data is generated at node x while Ix < 0 means that data is consumed at node x. For each node x ∈ N, we use Z(x) to denote the set of its neighboring nodes. Then the flow conservation law requires that for any node x that is not a sink, the total of data rates flowing into node x is equal to the total of data flowing out of node x plus or minus the data rate generated or consumed at node x itself. Namely,  Ix,y = Ix , x ∈ (N − D). (1) y∈Z(x)

Given the graph G representing a WSN and I := {Ix |x ∈ N}, we refer to the tuple (G, I) a network configuration NC. Given a NC, routing for a WSN can be casted as a global multi-source multi-sink anycast flow allocation optimization problem to determine the flows {Ix,y } along the links under the flow conservation constraints (1) and boundary conditions (2) such that certain global objective function F (G, I, {Ix,y |(x, y) ∈ E}) can be optimized. Single path (or minimum cost) routing that computes a minimum cost path for each source to one of the sinks is such a flow allocation scheme that allocates flows based only on the cost of the paths, but not on the flow rates. 2.2 PWave Routing Framework Intuitions and Principles. From physics, it is well known that if the energy level of a physical system is minimized, the system would be in most stable state, i.e. the system will tend to go back to this state after disturbances. A routing framework designed this way will thus be robust. With this intuition, we design our PWave routing framework to solve this optimization problem by minimizing a natural quadratic objective function (4), which is equivalent to the total energy of a corresponding electric network system (see Fig. 1). PWave solves the flow allocation optimization by assigning a potential field to the nodes in a WSN, namely, a function V : N → R+ , where R+ denote the set of nonnegative real numbers. The potential function V satisfies the following boundary conditions at the sink nodes (2) Vd = 0, d ∈ D and the flow distribution conditions at non-sink nodes Ix,y =

(Vx − Vy ) Rx,y

as well as the flow conservation constraints (1) at the non-sink nodes.

(3)

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Fig. 1. Analogy between WSNs and Resistive Electric Networks

The equation (3) specifies a localized rule on how data are routed at each node x based on local information, namely, its and its neighbors’ potentials: data only flow from node x towards one of its nodes y with lower potentials (Vy < Vx ) and the amount of data routed along the edge (x, y) is inversely proportional to R(x, y), or equivalently, proportional to gx,y := 1/Rx,y , which is referred to as the conductance of edge (x, y). The boundary conditions (2) ensure that the sink nodes have the lowest possible potential (namely, zero potential) so that data will always flow towards the sinks and are eventually “absorbed” at the sinks. As will be shown shortly, the potential field defined above guarantees the existence of a unique flow allocation {Ix,y : (x, y) ∈ E} such that it minimizes the following global objective function: E=

1 1 2 Ix,y Rx,y = gx,y (Vx − Vy )2 . 2 x,y 2 x,y

(4)

Moreover, we will see that the potential-based PWave routing framework also allows for a probabilistic routing/forwarding implementation at the packet level. More specifically, equation (3) allocation can be achieved in practice through forwarding a packet from node x to one of its lower potential neighbors y with probability given by px→y =

I x,y

Ix,i

(5)

i:i∈Z(x)∧V (i)
where Ix,i is computed from local potential values using eq.(3). In summary, the potential-based PWave routing framework enables us to achieve goals at three different levels: i) at the network-wide macroscopic level, it minimizes a natural global objective function (4); ii) at the intermediate flow level, it provides a localized rule to determine how data flows are routed; and iii) at microscopic packet level, it allows for a simple probabilistic packet forwarding mechanism to achieve both flow-level routing and network-wide design objectives.

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Example Applications. Before we leave this section, we remark that by choosing different interpretations (and thus different values) for the edge costs Rxy (or equivalently, the edge conductance, gxy ), we can use eq.(4) to optimize different design objectives in routing for WSNs. For example, if we set Rxy = 1, then data flows are approximately proportionally distributed and routed based on path hop counts. If we set Rxy equal to the data loss rate on an edge, then minimizing eq.(4) would yield a flow allocation/routing strategy that attempts to approximately equalize the data losses among different paths. As another example, if we set Rx,y as a combination of the per unit power consumed by transmitting one bit of data, denoted as CEi , and the current energy level, denoted as ENi , as follows: Ri,j =

1 CEi CEj =( + ) gi,j ENi ENj

(6)

the PWave routing framework yields a solution that approximately equalizes the power consumption among various paths to maximize the network lifetime. See [6] for detailed derivations.

3 Potential Field Estimation 3.1 Principles and Algorithm The potential field estimation problem is governed by eqs.(1, 3) under boundary conditions specified in eq. (2). The existence and uniqueness of the solution to this problem are well known from electric network theory [7]. Traditional way of solving this problem is to rewrite the problem in matrix form and compute the inverse of the matrix. This is obviously infeasible in WSN environment as centralized data collection and processing are needed. Inspired by the random walk interpretation of electric networks from [7,8], we propose an iterative and localized algorithm based on random walk games to progressively estimate the potential field . Consider experiments of random walks in graph G, illustrated in Fig. 2, where every node is marked with a fixed face value m. Starting from an arbitrary node x, a walker, Terminal

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Fig. 2. Illustration of the Random Walk Game

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initially with 0 money in hand, goes to one of its adjacent nodes with probability px,i for i ∈ Z(x). This walker keeps going in the same fashion inside the graph until it reaches one of the sink nodes, i.e. d1 or d2 . Every time the walker passes one node i, it collects a fixed amount of money equal to mi . After a large number of experiments, central limit theorem guarantees that the expectation of the total money collected by the walker, f (x), converges [8] to: deg(x) px,i f (i) + mx (7) f (x) = i=1

Obviously f (i) = 0, i ∈ D as a walker starting from a sink node immediately stops. After rewriting eqs. (1, 3) to yield the expression of the voltages, we observe that eq. (7) is equivalent to eqs. (1, 3) when px,i and mx are designed as follows: gi,x px,i = deg(x) (8) k=1 gk,x Ix mx = deg(x)

(9) gk,x This mathematical equivalence warrants that the expectation of the total money collected by a walker starting from node x converges to the potential value at node x. While this analogy provides a distributed way for individual nodes to estimate its potential value, this method is still impractical in a WSN environment because of the need for extra routing infrastructure support, due to route-back of the final collected amount, and the huge communication overhead due to required large number of experiments and long duration for each experiment. Motivated by the Relaxation Method [9], we address the issues listed above by restricting the random walk game to be within one-hop neighborhood of the starting point and apply equation (7) iteratively on all nodes until the whole network reaches equilibrium state. With this method, only local broadcasting among adjacent nodes is needed. The overall communication overhead can be reduced through adjusting of accuracy requirement. In addition, the nature of potential field being a smooth harmonic function ensures localized effect of perturbations, which we prove it in section 3.2, that further reduces potential field maintenance overhead. The pseudo code of this algorithm is presented in Algorithm 1. This pseudo code describes how the entire network reaches global equilibrium. Each node only needs to periodically execute the steps from line 12 to line 19. Though PotentialFieldConstruct only specifies a uniform absolute tolerance threshold for all nodes. In practice, non-uniform relative thresholds may be used to better reflect estimation accuracies at different potential levels. Our experimental results in section 4 show that significantly low overhead can be achieved by combining a coarsegrained estimation of the entire potential field with on-demand localized potential field refinements. k=1

3.2 Properties We now summarize the key properties of this algorithm that are of great value in ensuring efficient routing protocol design and executions in WSN. All formal proofs of these properties are described in [6] and omitted in this paper due to space constraint.

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Algorithm 1. PotentialFieldConstruct (N, I, Sinks, tolerance) Require: Set of all nodes N, array of packet generation rate I, set of sink nodes Sinks, error tolerance tolerance Ensure: The equilibrium potential field 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22:

Variables: P nodePotentials, x nodeId, for each x ∈ N if x ∈ Sinks then P [x] ← 0 else P [x] ← arbitrary non-negative number endif endfor equilibrium ← f alse while (equilibrium = true) equilibrium ← true for each x ∈ N if x ∈ / Sinks then newP ← apply eq. (7) else newP ← 0 endif if |P [x] − newP | ≥ tolerance then equilibrium ← f alse endif P [x] ← newP endfor endwhile return P

Properties: 1) Convergency:The PotentialFieldConstruct algorithm, when tolerance → 0, converges to the unique solution of the potential field estimation problem with arbitrary non-negative initial guess of potential values and in any iteration order. 2) Loop Free: Forwarding over equilibrium potential field is loop free. 3) No Local Minima: The equilibrium potential field does not have local minima in that node x has the minimum potential value among its neighbor nodes if and only if x is a sink node. 4) Proportional Traffic Allocation:Given two disjoint paths sharing only the starting and ending nodes, P ath1 and P ath2 , with corresponding effective resistances Re1 and Re2 . If Re1 < Re2, the flow rate allocated on P ath1 will be higher than that allocated on P ath2 . 5) Rich Links Attract More Traffic:When more parallel links are added to a path, higher flow rate will be allocated to that path. 6) Perturbation Spatial Decay:In a dense network, the absolute potential value changes caused by event at node x are attenuated to zero over the number of hops from node x. Property 1) guarantees the correctness of the algorithm. Property 2) and 3) enable efficient protocol design in PWave as there is no need for loop-preventing mechanisms and last resort of flooding for getting packets out of a local dead-end. Property 4) comes directly from Ohm’s Law and effectively guarantees that capable paths take more traffic. Property 5) comes from Rayleigh’s Monotonicity Law [7] and warrants that any new

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nodes or links always help to take more traffic share. Property 6)is the key property that ensures the scalability and network dynamics resilience of PWave since it guarantees that only local areas of the potential field need to be updated in react to local events.

4 Experimental Evaluations 4.1 Experimental Setup and Performance Metrics We have implemented the PWave routing algorithm and protocol in TinyOS and evaluated its performance using TOSSIM [10] simulation environment. Recognizing the asynchronous nature of PWave protocol and the lack of precise MAC timing and interference models in TOSSIM, we developed our own plug-in modules to count the protocol iteration steps. We conducted our experiments with a network setting with grid layout, denoted as NS1 and a setting with random layout, denoted as NS2. Both layouts contain 400 nodes. In NS1, the nodes are placed on grid locations of a (200m X 200m) square. In NS2, the nodes are randomly distributed in a (400m X 400m) square. The regular structure of NS1 enables better illustration of key concepts, while NS2 simulates a sensor layout closer to environmental monitoring applications.

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We evaluated the performance of PWave in terms of convergence time, communication overhead, and locality of effects of network changes (spatial effect). The convergence time is measured by the number of iterations of the PWave algorithm until equilibrium is reached (all changes in potential are below the given threshold). The overhead is measured by the total number of messages broadcasting needed to reach equilibrium. The spatial effect of a single network change is measured by the maximum number of hops from the point of change where there is a node with potential value affected by the initial network change. 4.2 Evaluation of the PWave Protocol Here we investigate the dynamic performance of PWave protocol in reacting to network dynamics. The other aspect of PWave’s performance, the initialization of the potential field, has lesser impact on the overall performance of PWave since it is a one-time cost that can be minimized through pre-computed distribution guess and amortized through long communication session. We first evaluate the locality of impact following a network event and then the sensitivity of PWave performance to the estimation accuracy and network density. Locality of Perturbations (Spatial Effect). Fig. 3(a) shows the spatial decay of a 10% data rate increase at (50,50) inside network NS1 with source at (90,90), sink at (0,0) and the radio range of 13m. We observe that this change has an exponentially spatial decay, essential for the scalability and resilience of PWave. We also observe that the event perturbation decays faster with larger radius range, which corresponds to higher network density. Thus better robustness through locality can be achieved with denser deployment of senor nodes. Fig. 3(b) shows the spatial decay effect for a network event of 1/3 link cost increase around node x at (193,190) inside NS2 network with source at (389,379), sink at (32,1) and the radio range of 25m. Observe that PWave still shows exponential decay while the event in Smallest Cost Field (SCF) propagates with constant value throughout the network. This result shows the resilience of PWave to network event. Last, observe that the link const change event is general in that it can include link outages and new nodes joining the network, and thus the above observations hold for a wide range of network events. PWave Sensitivity. Using the same setting from which Fig. 3(b) was generated, Fig. 3(c) shows the PWave and SCF performance for a range of relative accuracy requirements. First observe that SCF is insensitive to the relative accuracy requirement since SCF has constant event propagation. On the other hand, PWave shows a clear decrease in convergence time, communication overhead, and reduced spatial effect for higher levels of error tolerance. In particular, for relative tolerance greater than 0.6%, PWave incurs lower overhead and faster convergency than SCF, primarily due to the tighter affected region. From our experiments, this accuracy is sufficient for traffic allocation purpose. Using the same setting with a fixed relative accuracy of 0.6%, Fig. 3(d) shows that denser networks (larger radio range) have decreased convergence times, require smaller refreshing overhead, and have a smaller number of nodes impacted by a network change, in both PWave and SCF. But PWave incurs less overhead

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and converges much faster at higher density than SCF. We also observe that SCF’s impacted area (spacial effect) is larger than PWave. 4.3 Network Lifetime Maximization In the following we illustrate performance of PWave when applied in the context of network lifetime maximization (see section 2.2) and compare with other two state-ofthe-art protocols, Directed Diffusion [2] and Energy-aware Routing [4]. Our experiments use the NS1 network setting with four source nodes located closely at (144,135), (153,135), (153,144) and (144,144). Three sink nodes are located at (27,27), (144,27) and (27,144). All nodes in network have the same amount of battery energy level initially except sink nodes and source nodes which are set to have high energy level to guarantee that source and sink nodes will not run out of battery before intermediate nodes given that the purpose of this experiment is to evaluate the efficiency of the traffic balancing obtained from PWave and its competitors. To reduce simulation time, the battery energy level of each non-sink, no-source node is set to be able to handle(either receive or transmit) at most 10,000 packets. The life time of the network is defined as the duration from the start of experiment until the first node runs out of energy. 4

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We illustrate in Fig. 4(a) the potential field constructed by PWave under relative accuracy of 0.6% with 31 iteration rounds and 2314 message overhead, and observe its properties of monotonicity and lack of local minima. Fig. 4(b) shows that PWave achieves 2.7 to 8 times longer lifetime compared to the baseline shortest path Directed Diffusion. and up to 5 times longer lifetime over the energy-aware routing scheme. PWave achieves the major lifetime extension through better traffic balancing and take advantage of existence of multiple sinks none of the existing schemes are exploring. Fig. 5 shows the traffic distribution normalized to the total traffic. Observe that less traffic is allocated on nodes that are along longer paths from sources to sinks. For example, the sink at (27,27) received less traffic than the other two sinks due to its longer distance from the sources. While all nodes around a sink received traffic allocation, the ones that face the source nodes received more allocation due to their smaller distance to sources.

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This experiment thus verifies that PWave achieve balanced traffic allocations with more traffic allocated on shorter paths.

5 Related Work Well-studied network optimization is generally related to our work. The classic work in this area can be traced back to [11,9]. All of these work formulated the optimization problem over traditional unicast/multicast communication pattern with multiple commodity flow model. PWave address a single commodity flow between multiple sources and multiple sinks with anycast communication pattern. The key mathematical difference between these two settings lies in the end-to-end flow rate constraints. Traditional mode requires that traffic (one commodity) generated by a source must be equal to the traffic received by the corresponding destination while PWave only requires the sum of the traffic generated by all sources is equal to the sum of the traffic received by all destination nodes. Many multipath routing schemes for WSNs [3,4,5] are related to our work. But these schemes are based on heuristic alternative paths selection without clear global optimization objective. And they did not address the anycast problem. The traffic-aware routing scheme proposed in [12] is also relevant. [12] builds local potential field (using a taut elastic membrane analogy), around shortest path as an accessory to route data around hot spots. This scheme builds on top of link-state routing protocol and aims at Internet type networks. It requires substantial message exchanges and intensive computations, thus not applicable in WSNs.

6 Conclusion and Future Work In this paper, we presented a novel anycast routing framework that supports global optimization of custom objectives via a fully distributed, highly scalable and resilient protocol. Key properties of this framework are proved through theoretical analysis and verified through simulations. Using network lifetime maximization problem as one example, we illustrated the power of this framework by showing a 2.7 to 8 time lifetime

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extension over Directed Diffusion and up to 5 times lifetime extension over the energyaware multipath routing scheme proposed in [4]. As our immediate future work, we plan to pursue systematic performance evaluation in real world settings.

References 1. Intel: Intel Heterogeneous Sensor Networks Project (2004) http://www.intel.com/ research/exploratory/heterogeneous.htm. 2. Intanagonwiwat, C., etc.: Directed Diffusion: A Scalable and Robust Communication Paradigm for Sensor Networks. In: Proc. of ACM Mobicom’00. (2000) 3. Ganesan, D., etc.: Highly-Resilient Energy-Efficient Multipath Routing in Wireless Sensor Networks. ACM Mobile Computing and Communication Review 5(4) (2001) 4. Shah, R.C., Rabaey, J.: Energy Aware Routing for Low Energy Ad Hoc Sensor Networks. (In: Proc. of WCNC’02) 5. Ye, F., Zhong, G., Lu, S., Zhang, L.: GRAdient Broadcast: A Robust Data Delivery Protocol for Large Scale Sensor Networks. J. of Wireless Networks 11(3) (2005) 285–298 6. Liu, H., Zhang, Z., Srivastava, J., Firoiu, V.: PWave: Flexible Potentila-based Routing Framework for Wireless Sensor Networks. Technical report, (http://www-users.cs.umn. edu/˜hliu/pwave.pdf) 7. Doyle, P.G., Snell, J.L.: Random Walks and Electric Networks. Mathematical Assn. of America (1984) 8. Qian, H., Nassif, S., Sapatnekar, S.: Power Grid Analysis Using Random Walks. IEEE Tran. on CAD of Integrated Circuits and Systems 24(8) (2005) 1204–1224 9. Stern, T.: A Class of Decentralized Routing Algorithms Using Relaxation. IEEE Trans on Comm. (25(10)) 10. Levis, P., Lee, N., Welsh, M., Culler, D.: TOSSIM: Accurate and Scalable Simulation of Entire TinyOS Applications. In: Proceedings of SenSys’03. (2003) 126–137 11. Gallager, R.: A Minimum Delay Routing Algorithm Using Distributed Computation. IEEE Trans on Comm. (25(1)) 12. Basu, A., Lin, A., Ramanathan, S.: Routing Using Potentials: A Dynamic Traffic-Aware Routing Algorithm. Proceedings of ACM SIGCOMM’03. (2003)

Simple Models for the Performance Evaluation of a Class of Two-Hop Relay Protocols Ahmad Al Hanbali1,3 , Arzad A. Kherani2, and Philippe Nain1 1

INRIA, Sophia-Antipolis, Cedex 06902, France Dept. of Computer Science and Engineering, IIT Delhi, New Delhi, India 3 Dept. of Computer Science, Universit´e de Nice-Sophia Antipolis, France

2

Abstract. We evaluate the performance of a class of two-hop relay protocols for mobile ad hoc networks. The interest is on the multicopy two-hop relay (MTR) protocol, where the source may generate multiple copies of a packet and use relay nodes to deliver the packet (or a copy) to its destination, and on the twohop relay protocol with erasure coding. Performance metrics of interest are the time to deliver a single packet to its destination, the number of copies of the packet at delivery instant, and the total number of copies that the source generates. The packet copies at relay nodes have limited lifetime (time-to-live TTL). Via a Markovian analysis, the three performance metrics of the MTR protocol are obtained in closed-from in the case where the number of the copies in the network is limited. Also, we develop an approximation analysis in the case where the inter-meeting times between nodes are arbitrarily distributed and the TTLs of the copies are constant and all equal. In particular, we show that exponential intermeeting times yield stochastically smaller delivery delays than hyper-exponential inter-meeting times, and that exponential TTLs yield stochastically larger delivery delays than constant TTLs. Finally, we characterize the delivery delay and the number of transmissions in the two-hop relay protocol with erasure coding and compare this scheme with the multicopy scheme. Keywords: Mobile ad hoc network, Two-hop relay protocol, Erasure coding, Mobility model, Analytical model, Markovian analysis, Performance evaluation.

1 Introduction In mobile ad hoc networks (MANETs), since there is no fixed infrastructure and nodes are mobile, routes between nodes are set up and turn down dynamically. For this reason, MANETs often experience route failures and network disconnectivity, especially when the nodes are moving frequently and the network is sparse. Grossglauser and Tse [9] propose to make the mobile nodes serve as relays in order to increase the network throughput in MANETs. Their relay mechanism, called two-hop relay protocol, is simple: if there is no direct route between the source node and the destination node, the source node transmits its packets to the nearest neighbor node (called relay node) for delivery to the destination. Then, it was shown that with this protocol it is possible 

The authors acknowledge the support of the European IST project BIONETS and of the Network of Excellence (NoE) EuroNGI.

I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 191–202, 2007. c IFIP International Federation for Information Processing 2007 

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to schedule Θ(N ) concurrent successful transmissions per time-slot, where N is the number of nodes [9]. After that, it was observed that the delay experienced by the packets under this protocol is large [7,13,17]. In order to reduce this delay it is proposed in [5,13] to allow the source transmits the packet to all its neighboring nodes (not only to the nearest neighbor). In this paper we evaluate the performance of two variants of the basic two-hop relay protocol: the multicopy two-hop relay (MTR) protocol and the two-hop relay protocol with erasure coding when N is finite. Before describing these two variants that aim at improving the delay, let first introduce the nodes mobility model. All nodes move independently of each other according to the same random mobility model inside a two-dimensional bounded region. Two nodes may only communicate at certain points in time, called meeting times. The time that elapses between two consecutive meeting times of a given pair of nodes is called the inter-meeting time. The following will be assumed throughout: (A1) Transmission times are instantaneous. (A2) All inter-meeting times are independent and identically distributed (iid) random variables (rvs) with a common cumulative distribution function (CDF) G(·). Assumption (A1) will be justified in delay tolerant networks, where the incurred delay to send a packet may be very large with respect to the transmission times [1]. For Assumption(A2), in [15] it has been shown that when nodes move independently on a sphere and they have uniform (stationary) spatial distribution, the inter-meeting time distribution is approximately the exponential distribution with mean 1/λ for λt  1. Furthermore, in [8] the exponential approximation of inter-meeting times distribution was validated for the random mobility models inside a square of non-uniform spatial distribution such as the random waypoint model [3] and of uniform spatial distribution such as the random direction model [12]. Moreover, it was observed that assumption (A2) is “reasonable” as long the node transmission range is not “too large” with respect to the area where nodes move. On the other hand, if nodes are humans moving in a conference space it has been found that the inter-meeting times distribution shows a heavier-than-exponential tail [4]. In this paper, we will show the impact of considering arbitrary and exponential inter-meeting times distribution on the performance of the MTR protocol. See Section 3 for more details. We consider the scenario consisting of N + 1 mobile nodes: one source node, one destination node, and N − 1 relay nodes. The source has a single packet to transmit to the destination. We now introduce the two variants. MTR protocol. In the MTR protocol the source node may either transmit the packet directly to the destination node when both nodes come within transmission of one another, or use the relay nodes. In the latter case, if the source meets a relay node before meeting the destination, then it sends a copy of the packet to this relay node; this relay node will only transmit the packet to the destination when it comes close to it (as opposed to the epidemic routing protocol [20], also called the unrestricted relay protocol [8], where a relay node is allowed to send a copy (of its copy) to another relay node). Section 2 evaluates the performance of the MTR protocol in the case where the number of copies in the network is limited. We define, Td , the (packet) delivery delay as the first time when the destination receives the original packet or a copy, whichever arrives first to the destination. We assume

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that the packet at the source cannot be dropped before the transmission has taken place, i.e., before time Td if the packet joins the source at time t = 0. On the other hand, each copy has a time-to-live (TTL) associated with it: when a TTL expires, the relay node that holds the copy drops it. This relay node then becomes eligible to receive another copy. We assume that the source cannot transmit a copy to a relay node that already holds a copy. Two-hop relay protocol with erasure coding. The relay protocol is the basic two-hop relay protocol. A node may only transmit a piece of information either directly to the destination or to at most one relay node. In the two-hop relay protocol with erasure coding, the source introduces some redundancy in its transmissions and sends more data than the actual information. Upon receiving a piece of data (packet), the source produces n blocks of data. The transmission of the packet is completed when the destination receives the kth block, regardless of the identity of the k ≤ n blocks it has received [15,19]. More details are provided in Section 4, where the Laplace-Stieljes transform (LST) of the delivery delay and the z-transform of the number of transmissions are derived in closed-form. Note that under the above assumptions, the delivery delay obtained in our setting gives a lower-bound, as a consequence of the instantaneous transmission time. Second, the total number of copies per-packet generated gives an upper-bound. This is so because in the realistic context the source will not systematically transmit a packet to a relay node that it encounters. The rest of the paper is organized as follows: Section 2 evaluates the performance of the MTR protocol with the assumptions that the number of packet copies in the network is limited, and that inter-meeting times and TTLs are distributed exponentially. In Section 3, we show the impact of considering arbitrary distribution of inter-meeting times and constant TTLs on the delivery delay of MTR. Section 4 finds the delivery delay and the number of transmissions for the two-hop relay protocol with erasure coding, and compares with erasure coding scheme.

2 Performance of MTR Protocol with Limited Number of Copies In this section we consider the MTR protocol, with exponentially distributed node intermeeting times with parameter λ (i.e., G(t) = 1 − e−λt ), exponentially distributed TTLs with parameter μ, and where the number of copies of a packet in the network may not exceed K (including the packet at the source), where K is an arbitrary integer less than or equal to N (in [2, Sec. 3] K = N ). We recall that we only focus on the transmission of a single packet between a given source and a given destination, and that the packet at the source has no TTL (only copies have a TTL). The performance metrics of interest are: Td the time needed to deliver the packet to the destination, Cd the number of copies of the packet before the delivery to the destination, and Gd the total number of transmissions before the delivery to the destination. Note that the latter metric is related to the energy needed to deliver a packet to the destination. In this section we derive closed-form expressions for the E[Tdn ] for all n ≥ 1, P (Cd = j), and E[Gd ]. We conclude this section by showing how these results can be used to find the value of K that minimizes E[Gd ], subject to a constraint on E[Td ].

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Under the above assumptions it is easily seen that the system can be modeled as a finite-state absorbing Markov chain I = {I(t), t ≥ 0}, where I(t) ∈ {1, 2, . . . , K} gives the number of copies of the packet at time t < Td , and I(t) = a if t ≥ Td . The states 1, 2, . . . , K are the transient states and the state a is the absorbing state of I. Let q(i, j) denote the (i,j)-entry of, Q, the infinitesimal generator of I. It is easily found that q(i, i + 1) = (N − i)λ,

i = 1, . . . , K − 1,

q(i, i − 1) = (i − 1)μ, i = 2, . . . , K, q(i, i) = −[N λ + (i − 1)μ], i = 1, . . . , K − 1, q(K, K) = −[Kλ + (K − 1)μ], q(i, a) = iλ, i = 1, . . . , K, q(i, j) = 0, otherwise. The matrix Q can be written as  Q=

QK R 0 0

 ,

(1)

where QK = [q(i, j)]1≤i,j≤K , R = (q(1, a), . . . , q(K, a))T , and 0 is a K-dimensional row vector with all entries equal to 0. We will show below that for any initial state I(0), E[Tdn ], P (Cd = j), and E[Gd ] can be derived in closed-form if one has a closed-form expression for Q−1 K , the inverse of QK . We now derive Q−1 K in closed-form. We note that QK can be decomposed as QK = ˆ K + buuT , where Q ˆ K is the K-by-K sub-matrix composed of the first K rows and Q columns of the matrix QN , u = (0, · · · , 0, 1)T , and b = λ(N − K). By applying the Sherman-Morrison formula [16, P. 76] we find that ˆ −1 Q−1 K = QK −

b ˆ −1 u 1 + buT Q K

ˆ −1 uuT Q ˆ −1 . Q K K

(2)

ˆ −1 . EquivLet qK (i, j) be the (i, j)-entry of Q−1 ˆK (i, j) be the (i, j)-entry of Q K and q K alently, (2) rewrites qK (i, j) = qˆK (i, j) −

qK (K, j) λ(N − K)ˆ qK (i, K)ˆ . 1 + λ(N − K)ˆ qK (K, K)

(3)

ˆ −1 . It remains to find the entries qˆK (i, j) of Q K −1 The matrix QN was obtained in closed-form in [2, Appendix I]. On the other hand, ˆ −1 is related to Q−1 through the relation simple algebra shows that the (i, j)-entry of Q K N qˆK (i, j) = qN (i, j) +

λ(N − K)qN (i, K)qN (K + 1, j) 1 − λ(N − K)qN (K + 1, K)

(4)

for 1 ≤ i, j ≤ K. A closed-form expression for qN (i, j) was obtained in [2, Eq. 25] for any i and j.

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2.1 The Performance Metrics Given that I(0) = i, the nth order moment of Td , which is by definition equal to the time to absorption of I, is given by [14, Chap. 2, Eq. 2.2.7] n Ei [Tdn ] = (−1)n n!(αi Q−n K e) = (−1) n!

K 

(n)

qK (i, j)

(5)

j=1

for i = 1, . . . , K, where e is a K-dimensional column vector with all entries equal to 1, αi is a K-dimensional row vector with all entries equal to 0 except the ith one that is (n) equal to 1, and qK (i, j) is the (i, j)-entry of Q−n K that can be expressed in closed-form in terms of qK (i, j) which are given in (3)-(4). Given that I(0) = i, the probability distribution of the number of copies just at delivery time is [2, Sec. 3.2] Pi (Cd = j) = −jλqK (i, j),

i = 1, . . . , K.

(6)

Given that I(0) = i, the expected total number of transmissions before delivery is given by [2, Sec. 3.3]  1 Ei [Gd ] = αEi [Td ] + Ei [Cd ] + bqK (i, K) + δ , (7) 2 where α := (λN − μ), b = λ(N − K), and δ :=

1 ρ

− i − 1.

2.2 Minimizing the Consumed Energy The total number of copies that are transmitted is directly related to the energy consumed to deliver the packet to the destination. Our objective now is to use the above results to find, Kopt , the optimal value of K which minimizes the expected total number 25

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of copies that are transmitted before the delivery of the packet to the destination, subject to a constraint on the expected delivery delay, that is, min

{K:E (K) [Td ]≤C}

E (K) [Gd ],

where E (K) [Td ] := E1 [Td ] and E (K) [Gd ] := E1 [Gd ]. The superscript (K) emphasizes the dependency in the variable K. Since the integer mappings K → E (K) [Td ] and K → E (K) [Gd ] are strictly decreasing and strictly increasing, respectively, the solution to this constrained optimization problem is obtained for the smallest integer K in [1, N ] such that E (K) [Td ] ≤ C if E (N ) [Td ] ≤ C, and has no solution if E (N ) [Td ] > C. Figure 1 reports Kopt as a function of C for ρ = 1 and for three values of λ. We observe that Kopt has a sharp decay as C increases.

3 Impact of Arbitrary Inter-meeting and Constant TTLs on MTR In [4], it has been observed that the inter-meeting times distribution has heavier-thanexponential tail. This finding was the motivation to investigate the impact of arbitrary inter-meeting times distribution on the delivery delay of the MTR protocol. Throughout this section we assume that for any pair of nodes their inter-meeting times are iid with distribution G(t), and all inter-meetings are mutually independent. Let X be a generic rv with distribution G. Also define G∗ (s) = E[e−sX ] the LST of X. We assume that TTLs are constant and all equal to T . As a result, the stochastic process I is no longer a Markov process and a different approach has to be used in order to evaluate the delivery delay of the MTR protocol. For sake of simplicity we consider the case where K = N , i.e., there is no restriction on the number of packet copies in the network. For convenience we label the nodes so that node 0 is the source, node N is the destination, and nodes 1, 2, . . . , N − 1 are the relay nodes. Since K = N , we have st

Td = min(Xsd , D1 , . . . , DN −1 ),

(8)

st

where Xsd = X represents the inter-meeting time between the source and the destination, and Di is the time needed for relay node i = 1, 2, . . . , N − 1 to deliver a copy of the packet to the destination. Moreover, the rvs Xsd , D1 , . . . , DN −1 are mutually independent and the rvs D1 , . . . , DN −1 are identically distributed. Hence, P (Td < t) = 1 − (1 − G(t))P (Di > t)N −1 .

(9)

We need to determine P (Di > t). We shall actually find an approximation formula for P (Di > t) since finding an exact expression is a very difficult task, unless G(t) is the exponential distribution that is considered in the end of this section. From now on i is fixed in {1, . . . , N − 1}. We assume that the source, destination and relay node i are in steady-state at time t = 0, and that the relay node i does not hold a copy of the packet at t = 0 (only the source holds the original packet at t = 0). Let R record the number of times the relay node i has dropped a copy of the packet before it transmits it to the destination. On the event R = m + 1, let ak > 0 be the

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arrival time of the kth copy to the relay node i for k = 1, . . . , m + 1, let dk > ak be the time where the kth copy is dropped by relay node i for k = 1, . . . , m, and let em+1 be ˆ = a1 , Zk = ak+1 − dk the time where copy m + 1 reaches the destination. Define X ˆ for k = 1, . . . , m, and Z = em+1 − am+1 . Clearly, ˆ + Z1 + · · · + Zm + mT + Zˆ Di = X

(10)

ˆ Z1 , . . . , Zm , Yˆ are mutually on the event R = m + 1. Given that R = m + 1, the rvs X, independent; moreover the rvs Z1 , . . . , Zm are iid. Let D∗ (s) := E[e−sDi ] be the LST of Di . We have ˆ ˆ  −sT D∗ (s) = E[e−sX ]E[e−sZ ] (e E[e−sZk ])m P (R = m + 1). (11) m≥0

1. Evaluation of ZT∗ (s) := E[e−sZk ]: Recall that X denotes a generic inter-meeting time and that its density probability is g(·). Let hT (t) := dP (Zk < t)/dt be the probability density of Zk . The reason why we indicate the dependency on the parameter T in hT (t) will soon become apparent. If the st source does not meet the relay node i in (ak , ak +T ) then Zk = ak+1 −ak −T = X −T ,   otherwise Zk = ak+1 − ak − (T − (ak − ak )) where ak is first time the source meets the st st relay node i in (ak , ak + T ). The latter rewrites Zk = X1 + X2 − T with Xj = X for ∞ j = 1, 2. From this we deduce that ZT∗ (s) = 0 hT (t)e−st dt satisfies the following renewal equation  ∞  T ZT∗ (s) = e−st g(T + t)dt + g(u)ZT∗ −u (s)du. (12) 0

0

that ZT∗ (s)

satisfies an integral equation (of Fredholm type) from which We have shown ZT∗ (s) can be obtained numerically using standard techniques [10]. 2. Probability distribution of R: Finding the probability distribution of R is difficult. We will first assume that R is a geometric rv with parameter π = 1 − P (R = 1). It is possible to find an integral equation for π. However, for sake of simplicity, we will assume that the destination node is at equilibrium at time a1 , so that π = 1−Ge (T ), with Ge (t) t the excess probability distribution of G(t), that is, Ge (t) = (1/E[X]) 0 (1 − G(u))du. In summary, P (R = m + 1) ≈ (1 − π)π m , for m ≥ 0. Plugging the approximation of P (R = m + 1) in (11) gives that D∗ (s) ≈

ˆ

1 − π (1 − G∗ (s)) E[e−sZ ] , sE[X] 1 − πe−sT ZT∗ (s)

(13)

where ZT∗ (s) is the solution of the integral equation (12), and π = 1 − Ge (T ) (Hint: ˆ ˆ E[e−sX ] = (1 − G∗ (s))/sE[X]). It remains to evaluate E[e−sZ ]. Again, this is not ˆ an easy task. Clearly, e−sT ≤ E[e−sZ ] ≤ 1. For sake of simplicity, we will replace ˆ E[e−sZ ] by 1. This gives the final approximation D∗ (s) ≈

(1 − G∗ (s)) 1−π . sE[X] 1 − πe−sT ZT∗ (s)

(14)

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P (Di > t) is obtained by inverting (1 − D∗ (s))/s (since (1 − D∗ (s))/s =  ∞Finally, −st e P (Di > t)dt) with the help of the complex inversion formula [18, Chap. 7], 0 which yields  γ+i∞ 1 − D∗ (s) 1 ds, t > 0, (15) ets P (Di > t) = 2πi γ−i∞ s where the integration has to be performed along a line s = γ in the complex plane (in (15) i denotes the imaginary complex number). The real number γ must be chosen so that s = γ lies to the right of all singularities. Note that since P (Di > t) is a bounded function it is sufficient to take γ > 0. The approximation for FTd (t) := P (Td > t) has been computed when G(t) is an H hyper-exponential distribution, namely, G(t) = 1 − l=1 pl e−νl t , and compared to simulation results. The evaluation of the integral in (15) has been performed by using the procedure described in [6]. Numerical results are reported in Figure 2. Two hyper-exponential distributions, represented by the t-tuple (H, ν1 , . . . , νH , p1 , . . . , pN ), have been considered: (H1) (3, 0.09, 0.08, 0.07, 0.6, 0.3, 0.1) with mean 22.83sec., and (H2) (3, 0.05, 0.04, 0.03, 0.6, 0.3, 0.1) with mean 11.84sec.. The numerical results of the mathematical model were done using a C program for a network composed of one source, one destination, and N − 1 relay nodes. Let Td (app) and Td (sim) be the approximate and simulated delivery delays, respectively. Let FTd (app)(.) (resp. FTd (sim)(.)) denotes the complementary cumulative distribution function (CCDF) of Td (app) (resp. Td (sim)). Figure 2.(a) displays the mappings t → FTd (app) (t) and t → FTd (sim) (t) for the hyper-exponential distributions H1 and H2. We observe that the approximation is accurate for moderate value of N . Figure 2.(b) compares FTd (sim) (t) with the CCDF of Td in the case where the intermeeting times are exponentially distributed, where the latter distribution has been obtained in closed-form. See (16) in the following for details. We conclude from these results that Td under exponential inter-meeting times is stochastically smaller than Td under hyper-exponential inter-meeting times. This is related to the fact that the hyperexponential distribution has a fatter tail than the exponential distribution. We conclude this section by briefly addressing the simple case where the intermeeting times are distributed exponentially with rate λ, and the TTLs are constant and all equal to T . In this case we derive the closed-form expression of the delivery delay of the MTR protocol as follows T  m    (Am )k+1 − (Bm )k+1  1+ , (k + 1)! m=0 t

P (Di > t) = e

−λt

(16)

k=0

where Am := λ(t − mT ), Bm := λ[t − (m + 1)T ]+ , x designates the largest integer ≤ x, and [x]+ := max(0, x). Plugging (16) in (9) gives the CDF of Td . By comparing the CCDF of Td with constant TTL= T and with TTLs distributed exponentially with mean T , we deduced that Td with constant TTL is stochastically smaller than Td with TTL exponential.

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4 Two-Hop Relay with Erasure Coding We now consider a system where the source introduces some redundancy in its transmissions and sends more data than the actual information. The advantage of this mechanism is that it can considerably reduce the variance of the delivery delay at the expense of an increase of its expectation. One of these techniques is known as erasure coding [11]. Erasure coding with replication factor r works as follow. Upon receiving a packet of size M , the source produces n = r · M/b equal sized code blocks of size b, such that any of the k = (1 + ) · M/b code blocks can be used to reconstruct the packet. Here is a small constant, close to zero [11]. Thus, the destination is able to decode the packet if it receives k ≤ n blocks. On the other hand, when k = 1, the size of a block becomes almost equal to M , the packet size, and in this case the destination needs to receive a block in order to R(t)

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decode the packet. Thus for k = 1, the erasure coding scheme is the same as a simple multicopy scheme in which the source sends exactly one copy of a packet to n different relay nodes [19]. We will exploit this observation to compare erasure coding with the multicopy scheme in the following. Throughout this section the stochastic model is the following. There are N relay nodes, one source node, and one destination node. We assume that the source cannot send directly a packet to the destination. Inter-meeting times between any pair of nodes are exponentially distributed with rate λ, except for the pair source-destination. Under this setting, the only way to forward the data from the source to the destination is through the relay nodes. The source has only one packet to send to the destination, and the source implements the erasure coding algorithm with replication factor r and parameter k. Hence, the destination needs to receive k ≤ n of the blocks in order to decode the original packet. The forwarding mechanism used to deliver the blocks to the destination is the standard two-hop relay protocol. We assume that there is only one copy of a block in the network. A relay node can only relay one block at a time, and it is possible for a relay node that already delivered a block to the destination receives a new block when it again encounters the source. There is no TTL associated with the blocks. Let Td and Gd be the delivery delay and the total number of source-relay transmissions at the time when the kth block reaches the destination, respectively. Introduce the joint transform H(s, z) := E[e−sTd z Gd ], s ≥ 0, |z| ≤ 1. We now evaluate H(s, z). Let A(t) = (B(t), R(t)) denote a two-dimensional process such that A(t) = (m, l), 1 ≤ m ≤ n, 1 ≤ l ≤ k − 1, m + l ≤ n, if there are m relay nodes that hold m blocks (one block for each relay node) and the destination has received l blocks at time t < Td , and A(t) = a when t ≥ Td (a is an absorbing state). Under the above assumptions, {A(t), t ≥ 0} is a finite-state absorbing Markov process. Figure 3 displays the transition diagram of this Markov chain, where the y-axis represents R(t) and the x-axis represents the sum B(t) + R(t). More precisely, a point (i, l), i ≥ l, in the transition diagram means that the destination has received l blocks and that there are i − l relay nodes that hold i − l blocks (one block for each). Let ji ≥ 0 denote the number of jumps (transitions) along the horizontal line of index i ∈ {0, · · · , k − 1}. Let Si denote the total number of jumps along the lines of index less than or equal to i. Given Si−1 , the probability of making ji jumps along the horizontal line i is

−Si−1 +i)! Si −i P1 (ji ) = (N (N −Si +i)! N ji +1 , Si < n (17) (N −Si−1 +i)! 1 P2 (ji ) = (N −n+i)! N ji , Si = n, for 0 ≤ i ≤ k − 1. Let m∗ denote the index of the horizontal line such that Sm∗ −1 < n and Sm∗ = n. Conditioned on all the possible paths before absorption at {a} and given that A(0) = (0, 0), H(s, z) can be written as H(s, z) =

n−1 

···

j0 =1 ∗

×

jk−1 =0

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n−Sm∗ −2 n k−1   zN λ Sk−1 +k P1 (jl ) + ··· P2 (n − Sm∗ −1 ) s + Nλ j =1 j ∗ =0 l=0

0

 zN λ n+m∗ k−1

λ(n − l) , P1 (jl ) s + Nλ s + λ(n − l) ∗ l=m

m −1

(18)

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We now evaluate theexpectation and the variance of Td for different values of k, n, and N . Let σTd := var(Td )/E[Td ] denote the normalized standard deviation of Td . As noted earlier, erasure coding when k = 1 is similar to the multicopy scheme. Table 1 shows that E[Td ] increases with k and that σTd decreases with k. For instance, for N = 20 and n = 10 when k increases from 1 to 5 E[Td ] increases by a factor of 3 while σTd decreases by a factor of 7.5, thereby showing that erasure coding has a much lower variability than the multicopy scheme. A similar result was found in [19] under the assumption that the source instantaneously transmits all its n blocks to n different relay nodes. Table 1. Erasure coding (k > 1) vs multicopy scheme (k = 1) for different value of n and N (N, n) (20,10) (40,10) k 1 2 5 1 2 5 E[Td ] (sec.) 31.51 42.04 96.69 22 33.7 79.76 σTd 8.7 4.9 1.17 2.01 1.38 0.63

We conclude this section by investigating the behavior of TN∗ (s) := E[e−sTd ], the LST of Td , as N is large. We observed that as N becomes large the most probable path (MPP) is where all n blocks are first transmitted to n relay nodes, and then these relay nodes start to deliver these blocks to the destination. Further, it is easy to see that as N is large the system has a deterministic path MPP with probability one. Therefore, TN∗ (s) ≈

 N λ n k−1

λ(n − l) s + Nλ s + λ(n − l)

(19)

l=0

5 Concluding Remarks In this paper, we have studied a class of two-hop relay protocols. The interest was on the multicopy two-hop relay (MTR) protocol and on the two-hop relay protocol with erasure coding. Closed-form expressions have been derived for nth order moment of the time to deliver a packet to its destination, the distribution of the number of copies at delivery, and the expected total number of copies generated before delivery in the case where copies have limited lifetime (TTL) and where the number of copies in the network is limited. Also, We investigated the impact of arbitrary inter-meeting times distribution and constant TTLs on the delivery delay of the MTR protocol. In particular, we show that exponential inter-meeting times yield stochastically smaller delivery delay than hyper-exponential inter-meeting times. Finally, for the two-hop relay protocol with erasure coding the joint generating function of the delivery delay and of the number of transmissions was derived in closed-form. By analyzing these results, we found that the delivery delay in the case of erasure coding has much lower dispersion than the delivery delay of the multicopy scheme. As future work, we will study the delay when there are multiple sources with multiple packets to transmit to a set of destinations and where the relay nodes may have different mobility.

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References 1. Delay Tolerant Research Group, http://www.dtnrg.org. 2. A. Al Hanbali, P. Nain, and E. Altman, Performance of Two-hop Relay Routing Protocol With Limited Packet Lifetime, Proc. of Valuetools 2006, Pisa, Italy, Oct. 2006. 3. C. Bettstetter, H. Hartenstein, and X. Prez-Costa. Stochastic Properties of the Random Waypoint Mobility Model. ACM/Kluwer Wireless Networks, Special Issue on Modeling and Analysis of Mobile Networks, vol. 10, no. 5, pp. 555-567, Sept. 2004. 4. A. Chaintreau, P. Hui, J. Crowcroft, C. Diot, R. Gass, and J. Scott, Impact of Human Mobility on the Design of Opportunistic Forwarding Algorithm, Proc. of INFOCOM 2006, Barcelona, Spain, Apr. 2006. 5. R. De Moraes, H. Sadjadpour, and J. Garcia-Luna-Aceves, Throughput-Delay Analysis of Mobile Ad-hoc Networks with a Multi-Copy Relaying Strategy, Proc. of IEEE SECON, Santa Clara, CA, Oct. 2004. 6. H. Dubner and J. Abate, Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform, Journal of the ACM, Vol. 15, No. 1, pp. 115-123, Jan. 1968. 7. A. El Gamal, J. Mammen, B. Prabhakar, and D. Shah. Throughput-Delay Trade-off in Wireless Networks Proc. of INFOCOM 2004, Hong Kong, Apr. 2004. 8. R. Groenevelt, P. Nain, and G. Koole, The Message Delay in Mobile Ad Hoc Networks, Proc. of Performance 2005, Juan-les-Pins, France, October 2005. Published in Performance Evaluation, Vol. 62, Issues 1-4, Oct. 2005, pp. 210-228. 9. M. Grossglauser and D. Tse, Mobility Increases the Capacity of Ad hoc Wireless Networks, IEEE/ACM Transactions on Networking, Vol. 10, No. 4, Aug. 2002, pp. 477-486. 10. S. G. Mikhlin, Integral Equations. Pergamon Press, Oxford, 1964. 11. M. Mitzenmacher, Digital Fountains: A Survey and Look Forward, Proc. of IEEE Information Theory Workshop, TX, USA, Oct. 2004. 12. P. Nain, D. Towsley, B. Liu, and Z. Liu, Properties of Random Direction Models Proc. of INFOCOM 2005, Miami, FL, USA, Mar. 2005. 13. M. J. Neely and E. Modiano, Capacity and Delay Tradeoffs for Ad-Hoc MobileNetworks, IEEE Transactions on Information Theory, Vol. 51, No. 6, June 2005. 14. M. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press, 1981. 15. E. Perevalov and R. Blum, Delay Limited Capacity of Ad hoc Networks: Asymptotically Optimal Transmissiom and Relaying Strategy, Proc. of INFOCOM 2003, San Francisco, USA, Apr. 2003. 16. W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, 1988. 17. G. Sharma, R. Mazumdar, and N. Shroff Delay and Capacity Trade-offs in Mobile Ad Hoc Networks: A Global Perspective Proc. of INFOCOM 2006, Barcelona, Spain, Apr. 2006. 18. M. R. Spiegel, Schaum’s Outline of Theory and Problems of Laplace Transforms. McGrawHill, New York, 1965. 19. Y. Wang, S. Jain, M. Martonosi, and K. Fall, Erasure-coding based routing for opportunistic networks Proc. of SIGCOMM Wokshop on DTN, Philidelphia, PA, USA, Aug. 2005, 20. X. Zhang, J. Neglia, J. Kurose, and D. Towsley, Performance Modeling of Epidemic Routing Proc. of NETWORKING 2006, Coimbra, Portugal, May 2006.

Maximum Energy Welfare Routing in Wireless Sensor Networks Changsoo Ok1, Prasenjit Mitra2, Seokcheon Lee3, and Soundar Kumara1 1

The Department of Industrial Engineering, The Pennsylvania State University, University Park, PA 16802, USA {cuo108,skumara}@psu.edu 2 College of Information Sciences and Technology, The Pennsylvania State University, University Park, PA 16802, USA [email protected] 3 The School of Industrial Engineering, Purdue University, West Lafayette, IN 47907-20232, USA [email protected]

Abstract. Most routing algorithms for sensor networks focus on finding energy efficient paths to prolong the lifetime of sensor networks. As a result, the sensors on the efficient paths are depleted quickly, and consequently the sensor networks become incapable of monitoring events from some parts of their target areas. In many sensor network applications, the events have uncertainties in positions and generation patterns. Therefore, routing algorithms should be designed to consider not only energy efficiency, but also the amount of energy left in each sensor to avoid sensors running out of power early. This paper introduces a new metric, called Energy-Welfare, devised to consider average and balance of sensors’ remaining energies simultaneously. Using this metric, we design the Maximum Energy Welfare Routing algorithm, which achieves energy efficiency and energy balance of sensor networks simultaneously. Moreover, we demonstrate the effectiveness of the proposed routing algorithm by comparing with three existing routing algorithms. Keywords: Sensor Network, Distributed algorithm, Energy aware routing, Energy Welfare, Social welfare, Energy balance.

1 Introduction Sensor networks report predetermined events or transmit sensed data to the base station for further analysis [1, 2]. The sensors contain a fixed amount of stored power and the process of sending data consumes some of that stored power. It is desirable that the sensors run as long as possible. In this work, we propose a routing algorithm that attempts to route messages efficiently so as to maximize the life of a sensor network. Consequently, the design of the routing algorithm for sensor networks should also incorporate the following factors [2]. z Due to sensors’ limited power, the routing algorithm should have a design to allow finding efficient paths to prolong the lifetime of the sensor network. I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 203–214, 2007. © IFIP International Federation for Information Processing 2007

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z However, it is inevitable for most energy efficient routing algorithms to drive some sensors, which are close to the base station or on energy efficient paths, drained power quickly. As a result, the sensor networks become unable to detect events from regions where all sensors are nonfunctioning. Thus, in the sensor networks, data traffic should be dispersed and distributed over the whole network to extend its lifetime. z Although most existing routing algorithms assume that events are generated uniformly at each sensor, events could occur randomly [3], uniformly [4] over the target area, or repeatedly [5] at a specific part of the target area. Event patterns can change from one type to another over time. Therefore, the routing algorithm should be sufficiently robust for diverse event generation functions. This problem can be addressed by routing so as to utilize the energy uniformly over the entire sensor network. z In addition, a sensor network can consist of a large number of nodes for which a central control architecture does not apply. Therefore, the routing algorithm should adopt a local decision making scheme. Although the literature includes several routing algorithms, such as direct communication approach, hierarchical routing methods [6, 7], self-organized routing algorithm [4], and the other routing algorithms [8], little evidence exists for effectiveness and efficiency of these algorithms with respect to the considerations mentioned earlier.

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Fig. 1. An explanatory example for Energy Welfare Routing algorithm: Node 1 routes data to a path to maximize an Energy Welfare (Average×Equality) of sensor 1 and 2

We assume that the neighbors only get the information about the energy left in each neighbor and the energy required to transmit to the base station from that neighbor periodically. Individual sensors forward messages to neighbors that they think are on the “best” route to the base station. The determination of the optimal route is difficult because the individual sensors do not have the information about the

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dynamic topology of the entire network and the dynamic energy balances of each node on the network. This study proposes a new heuristic metric, called Energy Welfare, to achieve the efficiency and balance of energies of sensors simultaneously. Based on this metric, we propose a localized routing algorithm, the Maximum Energy Welfare (MaxEW) routing, to accomplish the two objectives. Figure 1 gives a simple example of the MaxEW routing. Ei and eij represent the residual energy of sensor i and energy required to transmit from node i to node j respectively. Sensor 1 has two paths to reach to the base station. Path 2 is more energy efficient than Path 1. However, if sensor 1 keeps using path 2, sensor 2 will run out its power while sensor 1 has sufficient energy. In MaxEW, sensors can avoid the traffic concentration to a sensor by using a metric, Energy Welfare (Average Equality), as a decision criterion. The Equality is in inverse proportion to the difference between energy levels of sensor 1 and 2. Based on the metric, sensor 1 chooses path 1 which causes higher energy welfare. The rest of this paper has the following organization: Section 2 presents the details of the considered sensor network. Section 3 defines energy equality and the welfare of sensor network as new metrics. After describing the details of the maximum energywelfare routing algorithms in Section 4, Section 5 presents extensive simulation results, and Section 6 details conclusions.

×

2 Sensor Network Model With n homogenous sensors randomly and uniformly distributed over a target area, every sensed data must be sent to the base station. Each sensor has limited battery power. Sensors can control their respective transmission power for minimal consumption to transmit to a destination [6, 7] and they have discrete adjustable transmission power levels [9-12]. This ability is necessary to allow the routing algorithm to maximize sensor networks’ operational times. Therefore, sensors can send data to either a neighbor or the base station directly, according to their routing policies [4, 6, 7]. The details of the problem are: 2.1 Energy Consumption Model Each sensor uses a fixed transmission power for communicating with its neighboring sensors while each sensor transmits data to the base station. The neighboring distance is defined as the maximal reachable distance with the fixed transmission power for neighboring sensors. For a given sensor the sensors within its neighboring distance are its “neighboring sensors” or “neighbors”. In this scheme, each node can be aware of the current energy level of its neighbors or energy required to transmit from its neighboring nodes to the base station by anticipating and/or eavesdropping data from the neighbors. Generally, sensors use their energy when they sense, receive and transmit data. However, the amount of energy consumption for sensing is unaffected by the routing algorithm and only a small difference exists between the power consumption of idle and receiving modes [13]. Therefore, consideration is only energy consumption by

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transmission in the design of the routing algorithms to maximize the lifetime of the sensor network. By normalization of the radio characteristic constant and the size of sensed data [4], the energy consumption model is simplified to E=d2, where E and d are the required energy and the transmission distance respectively. 2.2 The Lifetime of Sensor Network Validating the effectiveness of the proposed MaxEW routing algorithm uses the lifetime of sensor network as the performance measure [4, 6, 8, 11]. The definition of lifetime of a sensor network is the time or number of rounds that occur until the first node or a portion of nodes become incapable, due to energy depletion, of sending data to the base station directly or indirectly via its neighbors [4, 6, 8, 11, 14]. The portion (number of depleted nodes) can vary depending on the context of the sensor networks. In this paper, the lifetime of a sensor network is the number of rounds until the first (L1), 10% (L10), or 20% (L20) node(s) expend all their power [8, 11]. 2.3 Event Generation Functions For evaluation purposes, many previous studies of routing algorithms assumed that all sensors have uniform data or event generation rates [4, 6, 7]. In infrastructure monitoring applications, each sensor performs a sensing task every time, T, and has a homogeneous event generation function. However, in many sensor network applications, this assumption becomes unrealistic. In a monitoring application for the migration of a herd of animals, the animals might move along a path in the target area repeatedly [5]. While, in the case of forest fire detection, events can occur rarely and randomly over the target area [3]. Furthermore, some event generation functions can be a combination of uniform, random, and repeated types. Therefore, more reasonable is the consideration of several event types for evaluation of routing algorithms. The results section demonstrates that our algorithm is robust for the different types of event generation functions.

3 Energy Equality and Welfare To keep detecting events at an unknown position in a target area for as long as possible, routing algorithms should have a design to enable finding efficient paths, and, at the same time, prevent a particular set of sensors from being depleted early by a concentration of data traffic. In other words, the routing algorithms must achieve an energy balance for sensor networks while guaranteeing that sensors use their energies efficiently. Designing the routing algorithm first required a new measure for considering energy balance of sensor networks, as well as energy efficiency of routing algorithms. For this purpose, two definitions of Energy-Equality (EE) and EnergyWelfare (EW) apply.

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3.1 Energy-Equality (EE) To measure how well energy-balanced a sensor network is, we define the EnergyEquality (EE) of a given sensor network is Equation (1) and (2):

EE ( t , ε ) = 1 − I N ( t , ε ) IN

⎡1 (t , ε ) = 1 − ⎢ n ⎣⎢

∑

i∈ N

⎛ E i (t ) ⎞ ⎜⎜ E ( t ) ⎟⎟ ⎝ ⎠

1− ε

.

(1)

1

⎤ 1− ε . ⎥ ⎦⎥

(2)

I N (t , ε ) is the inequality(explained below) of the sensor’s residual batteries at

time, t. N and εare the set of nodes in the sensor network and the inequality aversion parameter. n and Ei(t) are the number of sensors and the remaining energy of sensor, i, at time, t, respectively. Basically, the derivation of the energy inequality index, I N (t , ε ) , is from the Atkinson inequality index [15]. Social scientists use the index to measure the inequality among entities with respect to their income. The aversion parameter ε reflects the strength of society’s penalty for inequality, and can take values ranging from zero to infinity. When ε equals zero, no penalty for inequality accrues. As ε rises, society penalizes inequality more. The values of ε that are typically used include, 1.5 and 2.5 [16, 17]. This aversion parameter provides a flexibility to apply this metric to diverse sensor network applications. 3.2 Energy-Welfare (EW) A drawback exists for only considering energy balance of a sensor network. If a routing algorithm only pursues the energy balance without considering energy efficiency, sensors’ residual energies might converge to a lower value. That is, sensors possibly use their energy in an inefficient way to achieve the energy-balance of the sensor network. Therefore, Energy-Welfare (EW) is the consideration of energy efficiency and energy balance of sensor networks simultaneously. EW is a simple form of weighting the average of sensors’ residual energies by EE. We can calculate EW using equation (3).

EW (t ) = E (t ) × EE (t , ε ) .

(3)

The equation for EW has the same form as Atkinson welfare function [18]. The EW is high where the average and equality of sensors’ remaining battery power are both high. A low average, or EE, leads to a low EW. Therefore, the EW is an appropriate metric to design a routing algorithm that improves sensor networks with energy efficiency and energy balance perspectives. Additionally, since a sensor

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network having a high EW, can monitor unknown position events for a long time, the EW has consideration as the preparedness of sensor networks for upcoming events.

4 Maximum Energy Welfare (MaxEW) Routing In this paper, we assume that each sensor uses a fixed transmission power for communicating with its neighboring nodes. To send a message from a sensor to the base station the total transmission power required is minimized if the sensor communicates directly with the base station. The sensors are aware of the minimum transmission power required to send a message to the base station and the current battery level of its neighbors. The basic idea of the proposed routing algorithm is simply to use a path which maximizes the EW of the sensors. When a node i needs to send data to the base station, it can transmit data to the base station directly or route the data to one of its neighbors (Ni). For evaluating these alternatives, node i calculates the EW of a local society which consists of its neighbor and itself for each alterative. That is, the node can anticipate the residual energies of its neighboring nodes and itself when the data is routed according to its decision as in (4).

{E (t ) : j ∈ N j

+ {i}} → {E j (t + 1) : j ∈ N i + {i}} . Di ( t )

i

(4)

Also, this node can calculate the EWij of these expected residual energies, Ej(t+1), for each decision, Di(t), by (5). By comparing these expected EWs, the node routes data to the path allowing the maximum EW of the local society, Ni+{i}.

EWij (t + 1) = E (t + 1)(1 − I N (ε ) (t + 1) ) .

(5)

Through this decision making scheme, MaxEW tries to maximize the energy welfare of the entire sensor network. In MaxEW, each sensor keeps a small size routing table only for its neighboring nodes. The routing table contains node identification number, minimum transmission power to the base station, and available energy, for each neighbor node. The details of the algorithm are: Initialize routing table. During the setup period, each sensor finds its minimum transmission power to the base station. Then, each sensor broadcasts a setup message to neighboring nodes with a pre-set transmission power. This setup message includes node ID., minimum transmission power to the base station, and available energy. Every node receiving this broadcast message registers the transmitting node as one of its neighbors. Since all nodes have an identical neighbor distance, two nodes within the neighbor distance are neighbors to each other. After the setup period, all sensors initialize their routing tables.

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Algorithm 1. MaxEW routing algorithm (at node i and time t)

∈

For all j Ni+{i} do If j = i then For all k Ni+{i} do If k = i then Ek(t+1) = Ek(t) - TEBk Else Ek(t+1) = Ek(t) End If End For Else For all k Ni+{i} do If k = i then Ek(t+1) = Ek(t) - TENk Else If k = j then Ek(t+1) = Ek(t) – TEBk Else Ek(t+1) = Ek(t) End If End For End If Compute EWij by (4) End For Choose J = ArgMax EWij and route data

∈

∈

j∈N i +{ BS }

(

)

Update routing table. A change of a neighbor’s energy level should be reflected in the routing table. When a sensor transmits data, all of its neighbors receive this data and get the current battery level of the transmitting sensor. As a result, whenever a sensor’s battery level changes, all routing tables including the corresponding sensor information are updated. Localized routing decision. Based on their routing tables, every node makes a local routing decision. Algorithm 1 gives a high-level description of the MaxEW algorithm of node i, at time, t. TEBk and TENk are the required transmission energies from node, k, to the base station and neighboring nodes, respectively. Also, EWij is the expected energy welfare of Ni +{i} when node i routes data to node, j. Based on this algorithm, node i selects J as the best candidate for transmitting data to the base station without considering whether J sends data directly to the base station or not. If the selection is that node i itself is the best node, it sends the data to the base station, finishing the routing process. Otherwise, the data is routed to node J and J performs the same process. This process continues until the base station receives the data. This localized decision making process results in a monotonic increase of EW because the best candidate can have a better indirect path than direct transmission.

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Base station ni nj

nk Routing path Possible path

Fig. 2. An example routing path: ni sends data to nj, nj to nk, then nk sends to the base station directly

Fig. 2 shows how the MaxEW algorithm operates over a sensor network. For a given data, ni chooses nj among several possible routes. After the data passes to nj, energy level of ni changes and the routing table of nj also changes. nj performs the same process sequentially. In the figure, nk sends data to the base station directly because the transmission of nk, itself results in the maximum EW of nk’s local society compared to other neighbors. MaxEW guarantees elimination of loops in any routing path. In MaxEW, a sensor routes data to a neighbor only if the neighbor incurs more energy welfare than the sensor itself. As this routing mechanism continues, the expected energy welfare of the original node is apparently greater than that of the next down-stream node. Therefore, MaxEW always assures finding a routing path to the base station without loops.

5 Experimental Results In this section, several experimental results validate the effectiveness of the MaxEW algorithm. The comparison of the algorithm is with three other algorithms discussed in [4, 7]: Direct Communication (DC), Minimum Transmission Energy (MTE), and Self-Organized routing (SOR). In DC, every sensor simply transmits data directly to the base station without considering any energy-efficient indirect path. MTE and SOR consider indirect routing to save sensor power but make routing decisions based on energy efficiency only. The MaxEW algorithm tries to achieve an energy balance of the network by maximizing the EW of a local society in a decentralized manner. Experimental results show that this approach is valid for extending the lifetime of sensor networks and robust for different event. The experiments use a sensor network in which 100 nodes have random and uniform deployment in a 100m×100m square area with the base station located at (50, 150)(see Fig. 3). In the sensor network, sensors have an initial battery level of 250,000. The initial energy levels are established by determining the amount of energy needed for the farthest node to transmit data to the base station 100 times with DC and also used in [4]. To discuss the effect of different event generation types on the lifetime of

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a sensor network, performed simulations uses uniform, random, and repeat event generation functions. In the case of the random distribution, 25% of sensors have events randomly occurring in each round. While, for the repeat events, the assumption is that sensors from (0, 0) to (50, 50) incur repeated events. Because a sensor network is generated randomly, 100 repeated experiments for each condition provides an average of the results. Lastly, neighbor distance of sensors (for MTE and MaxEW) and the aversion parameter ε (for MaxEW) have settings of 15m and 2.5 respectively. Table 1. Lifetime (L1, L10, L20) for Direct, MTE, SOR, and MaxEW with Uniform, Random, and Repeat Events

Direct MTE SOR MaxEW

L1 105.3 14.4 28.7 202.5

Uniform L10 123.4 67.1 145.9 258.3

L20 142.3 115.5 109.9 268.9

L1 492.7 74.6 111.3 1012.7

Random L10 L20 618.1 717.2 337.4 581.1 562.9 771.4 1239.9 1346.7

L1 107.8 30.0 154.1 685.6

Repeat L10 L20 145.8 193.3 223.7 415.6 316.9 418.2 970.6 1020.6

Table 1 gives the result for the lifetime of sensor network (L1, L10, L20) for Direct Communication, MTE, SOR, and MaxEW algorithms with three different event generation types. As shown in Table1, MaxEW shows a dominant performance compared with Direct, MTE and SOR over the time. Especially, in the case of L1, MaxEW gives approximately two to eight times better performance than the others. Fig. 4 shows how well MaxEW achieves the energy balance of sensors over the network. As discussed in [7], in the Direct (Fig. 4(a)), SOR (Fig. 4(c)) and MTE (Fig. 4(b)) routing scheme sensors far away and close to the base station ran out their energies around 150 round. While, in MaxEW, all sensors remain live and even have sufficient energy for responding upcoming events (Fig. 4(d)). Also notable is that Direct, MTE, and SOR missed some events during the first 150 rounds. However, MaxEW guaranteed that all data is transmitted to the base station for the same period.

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Fig. 5 shows the routing paths for four algorithms with repeated events in the regions from (0, 0) to (50, 50). In the case of Direct, MTE, and SOR, data traffic concentrates in specific sensors which have location in the region or on the efficient path. On the other hand, MaxEW tries to dissipate energy usage over the whole network to achieve energy balance. As a result, MaxEW can keep all sensors operating for as long as possible.

6 Conclusion and Future Works Sensor networks should be able to achieve energy balance as well as energy efficiency. Most energy-aware routing algorithms are only concerned about energy efficiency. This paper has presented a performance measure, called Energy Welfare, to consider energy balance and efficiency of sensor networks simultaneously. Based on this metric, the proposal is for a Maximum Energy Welfare (MaxEW) routing algorithm. We demonstrate the superiority of this routing algorithm to Direct Communication, MTE, and SOR with a lifetime metric, generally accepted for evaluation of routing algorithms. Additionally, from the experimental results, the conclusion is that MaxEW is robust for several event generation functions. To build the metric EW and MaxEW algorithm, we here use the Atkinson welfare function and set the inequality aversion parameter to 2.5. Many alternative welfare functions are available in social science, and this inequality aversion parameter is tunable. In the future, we will apply alternate social welfare functions and different aversion parameters to enhance our results. Currently, we used three types of event generation function for evaluation of our routing algorithm. Future work will involve development of more diverse and detailed event generation functions. In addition, we can consider a general multi-hop communication scenario where only a few sensors can communicate with the base station. In this scenario, the required transmission energy from a sensor to the base station can be calculated by the number of hop to the base station. As a future work, we will investigate how MaxEW works well in the general multi-hop scenario. Acknowledgments. This work was supported in part by NSF under the grant NSFSST 0427840. Any opinions, findings, and conclusions or recommendations presented in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation.

References 1. D. Estrin, R. Govindan, J. Heidemann, and S. Kumar, Next century challenges: scalable coordination in sensor networks, Proceedings of the 5th annual ACM/IEEE international conference on Mobile computing and networking, Seattle, Washington, United States, 263270 (1999). 2. I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, A survey on Sensor Networks, IEEE Communications Magazine, 38(8), 102-114 (2002).

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3. D. Braginsky and D. Estin, Rumor Routing Algorithm for Sensor Networks, the proceedings of the first Workshop on Sensor Networks and Applications (WSNA), 22-31 (2002). 4. A. Rogers, E. David, and N. R. Jennings, Self-organized routing for wireless microsensor networks, IEEE Transactions on Systems, Man and Cybernetics, Part A, 35(3), 349-359 (2005). 5. Z. Butler and D. Rus, Event-based motion control for mobile-sensor networks, IEEE Pervasive Computing, 2(4), 34-42 (2003). 6. S. Lindsey, C. Raghavendra, and K. M. Sivalingam, Data Gathering Algorithms in Sensor Networks Using Energy Metrics, IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, 13(9), 924-935 (2002). 7. W. R. Heinzelman, A. Chandrakasan, and H. Balakrishnan, Energy-Efficient Communication Protocol for Wireless Microsensor Networks, Proceedings of the 33rd Hawaii International Conference on System Sciences - 2000, (2000). 8. J. Chang and L. Tassiulas, Maximum Lifetime Routing in Wireless Sensor Networks, IEEE/ACM TRANSACTION ON NETWORKING, 12(4), 609-619 (2004). 9. J. Wanger and R. Cristescu, Power Control for Target Tracking in Sensor Networks, 2005 Conference on Information Sciences and Systems, The Johns Hopkins University, (2005). 10. R. Ramanathan and R. Rosales-Hain, Topology Control of Multihop Wireless Networks using Transmit Power Adjustment, INFOCOM 2000, 404-413 (2000). 11. H. Zhang and J. C. Hou, Maximizing α-Lifetime for Wireless Sensor Networks, SenMetrics 2005, 70-77 (2005). 12. R. Wattenhofer, L. Li, P. Bahl, and Y. Wang, Distributed topology control for power efficient operation in multihop wireless ad hoc networks, INFORCOM 2001, Anchorage, AK, USA, 1388-1397 (2001). 13. M. Stemm and R. H. Katz, Measuring and reducing energy consumption of network interface in hand-held devices, IEICE Transactions on Communications, E80-B(8), 11251131 (1997). 14. S. R. Gandham, M. Dawande, R. Prakash, and V. S., Energy Efficient Schemes for Wireless Sensor Networks with Multiple Mobile Base Stations, Proceedings of IEEE Globecom 2003, 377-381 (2003). 15. A. B. Atkinson, On the measurement of inequality, Journal of Economics Theory, 2(3), 244-263 (1970). 16. D. A. Seiver, A note on the measurement of income inequality with interval data, Review of Income and Wealth, 25(2), 229-233 (1979). 17. J. G. Williamson, Strategic wage goods, prices, and inequality, American Economic Review, 67(2), 29-41 (1977). 18. A. K. Sen and J. E. Foster, On Economic Inequality, (Oxford: Clarendon Press, 1997).

Analysis of Location Privacy/Energy Efficiency Tradeoffs in Wireless Sensor Networks Sergio Armenia1 , Giacomo Morabito2 , and Sergio Palazzo2 1

2

CNIT - Research Unit of Catania, Italy [email protected] Universita’ di Catania, DIIT, V.le A.Doria, Catania, Italy [email protected], [email protected]

Abstract. In this paper an analytical framework is proposed for the evaluation of the tradeoffs between location privacy and energy efficiency in wireless sensor networks. We assume that random routing is utilized to improve privacy. However, this involves an increase in the average path length and thus an increase in energy consumption. The privacy loss is measured using information theory concepts; indeed, it is calculated as the difference between the uncertainties on the target location before and after the attack. To evaluate both privacy loss and average energy consumption the behavior of the routing protocol is modeled through a Markov chain in which states represent the nodes traversed by a packet in its way to the sink. The analytical framework can be used by designers to evaluate the most appropriate setting of the random routing parameters depending on the privacy and/or energy efficiency requirements.

1

Introduction

It is well known that wireless networks have serious privacy problems. This is mainly because of the broadcast nature of the radio channel that allows all stations in proximity of the sender to overhear the frames sent. Even if network devices make use of encryption algorithms, confidentiality is usually provided for the data field only, whereas the header/tail fields remain in plain text. Therefore, given that during the normal activity there are frequently packets sent using broadcast address as destination, an eavesdropper can receive and process them without any effort and thus can obtain information about the sender. This, joined to the fact that wireless devices usually have a fixed address, gives the attackers the possibility to link device address to user identity or to device position as well to the type of application utilized. In wireless sensor networks (WSNs) the above problems are amplified and new issues arise. In fact, WSNs are based on the wireless multihop communication paradigm and therefore, eavesdropping attacks can be accomplished more easily. Furthermore, WSN applications are pervasive by nature and as a consequence, a lot of user sensible information can be stolen by attackers. In the recent past a lot of attention has been devoted to the key distribution in the WSN cryptography domain. Accordingly, several solutions have been proposed for pre-distributing keys or for reducing their size. I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 215–226, 2007. c IFIP International Federation for Information Processing 2007 

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However, secure cryptography does not guarantee privacy, as we have already said. Indeed, some research work has recently appeared that deals with the relationship between routing and location privacy in WSN. In fact, radio activity at an intermediate node can be used to obtain information about the position of the information source. In [3] a formal model of the source-location privacy problem is provided, and two popular classes of routing protocols, namely, flooding protocols and single path protocol, are analysed from the privacy and energy consumption standpoints. Based on such analysis a new technique called phantom routing is proposed that combines the advantages of both the above mentioned classes of routing protocols and provides suitable protection of the source location while not causing a noticeable increase in energy consumption. In [5] the authors propose GROW (Greedy Random Walk): a two way random walk to reduce the chance an eavesdropper can collect the source-location information. Note that both the above research contributions are simulations-based. Differently, in this paper we introduce an analytical framework for the evaluation of the tradeoff between location privacy and energy efficiency in wireless sensor networks. To this end we extend the definition of privacy loss based on information theory concepts, proposed in [1] for data mining systems, to the case of location privacy in sensor networks. More specifically, we focus on the relationship between random routing design choices and privacy loss as well as energy efficiency. Accordingly, we will derive a Markov-based model of the random routing behavior that allows to calculate the privacy loss as well as the average energy consumption. Numerical results confirm that, as expected, energy efficiency and privacy are competing requirements. The framework can be used by protocol designers to set appropriate tradeoffs between the two above requirements. The remainder of this paper is organised as follows: in Section 2 we present the system model along with a statement of the problem. In Section 3 we evaluate the privacy loss and the energy consumption. Some numerical results are provided in Section 4 and, finally, conclusions are drawn in Section 5.

2

Problem Statement and System Model

In this section we first state the problem of location-privacy in wireless sensor networks (WSNs). More in detail, in Section 2.1 we will define the problem using the panda-hunter game scenario, then, in Section 2.2 we introduce the system model that will be utilized in the following of the paper. 2.1

Statement of the Problem: The Panda-Hunter Game

The panda-hunter game is a well known reference scenario utilized for the study of source location privacy in WSNs [4,3]. Suppose that a set of sensor nodes has been deployed by the Save The Panda Organisation, in a random way within a large area in order to study and monitor

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panda habit. Sensor nodes are able to detect panda’s presence. At any time, while the panda freely moves, there is always a sensor node, called source node, that detects panda’s position. Such an observation must be periodically reported to a sink node, via multihop routing techniques. In this way the current position of the panda is approximately the position of the current source node. Thus, when the sink node receives a message from the source node, it will know the panda position. We suppose that transmissions are encrypted, so the source node ID field cannot be read by attackers. Moreover we assume that relationship between node ID and node location is known only by the sink node. In the area there is a hunter as well, with the role of adversary. He aims to catch the panda, thus he is an enemy from the Save The Panda Organisation standpoint. The hunter is not able to decrypt messages therefore, he cannot learn, at least not directly, location of the source node, but in order to get the worst case we considered the hunter, as in [3], non malicius, i.e. does not interfere with proper function of the network, device rich, i.e. he is equipped in such a way he can measure signal strenght and angle of arrival of any message, resource rich, i.e. he has unlimited amount of power, and informed, i.e. he knows location of the sink, and the network structure and protocols. Using his devices and resources the hunter can analyse messages at RF level, so he can try to capture panda by back-tracing the routing path used by messages until the source. As an example, consider the sensor network represented in Figure 1. There are N = 11 sensor nodes n0 , n1 , ..., n10 , with n0 representing the sink.

Fig. 1. Example of hunting activity

In Figure 1 we show the shortest path routing tree connecting each sensor node ni to the sink n0 , i.e., node n0 is the root of the tree. If the hunter is located near node n6 and detects radio activity, then a node in the set {n7 , n8 , n9 , n10 } is the source node. Instead, if no activity is detected, then the panda is near one of the remaining nodes, i.e., a node in the set {n1 , n2 , n3 , n4 , n5 } is the source node.

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Observe, that in any case the hunter splits the network and obtains information about the panda location. This leads to a strict connection between location privacy and routing protocol in a WSN. Routing protocols must be privacy-aware in order to save, or at least prolong, panda’s life.

Fig. 2. Example of random routing

A simple way to improve privacy is to introduce some randomness in the routing behavior. Indeed, in random routing the next relay is chosen randomly between all the neighbors of the current relay. As an example, in Figure 2 we show a path obtained applying random routing in the same WSN shown in Figure 1. In this case, the fact that node n3 is forwarding a packet does not mean that the source node is in the set {n3 , n4 }. However, the length of path followed by packets in random routing can increase significantly, which involves large energy consumption. In other words, the increase in privacy is achieved at the expenses of higher energy consumption. It follows that appropriate tradeoffs are needed. 2.2

System Model

Let us consider a WSN composed of M nodes denoted as n0 , n1 , ..., nM−1 . For any node ni , with i < M , we define Φ(ni ) the set of neighbors1 of ni and φ(ni ) the number of its neighbors, i.e., φ(ni ) = |Φ(ni )|. Now suppose that n0 is the sink and let us call d(ni ) the distance between node ni and the sink n0 . Obviously, d(n0 ) = 0 and d(ni ) = minn∈Φ(ni ) {d(n) + 1}. Observe that routing of packets towards the sink in a sensor networks can be modeled by means of a matrix Q ∈ (M−1)×(M−1) , the generic element of which, [Q]i,j , represents the probability that the next relay of a packet transmitted by ni is nj , with i and j ∈ [1, (M − 1)]. We define Q as the routing matrix. 1

We say that two nodes are neighbors if they are in the radio coverage of each other.

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In order to model random routing we define the best next relay Ψ (ni ) as the neighbour of ni which is closest to the sink, i.e., it is a node that satisfies the following relationship d (ψ(ni )) ≤ d(m), ∀m ∈ Φ(ni )

(1)

Let us stress that even if several nodes may satisfy the relationship in eq. (1), for each ni only one node ψ(ni ) is selected. Accordingly, if shortest path routing is utilized [Q][i,j] is equal to 1 if nj is the best next relay, i.e., if nj = ψ(ni ), and is equal to 0, otherwise. We define as p-random routing a routing algorithm which chooses the best next relay with probability p and any other neighbor node with equal probability. Accordingly, the routing matrix of a p-random routing protocol is ⎧ p if nj = ψ(ni ) and φ(ni ) > 1 ⎪ ⎪ ⎨ (1−p) if nj = ψ(ni ) and φ(ni ) > 1 (2) [Q]i,j = φ(ni )−1 ⎪ 1 if nj = ψ(ni ) and φ(ni ) = 1 ⎪ ⎩ 0 otherwise Note that if p is equal to 1, then random routing becomes a shortest path routing.

3

Performance Analysis

We define and derive the location privacy loss when p-random routing is applied in Sections 3.1. Then, in Section 3.2, we will derive the corresponding energy consumption. Such performance metrics will be evaluated as a function of the probability p. This allows us to evaluate appropriate tradeoffs between privacy loss and energy consumption. 3.1

Privacy Loss

A measure of privacy is crucial to the evaluation of privacy enhancement solutions. Accordingly, in the recent past some research effort has been devoted to the definition of an appropriate privacy metric. In [6] an overview of the most interesting solutions is provided. Here we extend the definition proposed in [1] to the location privacy case. Let S be the random variable representing the current position of the panda. We identify the location with the sensor node that detects the presence of the panda. Accordingly, at any time the random variable S can assume a value in the set {n0 , n1 , ..., nM−1 }. Now suppose that following an attack, the hunter can observe a variable X which is correlated to S and can assume one of the following N values: {x0 , x2 , · · · , xN −1 }. The loss of privacy is related to the amount of information gained by the hunter following the attack. Such information is given by the difference between

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the uncertainty on S before and after knowing X. In the context of the information theory the measure of uncertainty of a random variable can be evaluated as the entropy of such a variable, H(S). In [1] the loss of privacy is calculated as: ρ = 1 − 2−I(S,X)

(3)

where I(S, X) is the mutual information between S and X and is given by I(S, X) = H(S) − H(S|X). The uncertainty on S is (see [7] for example) defined as: H(S) = −

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where pS (nm ) represents the probability that the source node is nm , whereas the uncertainty on S given X is H(S|X) = −

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where pSX (nm , xn ) represents the joint probability that S assumes the value nm and X assumes the value xn , whereas pS (nm |xn ) represents the probability that S assumes the value nm given that X assumes the value xn . Obviously, the probability pS (nm |xn ) can be calculated as pS (nm |xn ) =

pSX (nm , xn ) pSX (nm , xn ) = M−1 pX (xn ) i=0 pSX (ni , xn )

(6)

Suppose that all locations are equiprobable, i.e., pS (nm ) = 1/M for any nm . Accordingly, the uncertainty on S given in eq. (4) can be calculated as H(S) = log2 M . Also, suppose that the hunter attacks the WSN at node n∗ . Following the attack, the hunter detects radio activity if the path between the source node and the sink passes through the node n∗ and viceversa. Accordingly, X can assume only two values:  0 if there is no radio activity at node n∗ X= (7) 1 if there is radio activity at node n∗ As a consequence, we can rewrite eq. (5) as H(S|X) =

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In eq. (8) we need to calculate the probability pSX (nm , x) which can also be used in eq. (6) to calculate pS (nm |xn ). The probability pS (nm |xn ) is given by pSX (nm , x) = pX (x|nm ) · pS (nm ) = pX (x|nm )/M

(9)

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Observe that pX (x|nm ) represents the probability that a packet generated by node nm does not pass through n∗ , if x = 0, and that such packet passes at least ones through n∗ , if x = 1. Now we will calculate pX (1|nm ); once this is known, pX (0|nm ) can be easily evaluated as pX (0|nm ) = 1 − pX (1|nm ) (10) Recall that pX (1|nm ) is the probability that a packet generated by node nm passes through node n∗ at least once before reaching the sink n0 . Let V be the random variable representing the hop at which the packet visits for the first time node n∗ . Applying the theorem of the total probability, the probability pX (1|nm ) can be calculated as the sum of probabilities that a packet generated by node nm visits at the V -th hop node n∗ , for any value of V , i.e., pX (1|nm ) =

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The probability in the sum in the right handside of eq. (11) is the probability that the packet generated by nm does not visit node n∗ and does not reach the sink until hop (v − 1), and, finally, at the v-th hop visits node n∗ . This can be calculated as: ∗

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where: – w(j) is an array of M − 1 elements, w(j) ∈ M−1 , all set equal to zero, with the exception of the j-th element which is equal to 1, i.e.,  0 if i = j and 1 ≤ i ≤ M − 1 (13) [w(j) ]i = 1 if i = j and 1 ≤ i ≤ M − 1 – G is an [M − 1] × [M − 1] matrix, G ∈ [M−1]×[M−1] , and its generic element [G][i,j] represents the probability that a packet received by node ni will be relayed to node nj , with nj = n∗ , and is not relayed by node n∗ . This can be obtained as follows:  [Q][i,j] if j = n∗ (14) [G][i,j] = 0 if j = n∗ – [w]T represents the transponse of the array w. Substituting eq. (12) in eq. (11) we can easily obtain:  pX (1|nm ) = w

(m)

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By applying the spectral decomposition to matrix G = D ·B ·D−1 , where B is a diagonal matrix containing the eigenvalues βi of G and D is the matrix whose columns are the corresponding eigenvectors, we can rewrite eq. (15) as follows: ∞  ∗ (m) v pX (1|nm ) = w ·D· B · D−1 · [w(n ) ]T (16) v=0

We call K the sum in the right hand side of eq. (16). We can easily obtain that K is a diagonal matrix whose generic element is  1/(1 − βi ) if i = j [K][i,j] = (17) 0 otherwise. Accordingly, eq. (16) can be rewritten as ∗

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(18)

where K has been calculated in eq. (17). Once pX (1|nm ) has been calculated we have all the parameters required for the calculation of the uncertainty on S given X, i.e., H(S|X). Note that the value of privacy loss ρ depends on n∗ . Since the hunter knows the structure and protocols of the network, the node n∗ which maximizes the privacy loss will be selected. As a consequence, the WSN gives a privacy loss γ given by γ = maxn∗ {ρ}. 3.2

Energy Consumption

The energy consumption for routing a packet from its source to the sink can be calculated as the product of the energy cost for a single hop transmission, c, and the number of hops between the source node and the sink2 . We call Z the random variable representing the number of hops needed for a packet to reach the sink. The average energy consumption, , needed to route a packet to the destination can be calculated as = c · E{Z} = c ·

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where E{Z} represents the average value of Z and pZ (z) represents the probability that the number of hops between the source and the destination is equal to z. The probability pZ (z) is the probability that a packet does not reach the sink in (z − 1) hops and finally arrives at the sink at the z-th hop. Therefore, it is easy to show that pZ (z) can be written in compact form as 

pZ (z) = π (S ) · P z−1 · ω T

(20)

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Observe that c can also take possible retransmissions into account. In this sense, analysis of c is simple and not reported in this paper for space constraints.

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– π (S ) is an array of (M − 1) elements, π (S ) ∈ M−1 . Its generic element is given by:

  π (S ) = pS (nm ) = 1/M with 1 ≤ m < M . (21) m

– P is an [M − 1] × [M − 1] matrix, i.e., P ∈ [M−1]×[M−1] . Its generic element [P ][i,j] represents the probability that a packet received by node ni is transmitted to node nj , with nj = n0 . Accordingly, the generic element of P is given by: if i and j ∈ {1, 2, ..., M − 1}

[P ][i,j] = [Q][i,j]

(22)

– ω is an array of M − 1 elements, i.e., ω ∈ M−1 . Its generic element [ω]m , with 1 ≤ m < M represents the probability that a packet is relayed by node nm to the destination. Accordingly, [ω]m = [Q][m,0]

(23)

Applying the spectral decomposition of P and following a procedure analogous to that presented in Section 3.1, we can rewrite eq. (19) as 

= c · π (S ) · T · H · T −1 · ω T

(24)

In eq. (24) the matrix H is a diagonal matrix and its generic element is  1/[(1 − λi )]2 if i = j [H][i,j] = (25) 0 otherwise where λi is the i-th eigenvalue of P and T is the matrix of the eigenvectors of P.

4

Numerical Examples

In this section we apply the proposed analytical framework to describe how this can be used to evaluate the tradeoffs between location privacy and energy efficiency in WSN. We consider a network of M sensor nodes uniformly distributed on a squared area of size 1 km × 1 km. We assume that all sensor nodes have coverage radius equal to R = 200 m. Once position of sensor nodes is set and the value of the parameter p, characterizing the random routing, is known, it is possibile to construct the routing matrix Q as given in eq. (2). Starting from the routing matrix Q it is possible to evaluate the privacy loss γ and the average energy consumption as reported in Section 3. All values in the following figures have been evaluated as the average of the results obtained in 20 cases. For each case, a new distribution of sensor nodes has been generated. Moreover, for each case individual routes are chosen considering the same sink node and a source node chosen in a random fashion based on uniform distribution.

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Fig. 3. Privacy loss, γ, versus the probability p for different values of the number of sensor nodes, i.e., M = 50 and M = 100

In Figure 3 we show the privacy loss, calculated as described in Section 3.1, versus the value of the probability p for two different values of the number of nodes, i.e., M = 50 and M = 100. In Figure 3 the privacy loss increases as the probability p becomes higher. This is an expected result. Indeed, using low values of p makes the routing behavior fuzzy and therefore, the hunter cannot obtain significant information attacking the network.

Fig. 4. Normalized energy consumption /c versus the probability p for different values of the number of nodes, i.e., M = 50 and M = 100

In Figure 4 we show the average energy consumption to deliver a packet to the sink, , versus the probability p for M = 50 and M = 100. More specifically, in Figure 4 we show the values of the ratio /c. We present normalized energy consumption values because c depends on the specific communication technology utilized, and not on the routing algorithm. As expected, the energy consumption decreases as the value of the probability p increases; furthermore, the higher the

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Fig. 5. (Upper plot:) Average energy consumption  versus privacy loss γ and (Bottom plot:) The value of the probability p versus the corresponding privacy loss γ

number of sensor nodes M , the lower the energy consumption. This is because, if there are more nodes, it is likely to find better next relays than in case there are few nodes. To highlight the tradeoff between privacy loss and energy efficiency, in Figure 5 we show two plots. In the upper plot we represent the normalized energy consumption, /c, versus the corresponding value of the location privacy loss, γ. As expected, the privacy loss increases as the energy consumption decreases. This figure has been obtained considering M = 100 nodes and can be utilized by the designer to select an appropriate tradeoff between energy efficiency and privacy. Once a point in the curve is chosen, the designer can use the bottom plot to obtain the corresponding value of p that gives the selected performance.

5

Conclusion

In this paper we have presented an analytical framework for the evaluation of the tradeoff between location privacy and energy efficiency in a WSN applying random routing to increase privacy protection. The proposed framework is based on a Markov-based modeling of the random routing behavior. The framework can be used by network designers to evaluate the most appropriate value of the probability p characterizing the random routing behavior in accordance with the application requirements.

Acknowledgments This paper has been partially supported by European Commission under contract DISCREET (FP6-2004-IST-4 contract no. 27679).

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References 1. D. Agrawal, C. Aggarwal. On the Design and Quantification of Privacy Preserving Data Mining Algorithms. Proc. of the Twentieth ACM SIGACT-SIGMODSIGART, Santa Barbara, California, USA. May 2001. 2. M. Anand, Z. G. Ives, I. Lee. Quantifying Eavesdropping Vulnerability In Sensor Networks. Department of Computer & Information Science, University of Pennsylvania, 2005. 3. P. Kamat, Y. Zhang, W. Trappe, C. Ozturk. Enhancing Source-Location Privacy in Sensor Network Routing. Proc. of International Conference on Distributed Computing Systems (ICDCS 2005), Columbus, OH, USA. June 2005. 4. C. Ozturk, Y. Zhang, W. Trappe, M. Ott. Source-Location Privacy for Networks of Energy-Constrained Sensors. In Proc. of IEEE IEEE Workshop on Software Technologies for Embedded and Ubiquitous Computing Systems (WSTFEUS), Vienna, Austria. May 2004. 5. Y. Xi, L. Schwiebert, W. Shi. Preserving Source Location Privacy in MonitoringBased Wireless Sensor Networks. Department of Computer Science, Wayne State University, 2006. 6. DISCREET Project, State of the art Deliverable. http://www.ist-discreet.org/ Deliverables/D2103.pdf 7. S. Haykin. Communication Systems, 4th edition.

Efficient Error Recovery Using Network Coding in Underwater Sensor Networks Zheng Guo, Bing Wang, and Jun-Hong Cui Computer Science & Engineering Department, University of Connecticut, Storrs, CT, 06269 {guozheng,bing,jcui}@engr.uconn.edu

Abstract. Before the wide deployment of underwater sensor networks becomes a reality, one of the challenges that needs to be resolved is efficient error recovery in the presence of high error rates, node mobility and long propagation delays. In this paper, we propose an efficient error-recovery scheme that carefully couples network coding and multipath routing. Through an analytical study, we provide guidance on how to choose parameters in our scheme and demonstrate that our scheme is efficient in both error recovery and energy consumption. We evaluate the performance of our scheme using simulation and our simulation confirms the results from the analytical study.

1 Introduction Underwater sensor networks are ideal vehicles for monitoring aqueous environments. However, before the wide deployment of underwater sensor networks becomes a reality, a range of challenges must be tackled [1,2,3]. One such challenge is efficient error recovery in the presence of high error rates, node mobility and long propagation delays (caused by fast fading acoustic channel, water currents and slow acoustic communication). Using common error-recovery techniques such as Automatic Repeat reQuest (ARQ) and Forward Error Correction (FEC) in underwater sensor networks has the following drawbacks. ARQ-based schemes require the receiver to detect losses and then request the sender to retransmit packets. This may lead to long delays. FEC-based schemes proactively add redundant packets to eliminate retransmission from the source. The FEC can be applied on an end-to-end or hop-by-hop basis (as in [4]). However, in either case, the proper amount of redundancy is hard to decide due to the difficulty of obtaining accurate error-rate estimates [3]. In our prior study [5], we demonstrate that network coding is a promising technique for error recovery in underwater sensor networks. The main idea of network coding [6,7] is that, instead of simply forwarding a packet, a node may code several incoming packets into one or multiple outgoing packets. Network coding is suitable for underwater sensor networks because (1) underwater sensor nodes are usually larger than land-based sensors and posses more computational capabilities [8]; (2) the broadcast property of acoustic channels naturally renders multiple highly interleaved routes 

This work is supported in part by the NSF CAREER Grant No. 0644190 and in part by the Uconn Large Grant FRS 449251.

I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 227–238, 2007. c IFIP International Federation for Information Processing 2007 

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from a source to a sink. The computational power at the sensor nodes coupled with the multiple routes provides ample opportunity to apply network coding. In this paper, building upon our preliminary work [5], we provide an in-depth study on using network coding in underwater sensor networks. Our main contributions are as follows. First, we propose an error-recovery scheme that carefully couples network coding and multipath routing. Second, we analytically study the performance of this scheme along with several other error-recovery schemes. Our analysis provides guidance on how to choose parameters in our scheme and demonstrates that, among the multiple schemes, our scheme is most efficient in terms of error recovery and energy consumption. Last, we evaluate the performance of our scheme using simulation and the simulation confirms the results from the analytical study. As related work, multipath routing schemes have been proposed for error resilience in sensor networks (e.g., [9,8]). Our scheme carefully combines network coding and multipath routing and provides much better error recovery than using multipath routing alone (see Sections 4 and 5). The study of [10] provides error resilience using multiple virtual sinks: a source forwards packets to multiple high-bandwidth virtual sinks, which then forward the packets to the final destination. This scheme requires a specialized delivery infrastructure while our scheme does not have such a requirement. The rest of the paper is organized as follows. Section 2 describes the problem setting. Section 3 describes our error-recovery scheme based on network coding. Sections 4 and 5 study the performance of our scheme along with several other schemes using analysis and simulation respectively. Finally, Section 6 concludes the paper and presents future work.

2 Problem Setting We now describe the problem setting. Consider a source-sink pair in an underwater sensor network. The path (or multipath) from the source to the sink is determined by a single-path (or multipath) routing algorithm. We refer to the intermediate nodes on the path(s) as relays. We consider several error-recovery schemes including single-path forwarding, endto-end FEC, hop-by-hop FEC, multipath forwarding and network coding. In single-path and multipath forwarding, packets are simply forwarded, without any coding. Singlepath forwarding is a baseline scheme since it does not exploit any extra mechanism for error recovery. Multipath forwarding recovers error through redundant packets over the multiple paths (a relay does not forward duplicate packets). FEC-based schemes use a single path from the source to the sink: end-to-end FEC encodes packets at the source and decodes them at the the sink; in hop-by-hop FEC, each relay on the path decodes incoming packets, encodes the recovered packets, and then forwards them to the next hop. Network coding requires multiple paths from the source to the sink; a node encodes incoming packets into one or multiple outgoing packets, as to be described in detail in Section 3. A packet successfully received (under single or multipath forwarding) or recovered (under FEC or network coding) is referred to as a successfully delivered packet. Since efficient error-recovery schemes for underwater sensor networks must achieve high

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error-recovery rate and conserve sensor node energy simultaneously, we consider the following two metrics. The first metric is the number of successfully delivered packets over the total number packets from the source, referred to as successful delivery ratio, denoted as R. The second metric is the total number of transmissions from the source to the sink (including transmissions from the source and relays) normalized by the successful delivery ratio. Since the number of transmissions roughly corresponds to the amount of energy consumed in the network, we refer to this metric as normalized energy consumption, denoted as T . This metric represents the average number of transmissions required for a successfully delivered packet. We next describe our network coding scheme for underwater sensor networks and then evaluate the various schemes using analysis and simulation.

3 Using Network Coding in Underwater Sensor Networks We now describe our error-recovery scheme based on network coding. This scheme carefully couples network coding and multipath routing to achieve a good balance between error recovery and energy consumption. In the following, we first describe how to apply network coding (we use random linear coding [11] due to its simplicity) given a set of paths from a source to a sink. We then describe how to adapt the multiple paths or the amount of redundancy to improve the efficiency of network coding. 3.1 Network Coding Scheme Packets from the source are divided into generations, each generation contains K packets. The source linearly combines K packets in a generation using randomly generated coefficients. More specifically, let X1 , . . . , XK denote the K packets in a generation. The source linearly combines these K packets to compute K  outgoing packets, deK noted as Y1 , Y2 , . . . , YK  where Yi = j=1 gij Xj . The coefficient gij is picked randomly from a finite field F2q . The set of coefficients (gi1 , . . . , giK ) is referred as the encoding vector for Yi [7] and are carried in a packet as overhead. We choose K  ≥ K since adding a small amount of redundancy at the source (e.g., K  = K + 2) reduces the impact of packet loss on the first hop (which cannot be recovered at later hops) and improves error recovery at the sink [5]. A relay in forwarding paths stores incoming packets from different routes in a local buffer for a certain period of time, then linearly combines the buffered packets belonging to the same generation. Suppose a relay, r, receives M incoming packr . Let (fi1 , . . . , fiK ) denote the encoding vector carried by Xir , i = ets, X1r , . . . , XM 1, . . . , M . Since transmitting dependent packets is not useful for decoding at the sink, relay r computes M  outgoing packets, where M  is the rank of the coefficient matrix r (fij ), i = 1, . . . , M , j = 1, . . . , K. Therefore, M  ≤ min(M, K). Let Y1r , . . . , YM   M r r r denote the outgoing packets, Yi = j=1 hij Xj , where hij is picked randomly from r r the finite field F2q . Let (gi1 , . . . , giK ) denote the encoding vector of Yir , i = 1, . . . , M  . M r r Then gij = l=1 hil flj . When the sink receives K packets with linearly independent encoding vectors, it recovers the original packets by matrix inversion [7]. The complexity is O(K 3 ).

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sin k

s o u rc e

s o u rc e /s in k m u lti-p a th re la y o th er n o d es

Fig. 1. Illustration of transmitting a packet along multiple paths from the source to the sink. Nodes in a dashed circle form a relay set.

3.2 Path or Redundancy Adaption for Network Coding The efficiency of network coding relies on the quality of the underlying paths determined by a multipath routing algorithm. We next describe a multipath property under which network coding is efficient (in terms of both error recovery and energy consumption). Fig. 1 illustrates the process of transmitting a packet along a multipath. The source broadcasts the packet to its downstream neighbors (nodes within its transmission range and in the forwarding paths), referred to as a relay set. Nodes in the relay set further forward the packet to their neighbors, forming another relay set. Intuitively, a multipath suitable for network coding should contain a similar number of nodes in each relay set. This is because, a relay set with too few nodes may not provide sufficient redundancy; a relay set with too many nodes wastes energy to provide more redundancy than what is necessary for error recovery. We develop two schemes to adjust the multipath or the amount of redundancy to improve the efficiency of network coding. In both schemes, a node uses the number of its downstream neighbors to approximate the size of its downstream relay set. This is because the former can be easily estimated through localization service (e.g., [12]) and localized communication between a node and its neighbors while the latter is difficult to estimate. The first scheme requires that sensor nodes have multiple levels of transmission power [13]. A node selects a transmission power so that the estimated number of downstream neighbors is between Nl and Nu , where Nl and Nu are lower and upper thresholds respectively. We refer to this scheme as transmission-range adaption. In the second scheme, each node has a fixed transmission range and a node adapts the amount of redundancy that it injects to the network. More specifically, a node with less than a Nl downstream neighbors encodes more outgoing packets to increase the amount of redundancy. Similarly, a node with more than Nu downstream neighbors encodes less outgoing packets to reduce the amount of redundancy (we only do this when the coefficient matrix at the node has a full rank of K). We refer to this scheme as redundancy adaption. Our analytical results in the next section provide guidance on how to choose parameters for the above two adaption schemes. Note that both schemes only require localized

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information and hence are easy to deploy. Furthermore, they can be applied to mobile underwater sensor networks when coupled with a multipath routing scheme that supports mobility (e.g., [8]).

4 Analytical Study We now analytically study the performance of the various error-recovery schemes in Section 2. Our goal is two-fold: (1) analytically compare the efficiency of the various schemes; (2) provide guidance on how to choose parameters in network coding. In the interest of space, we only present the results for multi-path forwarding and network coding; the results for other schemes can be found in [14]. Multi-path forwarding and network coding use the same multipath from the source to the sink. Assume that there are H relay sets from the source to the sink, indexed them from 1 to H (see Fig. 1). The sink is in the H-th relay set. Let Ni be the number of relays in the i-th relay set. For simplicity, we assume that the relay sets do not intersect. Furthermore, a node in a relay set can receive from all nodes in the previous relay set. Last, a node only uses packets forwarded from its previous relay set (i.e., packets received from nodes in the same relay set are discarded). For both schemes, we derive the normalized energy consumption, T , from the successful delivery ratio, R, as follows. Consider an arbitrary packet (regardless of being successfully delivered or not), let Ti denote the average number of times that it is transmitted from the nodes in the previous relay set (or the source) to those in the i-th relay set. Then H Ti (1) T = i=1 R We assume that the acoustic channels have the bit error rate of pb . Let p be the probability that a packet has bit error. Then p = 1 − (1 − pb )L for independent bit errors and a packet size of L bits. We next present the analysis for multipath forwarding and network coding. 4.1 Analysis of Multipath Forwarding Consider an arbitrary packet P . Let αi be the probability that a node in the i-th relay set receives packet P . Let αi,n be the probability that n nodes in the i-th relay set receive packet P , n = 0, . . . , Ni . Assume that packet losses are independent. Then  1−p i=1 (2) αi = Ni−1 n α (1 − p ), 2≤i≤H i−1,n n=0 This is because, for a node in the first relay set, the probability that it receives packet P from the source is 1 − p; when i ≥ 2, a node in the i-th relay set receives packet P when it receives at least one copy of this packet from the (i − 1)-th relay set. Assume that packet transmissions to nodes in a relay set are independent. Then   Ni n (3) αi,n = αi (1 − αi )Ni −n , n = 0, . . . , Ni n

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Since packet P is an arbitrary packet and the sink is in the H-th set, we have R = αH . The above results indicate that αH can be obtained in the following manner. We first obtain α1,n from α1 (of value 1 − p), and then obtain α2 using α1,n . This process continues until eventually αH is obtained. Since a node forwards packet P at most once, we have  1, i=1 Ti = (4) αi−1 Ni−1 , 2 ≤ i ≤ H After obtaining R and Ti , we calculate the normalized energy consumption T from (1). 4.2 Analysis of Network Coding Consider an arbitrary generation of K packets. Under linear random coding, when a sink receives at least K packets in the generation, the probability that it can recover the K original packets is high for a sufficiently large finite field [11]. Therefore, for simplicity, we assume that the sink recovers the K original packets as long as it receives at least K packets in the generation. We do not differentiate nodes in the same relay set. Let βi,k be the probability that a node in the i-th relay set receives k packets (when 0 ≤ k < K) or at least k packets (when k = K) from all nodes in the previous relay set, 1 ≤ i ≤ H. Since the sink is in the H-th relay set and the generation is arbitrary, we have R = βH,K . We next derive βi,k , 1 ≤ i ≤ H, 0 ≤ k ≤ K. The nodes in the first relay set receive packets from the source. Therefore     K (1 − p)k pK −k , 0 ≤ k < K k  (5) β1,k = 1 − K−1 k=K j=0 β1,j where K  ≥ K is the number of encoded packets from the source. For i ≥ 1, 0 ≤ k < K, we obtain βi+1,k as follows. We index the nodes in the i-th relay from 1 to Ni . Let γi,j,k denote the probability that a node in the i-th relay set receives k packets from the j-th node in the previous relay set, 1 ≤ i ≤ H, 1 ≤ j ≤ Ni−1 , 0 ≤ k < K. Since each relay transmits no more than K packets, we have γi,j,k =

K

βi−1,k

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(6)

For a node in the (i+1)-th set, let kj be the number of packets that it receives from the jth node in the previous relay set. To obtain βi+1,k , we need to consider all combinations Ni of kj ’s such that j=1 kj = k, kj = 0, . . . , k. That is, Ni



βi+1,k = kj =0,...,k

s.t.

 Ni

j=1 j=1 kj =k

γi+1,j,kj

(7)

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For a small generation size K, the above quantity is easy to compute. We use small K (e.g., K = 3) since our study [5] indicates that it is sufficient to achieve good performance using small K (also confirmed by simulation in the settings of Section 5). We obtain βi+1,K from βi+1,k , 0 ≤ k < K as βi+1,K = 1 −

K−1

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(8)

k=0

From the above, we calculate R = βH,K as follows. We first obtain β1,k , which is used to compute γ2,j,n and β2,k , 0 ≤ k ≤ K. This process continues until eventually βH,K is obtained. Since a relay transmits no more than K packets, we have   K /K, i=1 Ti = Ni−1 K (9) kβ , 2≤i≤H i−1,k k=0 K After obtaining R and Ti , we calculate the normalized energy consumption T from (1). 4.3 Numerical Results

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We next compare the various schemes based on our analytical results. The bit error rate is in the range of 10−4 to 1.5 × 10−3 to account for potential high loss rate in underwater sensor network (e.g., due to fast channel fading). For network coding, a generation contains 3 packets (e.g., K = 3). The source transmits K  = 5 packets. For multipath forwarding and network coding, we set the number of relay sets, H, to 7 or 9, and assume all relay sets contain the same number of nodes, i.e., Ni = N , i = 1, . . . , H. Similarly, for single-path forwarding and FEC, we set the number of hops from the source to the sink to 7 or 9. For FEC, each block contains 3 packets (same as the generation size in network coding) and the amount of redundancy is 3N − 3 since a relay set contains N nodes in multipath forwarding and network coding. 6

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Fig. 2 plots the successful delivery ratio and normalized energy consumption for various schemes when H = 9. We observe that network coding outperforms the other schemes: it achieves the highest successful delivery ratio and the lowest normalized energy consumption for the range of bit error rates when N = 3 (i.e., each relay set contains 3 nodes). Furthermore, network coding achieves similar performance when H = 7 (not plotted), indicating that it is insensitive to the length of the path (network size). We also observe that when the number of nodes in each relay set, N , is decreased from 3 to 2, the successful delivery ratio of network coding drops sharply. Based on the above results, we set Nl = Nl = 3 in our simulation 5. From Fig. 2, we also observe that multipath forwarding achieves a similar normalized energy consumption and a lower successful delivery ratio than network coding for the same value of N . The successful delivery ratio under hop-by-hop FEC is sensitive to both the bit error rate and the number of hops on the path (network size), indicating that the amount of redundancy needs to be carefully selected according to these two parameters. The successful delivery ratio under single-path forwarding and end-to-end FEC decreases significantly as the bit error rate increases, indicating that they are not suitable for high error-rate underwater sensor networks.

5 Simulation Study We now evaluate the performance of the various error-recovery schemes using simulation. The underwater sensor network is deployed in a cubic target area of 1km × 1km × 1km, which is a reasonable network size for underwater sensor networks. The source and sink are deployed respectively at bottom corner and surface corner, on the diagonal of the cube. The MAC layer supports broadcasting. The routes from the source to the sink is determined by Vector-based Forwarding (VBF) [8]. In VBF, a routing pipe is a pipe centered around the vector from the source to the sink. Nodes inside the routing pipe are responsible for routing packets from the source to the sink; nodes outside the routing pipe simply discard all incoming packets. The relay set formation depends on node density and routing protocol used, using VBF is easy to format relay sets and we will propose two techniques in 5.2 to adjust the relay sets. Each packet is 50 bytes. For network coding, each generation contains K = 3 packets; the source outputs K  = 5 packets for each generation and each relay outputs no more than 3 packets. We choose a finite field of F28 [11], leading to packets of 53 bytes (including 3-byte encoding vector). A relay has a memory to store 10 packets for each generation; packets transmitted from the node are removed from the memory. We look at two types of sensor deployment: grid random deployment and uniform random deployment. In grid random deployment, the target area is divided into grids; a number of nodes are randomly deployed in each grid. In uniform random deployment, nodes are uniformly randomly deployed in the area. Grid random deployment covers the area more evenly than uniform random deployment while uniform random deployment is easier to deploy. The comparative results of the various schemes from simulation are consistent with those from analytical study. We focus on the performance of network coding and multipath forwarding in the following.

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Fig. 3. Simulation results under grid random deployment

5.1 Performance Under Grid Random Deployment In grid random deployment, the target area is divided into 125 grids, each grid is 200m× 200m × 200m. Each grid contains 2 nodes, randomly distributed in the grid. Based on the analytical results in Section 4, we set the transmission power and pipe radius of a node to cover 3 to 4 downstream neighbors (with an average of 3.1). This is achieved when each node uses a transmission range of 300 m [15] and a pipe radius of 150 m. Figures 3 (a) and (b) plot the successful delivery ratio and normalized energy consumption for network coding and multipath forwarding. The confidence intervals (from 20 simulation runs) are tight and hence omitted. We also plot the analytical results when N = 3 (i.e., each relay set contains 3 nodes). For network coding, we observe that the simulation results are very close to those from the analysis, indicating that the analysis provides a good approximation and guidance on choosing parameters in network coding. For multipath forwarding, the analytical results are slightly (no more than 8%) higher than those from the simulation. This might be because we assume a node can hear from all nodes from its previous relay set in the analysis, which provides an overestimate of the successful delivery ratio. We observe that network coding provides significantly better error recoveries than multipath forwarding for high bit error rates. The normalized energy consumption under network coding is slightly higher than that under multipath forwarding because the source adds redundancy and more packets are forwarded at a relay in network coding (a relay discards duplicate packets in multipath forwarding). For the sake of comparison, we also plot the analytical result under hop-by-hop FEC in Fig. 3. When using this scheme, the number of hops (on the single path) from the source to the sink is 9, and a block contains 3 packets (to be consistent with the generation size in network coding). Each blocks adds 28/9 ∗ 3 − 3 = 7 redundant packets since the routing pipe used in network coding and multipath forwarding contains 28 nodes. Note that, although we purposely add a higher amount of redundancy for hopby-hop FEC, it still achieves much lower successful delivery ratio than network coding for relatively high bit error rates.

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We now demonstrate that it is indeed important for a node to have 3 to 4 downstream neighbors for efficient network coding, as indicated by the analytical results. For this purpose, we either fix the transmission range to 300 m and vary the pipe radius or fix the pipe radius to 150 m and vary the transmission range. The results are plotted in Figures 4(a) and (b) respectively, where the bit error rate is 1.5 × 10−3 . In both cases, we observe that a good balance between error recovery and energy consumption is achieved when the transmission range is 300 m and the pipe radius is 150 m (i.e., when a node has 3 to 4 downstream neighbors).

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Fig. 4. Successful delivery ratio and normalized energy consumption under grid random deployment: (a) Transmission range is 300 m, (b) Pipe radius is 150m

5.2 Performance Under Uniform Random Deployment We now present the results under uniform random deployment. Under this type of deployment, we find that using the same transmission range and pipe radius for all the nodes cannot ensure 3 to 4 downstream neighbors for each node. We therefore allow a node to adjust its transmission range or the amount of redundancy that it injects into the network. We first present the result under transmission-range adaptation. The pipe radius is set to 150 m. A node set its transmission range to have 3 to 4 downstream neighbors (with an average of 3.3). The resulting transmission ranges are from 100 to 400 m for all the nodes. Fig. 5 plots the successful delivery ratio under network coding. We observe that transmission-range adaption achieves a similar successful delivery ratio as that from the analytical result using N = 3. This indicates that transmission-range adaption is effective for error recovery. For comparison, we obtain the results when all nodes uses a transmission range of 300 m. We observe that it achieves significantly lower successful delivery ratio (see Fig. 5) and higher normalized energy consumption (not plotted) than those under transmission-range adaption. We next present the results when all nodes uses the same transmission range of 300 m and adjusts the amount of redundancy according to the number of its downstream neighbors. In Fig. 6, a node adds one more outgoing packet when it has less than 3

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downstream neighbors and removes an outgoing packet when it has more than 6 downstream neighbors. We observe that this adaption achieves a similar successful delivery ratio as that from the analysis using N = 3 with only slightly higher normalized energy consumption (not plotted). The above results demonstrate that adjusting redundancy is also helpful for efficient error recovery under network coding.

6 Conclusion and Future Work In this paper, we first proposed an efficient error-recovery scheme that carefully couples network coding and multipath routing for underwater sensor networks. We analytically studied the performance of our scheme along with several other error-recovery schemes. Our analysis provided guidance on how to choose parameters in our scheme and demonstrated that our scheme is most efficient among the multiple schemes. Finally, we evaluated the performance of our scheme using simulation. Our simulation results confirmed the analytical study that our scheme is efficient in both error recovery and energy consumption. As future work, we are pursuing in three directions: (1) analyzing the traffic congestion and delay for network coding; (2) using network coding in multicast applications

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in underwater sensor networks, e.g., command distribution or software update from one source to all other nodes; (3) using network coding in the architecture with multiple virtual sinks.

References 1. I. F. Akyildiz, D. Pompili, and T. Melodia, “Challenges for efficient communication in underwater acoustic sensor networks,” ACM SIGBED Review, vol. 1, July 2004. 2. J. Heidemann, W. Ye, J. Wills, A. Syed, and Y. Li, “Research challenges and applications for underwater sensor networking,” in Proceedings of the IEEE Wireless Communications and Networking Conference, Las Vegas, Nevada, USA. 3. J. H. Cui, J. Kong, M. Gerla, and S. Zhou, “Challenges: Building scalable mobile underwater wireless sensor networks for aquatic applications,” in IEEE Network, Special Issue on Wireless Sensor Networking, June 2006. 4. P. Xie and J. H. Cui, “SDRT: A reliable data transport protocol for underwater sensor networks,” tech. rep., University of Connecticut, Computer Science and Engineering Dept., February 2006. 5. Z. Guo, P. Xie, J.-H. Cui, and B. Wang, “On applying network coding to underwater sensor networks,” in Proceedings of ACM WUWNet’06, Los angeles, CA, September 2006. 6. R. Ahlswede, N. Cai, S. R. Li, and R. W. Yeung, “Network information flow,” IEEE Transactions on Information Theory, vol. 46, July 2000. 7. C. Fragouli, J.-Y. L. Boudec, and J. Widmer, “Network coding: An instant primer,” ACM SIGCOMM Computer Communication Review, January 2006. 8. P. Xie, J. H. Cui, and L. Lao, “VBF: Vector-based forwarding protocol for underwater sensor networks,” in Proceedings of IFIP Networking’06, Coimbra, Portugal, May 2006. 9. D. Ganesan, R. Govindan, S. Shenker, and D. Estrin, “Highly-resilient, energy-efficient multipath routing in wireless sensor networks,” ACM SIGMOBILE Mobile Computing and Communication Review, vol. 5, no. 4, 2001. 10. W. K. Seah and H. Tan, “Multipath virtual sink architecture for underwater sensor networks,” in Proceedings of the MTS/IEEE OCEANS2006 Asia Pacific Conference, May 2006. 11. T. Ho, R. Koetter, M. Medard, D. R. Karger, and M. Effros, “The benefits of coding over routing in a randomized setting,” in International Symposium on Information Theory (ISIT), 2003. 12. V. Chandrasekhar, W. K. Seah, Y. S. Choo, and H. V. Ee, “Localization in underwater sensor networks - survey and challenges,” in Proceedings of ACM WUWNet’06, Los angeles, CA. 13. J. Wills, W. Ye, and J. Heidemann, “Low-power acoustic modem for dense underwater sensor networks,” in Proceedings of ACM WUWNet’06, Los angeles, CA, September 2006. 14. Z. Guo, B. Wang, and J.-H. Cui, “Efficient error recovery using network coding in underwater sensor netowrks,” tech. rep., University of Connecticut, Computer Science and Engineering Dept., November 2006. 15. D. B. Kilfoyle and A. B. Baggeroer, “The state of the art in underwater acoustic telemetry,” IEEE Journal of Oceanic Engineering, vol. OE-25, no. 5, pp. 4–27, 2000.

Key Predistribution Schemes for Sensor Networks for Continuous Deployment Scenario* Abdülhakim Ünlü, Önsel Armağan, Albert Levi, Erkay Savaş, and Özgür Erçetin Sabanci University, Istanbul, Turkey {aunlu,onsel}@su.sabanciuniv.edu {levi,erkays,oercetin}@sabanciuniv.edu

Abstract. In sensor networks, secure communication among sensor nodes requires secure links and consequently secure key establishment. Due to resource constraints, achieving such key establishment is non-trivial. Recently some random key predistribution techniques have been proposed to establish pairwise keys. Some of these approaches assume certain deployment knowledge is available prior to deployment and nodes are deployed in groups/bundles. In this paper, we propose another practical deployment model where nodes are deployed over a line one by one in a continuous fashion. In this model, sensor nodes can also be deployed over multiple parallel lines to cover two-dimensional area. Based on this model, we develop two key predistribution schemes. Analysis and simulation results show that our key predistribution schemes make use of the deployment knowledge better than the existing schemes. Thus they perform better than other location-aware protocols using the metrics of connectivity, resiliency, memory usage and communication cost for key establishment.

1 Introduction In sensor networks [1], confidentiality, privacy and authenticity of communication between sensor nodes are important when nodes are deployed in an environment where there are adversaries. In order to fulfill these security requirements, cryptographic techniques are employed. Generally symmetric cryptography is used to provide security in sensor networks. In order to use symmetric key cryptography, communicating sensor nodes must share the same key. Distribution of keys to large amount of sensor nodes, so that they can establish secure links, is an active research area. Generally key predistribution schemes [2-8], where the keys are stored in sensor nodes before deployment, are used for this purpose. A naïve way of key predistribution is to generate a master key and install this master key to all nodes before the deployment. However in this scheme, when a node is captured, the master key is also captured and all secure links in the sensor network are compromised. *

Albert Levi and Abdülhakim Ünlü are supported by the Scientific and Technological Research Council of Turkey under project number 104E071. Erkay Savaş is supported by the Scientific and Technological Research Council of Turkey under project number 104E007.

I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 239–250, 2007. © IFIP International Federation for Information Processing 2007

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Another extreme key predistribution way is to assign unique link keys for each node. In this method, compromise of one node leads to compromise of only that node’s links. However, this method is not scalable since the total number keys to be predistributed per node should be as much as the number of nodes in the network in order to guarantee that after deployment each neighboring node pair shares a key. In order to overcome this scalability problem and effectively use the node memory, Eschenauer and Gligor proposed a probabilistic key predistribution scheme [5]. In this scheme, before sensor deployment, a key server creates a key ring for each node, by picking a limited amount of random keys from a large key pool. Then the key server loads the key ring to memory of each node. After deployment, sensor nodes in the field let their neighbors know which keys they have. If two neighboring nodes share one or more identical keys, then they can establish a secure link. After this shared key discovery with direct neighbors, neighboring node pairs that do not share keys can establish secure links in multiple hops. If the local connectivity (in terms of secure links) is above a certain threshold, then random graph theory [9] states that overall sensor network will be cryptographically connected with high probability. Du et al. utilized Blom’s key management scheme [12] in a key predistribution scheme for sensor networks [4]. This scheme shows a threshold property; until λ nodes are captured, the network is perfectly secure, but after λ nodes are compromised all secure links are compromised. Some recent papers on random key predistribution [3,7,10,11] utilized expected location information of sensor nodes in their models. In all these location-aware approaches, it is assumed that nodes are prepared in small groups and deployed as bundles, e.g. groups of nodes can be dropped from a plane, similar to parachuting troops or dropping cargo. The nodes in the same group have a very large chance to be in the range of each other. Moreover, the node groups that are dropped next to each other also have a chance to be close to each other on the ground. Using this deployment location knowledge, key pools and key rings are arranged and performance of key predistribution schemes can be improved substantially. In location aware schemes, the node deployment model is one of the most important design criteria that directly affects the performance of the scheme. As discussed above, a batch deployment strategy is assumed in the location aware random key predistribution schemes proposed in the literature. Such a deployment strategy may not be appropriate for scenarios like borderline or perimeter defense - if sensors are deployed in bundles, it is likely that there will be places on the border with a few or no sensor nodes. Moreover, there is still room to further improve the performance, in terms of connectivity, resiliency and memory usage, of location-aware key predistribution schemes with more realistic deployment models. 1.1 Our Contribution We introduce a new deployment model, called the continuous deployment model, and develop two key pre-distribution schemes on this model. The main idea behind the continuous deployment model is to drop the nodes one by one (i.e. not in batches) continuously from an aerial vehicle. The aerial vehicle may follow a continuous line for perimeter defense applications. In applications that need area coverage, the vehicle may follow a route with several parallel lines. We use the latter scenario, which is

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more complicated than the former one, in the development and the analysis of key pre-distribution schemes developed based on the continuous deployment model. In our first key pre-distribution scheme, it is assumed we know the order in which the nodes are dropped off for each line. For key predistribution in this scheme, we take a deterministic approach and assign pairwise keys to sensor nodes. In our second key predistribution scheme, we relaxed the order assumption such that the dropping order of the sensor nodes is not known, but the nodes to be dropped for each line are grouped. Here we use a probabilistic key predistribution mechanism; for each line, each node is assigned some keys from the key pools. We anticipate that the use of more deployment knowledge, as in the methods that we proposed, would improve the performance of the system. We performed analytical and simulation-based performance evaluation of the proposed schemes and show that the proposed approach actually improves key predistribution performance over Du et al.’s scheme [3], in which the nodes are deployed in groups, in terms of connectivity, resiliency against node capture and memory usage.

2 The Continuous Deployment Model In this section, we introduce a practical deployment model, where nodes are deployed sequentially but not in batches. In our deployment model the nodes are dropped one by one following a trajectory. This model can be easily realized by dropping nodes through a pipe in a plane as the plane flies over a known route. For example, if a rectangular area is to be covered with sensor nodes, the plane takes a route where it scans the rectangular area line by line. Figure 1 shows an example sensor network deployed in this model.

Fig. 1. A sample sensor network

The point where a node is dropped out of plane or helicopter is called its deployment point. However, due to several reasons its actual position drifts from deployment point. The actual position of a node on the field after deployment is named its resident point. Both deployment and resident points are defined in two-dimensional space. In the rest of the paper, the deployment area is assumed to be a rectangular one. In this area, there are L parallel lines and N nodes per line. Our deployment model assumes fixed intervals between the deployment points of two consecutive nodes of a line. The deployment point of ith node on jth line is denoted as dji, where j=1 ... L and i=1 ... N. Similarly the resident point of that node is denoted as rji.

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The resident point of a node may float away from its deployment point. Due to this fact, two nodes with deployment point dli and dlj, where dli < dlj, can be at resident points rli and rlj where rli > rlj. In our model, two nodes can be neighbors according to their deployment points, but they can be out of each others’ coverage after deployment. We call two nodes neighbors only if their resident points are close enough so that they can directly communicate over radio. The density of the lines and node dropping frequency are important system parameters to keep the resulting sensor network connected. Our model utilizes two-dimensional Gaussian distribution function to determine probability of a node being at a resident point based on its deployment point.

3 Continuous Key Predistribution Scheme Key distribution for our deployment model can be performed in two ways. In the first way, we assume that the deployment order of individual nodes is known. In this way, the neighboring relationships, in terms of the deployment points, are known. Such knowledge yields very efficient key distribution method that will be discussed later. However, in order to realize this, we have to transfer cryptographic materials to the nodes just before dropping them, so we need to have a complex setup inside the plane. Alternatively, we may transfer cryptographic materials before loading them to plane, but we have to preserve nodes’ order by, for example, keeping all the sensor nodes in pipes. In the second way, a line of nodes is treated as a single group. We do not assume knowledge of order of nodes; we just form groups of nodes and then store cryptographic material according to the key distribution scheme that will be explained later. Then, we deploy each group as a line in a random order. This approach is simpler to realize than the first method, but it has some performance deficiencies that will be discussed in this paper. We propose two different key predistribution schemes, Scheme I and Scheme II, for the above two ways. Both of them follow well-known three phase approach as in other key predistribution schemes proposed in the literature. First phase is the “predistribution” phase, where keys are stored in nodes according to a method proposed by the scheme. Second phase is the “direct key establishment” phase, where nodes discover their neighbors and find out if they share common keys with their neighbors to form secure link. Third phase is the “path key establishment phase”, where a node tries to find secure paths to its neighbors, with which it does not share common keys, in order to establish secure link. A secure link exists between two nodes if they both own at least one key in common and they are neighbors. We assume that all keys have unique IDs. 3.1 Key Predistribution Scheme I Parameters and the symbols used in this scheme are: N number of nodes on a line L number of lines that makes up the sensor network M number of keys shared with nodes on the same line

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number of keys shared with nodes on adjacent line distance between deployment points on a line radio range of a node ith line, where i=1 .. L deployment point of jth node on line Li, j=1 .. N the id of the sensor node with deployment point dij resident point of jth node on line Li, where j=1 .. N

Along with the deployment model examined in the previous section, sensor nodes, which are placed adjacent in the pipe, have high probability of being neighbors after deployment. Similarly, sensor nodes, which have similar locations in consecutive pipes, maintain the likelihood of being neighbors. As a result of this observation, we infer that a pairwise key predistribution method would work efficiently. Thus, we adopted such a strategy in our method. There are three phases in this scheme as described above: (i) Predistribution Phase, (ii) Direct Key Establishment Phase, and (iii) Path Key Establishment Phase. Predistribution phase. This phase is split into two: inline key predistribution and cross-line key predistribution. Inline key predistribution is for the nodes within the same line of deployment. Cross-line key predistribution is for the nodes in adjacent lines. Figure 2 depicts this phase. Q nodes Li+1 M nodes Li si1

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Inline Key Predistribution. The setup server creates and stores pairwise keys in sensor nodes such that each node shares keys with its M neighbors on the current line. More formally, for all i=1 .. L, and j=1 .. N, the setup server creates M keys to be stored in sij such that sij and its M neighboring sensor nodes, si(j-M/2),…,si(j1),si(j+1),….,si(j+M/2),share unique keys. Cross-Line Key Predistribution. Sensor nodes also share keys with their neighbors in neighboring lines. For all i=1 .. L, and j=1 .. N, the setup server creates 2*Q keys to be stored in sij such that this node shares unique pairwise keys with Q nodes from the lower line, s(i-1)(j-Q/2),…….,s(i-1)(j+Q/2), and also Q nodes from an upper line, s(i+1)(jQ/2),…….,s(i+1)(j+Q/2). After these two processes, a sensor node will have M+2Q keys before deployment.

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Direct Key Establishment Phase. After deployment, sensor nodes communicate with their neighbor nodes to discover shared keys in order to establish secure links Shared key discovery is trivial, since sensor nodes already have IDs of nodes with which they share pairwise keys. So a node only needs to know the IDs of its neighbors. When a node finds a matching node in its neighborhood, they can immediately start using their pairwise shared key. Unauthorized entities cannot know the IDs of keys used to secure links or IDs of keys in any node, since only node IDs are to be transmitted over unencrypted links,. This phase is indifferent for both nodes on the same line and nodes on the adjacent lines. Path Key Establishment Phase. After direct key establishment phase, a node may end up with a case where it has neighbors that it cannot find a shared key to establish a secure link. Thus, these two neighboring nodes without a secure link will have to find a secure path, which is a path of secure links, through their other neighbors. The process of establishing a secure link over a secure path is called path key establishment. The process works as follows. Assume node sij does not have a secure link with its neighbor node sik. Node sij asks its 1-hop neighbors, with which it has secure links, to see if they also have secure links with node sik. If any of the neighbors, say sin, has such a secure link, then sin generates a random key and sends the key to both node sij and sik over secure links. Then the nodes sij and sik use this key to establish a secure link. If none of the 1-hop neighbors have secure link with node sik, then node sij asks its 2-hop neighbors. If not found again, sij asks to next hop neighbors until it finds a node that shares key with sik. If the graph of secure links is a connected graph, a node eventually finds a secure path to any node in the sensor network. In our analysis, we will show that a node can reach all its neighbors with high probability in three hops of secure links. 3.2 Key Predistribution Scheme II Parameters and the symbols used in this scheme are: N L Li Si sI sc MI Mc K d A Aij dli rli sij kij

number of nodes on a line number of lines that makes up the sensor network ith line, where i=1 .. L key space of line i number of nodes a key in Si is distributed on Li number of nodes a key in Si is distributed on neighbors of Li memory space of nodes of Li for keys from Si memory space of nodes of neighbors of Li for keys from Si number of unique keys in a key space distance between deployment points on a line radio range of a node circular area around node sij, where sij can send and receive radio signals deployment point of node i on line l resident point of node i on line l the id of sensor node with deployment point dij the id of jth key in key space Si

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In this model, we do not assume a particular order in the deployment points of the nodes of a line. Thus we use less deployment knowledge as compared to predistribution scheme I. Although the scheme is still based on pairwise key distribution some redundancy should also be added in order to achieve a reasonable level of connectivity. Setup server generates groups of unique keys for each line. This keys form the key space, Si, of line i. There are K keys in each key space, and a node from line i gets keys from Si, Si-1 and Si+1 according to the key predistribution method. The duplication of each key is limited and determined parametrically. Similar to Scheme I, this scheme has three phases; predistribution, direct key establishment and path key establishment. Predistribution Phase. In key predistribution step, we describe the method how keys are distributed to nodes on various lines. Setup server generates key spaces for each line, Si, where i = 1 .. L, then distributes sI and sc copies of each key as explained below. Our aim here is to distribute the keys such that nodes that are expected to be near share more keys. Key predistribution method for each kij, where i = 1 .. L and j = 1.. N, is as follows: 1. 2. 3.

Key kij is randomly generated for key space of Si of line Li. sI nodes with sufficient space in their MI are randomly selected on Li and kij is installed in those sI nodes. sc nodes with sufficient space in their Mc are selected randomly from each neighboring lines of Li. So, 2sc nodes are selected from two neighboring lines. Then kij is installed in those sc nodes in each neighboring line.

At the end of key predistribution phase, each key from key space Si has a total of (sI + 2sc) copies on three lines; sI copies in Li and 2sc copies in Li-1 and Li+1. And each node has a total of MI + Mc keys installed. We can calculate K, the size of each key space Si, i = 1 .. L, by using sc, sI, MI, and Mc. Since there are N sensor nodes on line i, and since setup server loads exactly MI unique keys from Si into each node on line i, setup server will need NM I keys. Each key from Si will have sI copies on line i. Also, sc copies of keys from Si+1 and Si-1 will be loaded into nodes from line i, and each node has Mc memory for keys from neighboring key spaces. Then, number of unique keys in any key space, K, can be computed as follows:

K = NM I s I = NM c 2s c Direct Key Establishment Phase. After deployment, nodes have to find shared keys with its neighbors. This phase is similar to the basic scheme [5]. Here, each node needs to know which keys its neighbors have so that it can decide which keys they share. Each node broadcasts a message containing the indices of the keys it carries. Nodes can use these broadcast messages to find out if they share common keys with their neighbors. If a node can find a shared key with one of its neighbors, it can use that key to establish a secure link between itself and its neighbor. Path Key Establishment Phase. If two neighboring nodes cannot find a shared key directly, they have to reach a common key over a secure path. This method is identical to the path key establishment method in Scheme I.

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4 Performance Analysis In our analysis and simulation, we use the following configuration. Deployment area is 1000m x 1000m. There are 50 deployment lines, i.e. L=50, and the distance between lines is 20m. On each deployment line there are 200 nodes, i.e. N=200. Total number of sensor nodes, NxL, is 10000. Distance between two adjacent deployment points, d, is 5m. Communication range, R, for each node is 40m. Standard deviation of normal distribution, σ, is 10m. For scheme II, total number of unique keys is 50K = 100000. 4.1 Local and Global Connectivity In this section, we show our simulation results of the probability of a node sharing a key with its neighbors. This probability is called local connectivity, Plocal. The detailed formulation for Plocal could not be given here due to space limitations. Figure 3 shows local connectivity versus memory usage m. We compare results for our scheme I and scheme II with Du et al’s [3] scheme. Scheme II has higher connectivity than [3] for all values of m. For scheme II, different values of sI and sc results in different Plocal values even for the same memory usage. In our experiments for various m values, we obtained best results when sI and sc are equal. Scheme I outperforms both scheme II and Du’s scheme for low m values. In our simulations, scheme I reached a maximum local connectivity value of 0.8518 at M=28 and Q=26 that yields m=80. As the number of keys used increases after m=80, local connectivity stays the same. Increasing M and Q, and consequently m, values means that a node shares keys with distant nodes. This will not contribute to the local connectivity, because distant nodes have very small probability of falling within that node’s communication range. Simulation results in Figure 3 confirm our explanation. There are two factors that makes scheme II’s connectivity performance better than Du et al.’s scheme. Firstly, in our schemes we use more deployment knowledge such that in Du’s scheme there is a single deployment point for each bundle of nodes, whereas in scheme II there are deployment points for each node. Secondly, in scheme II, 1 0.9 0.8

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we distribute copies of a key homogeneously. We distribute copies of a key to both upper and lower neighboring lines, so a node can use keys in its Mc to establish secure links with nodes on the same line, on its direct neighbor lines and nodes on two lines away. In addition, by introducing sI and sc, we can have a fixed number of copies of all keys. Du’s scheme can have the same average number of copies of keys with same m values but a particular key can have a much higher or much lower number of copies. Fixing number of copies in scheme II contributes to homogeneity of key distribution. A high local connectivity value means that a node can communicate with most of its neighbors securely. However, a high local connectivity value does not guarantee that there will not be isolated parts in the network. Thus, we need to examine that whether our schemes can create too many isolated components or not. We measured, global connectivity, which is the ratio of size of largest isolated part to the size of whole network, through simulations. The results show that 100% global connectivity is reached when m is as low as 10 for Scheme I and 30 for Scheme II. Since we determine the deployment point of all nodes in Scheme I and fix the number of copies of a key in Scheme II, we minimize the possibility that network has more than one isolated part. Our simulation results support this idea. 4.2

Resiliency Against Node Capture

We investigate the effects of compromised nodes on direct key establishment. We assume that total c randomly chosen nodes are compromised. The fraction of additional communications that can be compromised based on the information from the compromised nodes defines the resiliency of our system. This section is focused on the resiliency of Scheme II against node capture attacks. Scheme I uses pairwise keys, therefore it is %100 resilient against compromising of sensor nodes. Let kaj denote a key generated for line La. Assume kaj is used for a link between two nodes that are not compromised. We know that there are Si copies of kaj on the nodes of La, Sc copies of kaj on the nodes of La-1 and Sc copies of kaj on the nodes of La+1. Thus, in order to compromise kaj, adversary should compromise nodes from La-1, La, and La+1. If there are j compromised nodes on La, the probability that kaj is not compromised on line La is given as: ⎛N − pcomp _ i ( j ) = ⎜⎜ ⎝ sI

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Thus, if there are x compromised nodes on La-1, y compromised nodes on La and z compromised nodes on La+1, the probability that kaj is not compromised becomes Pcomp_c(x)*Pcomp_i(y)*Pcomp_c(z) .The probability that there are x compromised nodes on line La-1, y compromised nodes on line La and z compromised nodes on line La+1 is calculated as: ⎛ c ⎞⎛ c − x ⎞⎛ c − x − ⎟⎟⎜⎜ pc _ xyz = ⎜⎜ ⎟⎟⎜⎜ ⎝ x ⎠⎝ y ⎠⎝ z

y ⎞⎛ 1 ⎞ x ⎛ 1 ⎞ y ⎛ 1 ⎞ z ⎛ L − 3 ⎞ c− x− y− z ⎟⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎠⎝ L ⎠ ⎝ L ⎠ ⎝ L ⎠ ⎝ L ⎠

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By using equations 1, 2, and 3, we calculate the probability that an adversary obtains a key, which is used for a link between two nodes that are not compromised, out of randomly compromised c nodes as given below: N N −2

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Comparison of our scheme II and Du et al.’s [3] scheme is shown in Figures 4 and 5. In both schemes probability of a link being compromised, Pcomp_all, is plotted against number of nodes captured. In Figure 4, number of keys in a node is taken as 60 and number of nodes is 10000 for both schemes. In Figure 5, we fix local connectivity to 0.86 for both schemes. Our scheme is outperforms Du’s scheme, because we can reach a local connectivity of 0.86 with only m=90 keys in a node, whereas Du’s scheme requires m=140 to reach the same local connectivity. Probability of a secure link being compromised when a number of nodes are captured is directly proportional to the number of copies of a key. In scheme II, number of copies of a key is a parameter determined by sI and sc. In Figure 5, for scheme II there are 3+2*3 = 9 copies of a key. In Du et al.’s scheme, a key has a random number of copies but we can find an average number of copies of a key by using |S|, number of unique keys in the sensor network, N, number of total nodes and m, number of keys in each node: k average = N ⋅ m S . Because we used the same m values for both scheme II and Du’s scheme in Figure 4, there were six copies of a key for both schemes and we got very similar results for both schemes as shown in the figure. 0.09 Our Scheme 2 Du's Scheme

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4.3 Path Key Establishment Overhead As the number of hops in path key establishment phase increases, a node can reach more of its neighbors and communication cost increases. We analyzed path key establishment through simulations for scheme II and depicted the results in Figure 6.

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The ratio of neighbors that a node can reach in i hops is defined as pl(i). Obviously, pl(1) gives local connectivity. Our scheme performs better than Du et al.’s scheme [3] such that our scheme needs less number of hops for small m values. It can be observed from Figure 6 that for m=60 or larger values of m, a node can reach all its neighbors in at most two hops. In [3], only 63% of the nodes reach their neighbors in at most two hops when m=60. Moreover, in [3], m should be 200 in order for a node to reach all of its neighbors in at most two hops. 0.18 Our Scheme 2 Du's Scheme

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5 Conclusions In this paper, we proposed a new deployment model and two novel key predistribution schemes based on the proposed model. In our deployment model, we proposed

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the nodes to be deployed in lines in a continuous fashion. This model is practical and can be realized easily. In the proposed scheme I, we assume to know the deployment points of each node and with that knowledge we distribute pairwise keys to each node to be used for communication between its neighbors. In scheme II, we loosen this assumption and assume that a node can be at any deployment point in a known line. We compared our schemes with Du et al.’s key predistribution scheme [3]. Performance evaluation showed that scheme I can reach high local connectivity values even with small memory usage. This is due to the assumption in scheme I that we can know the neighbors of each node according to their deployment points. However, there is an upper limit in local connectivity; other schemes can have better local connectivity with high memory usage, whereas local connectivity in scheme I stays the same at 0.85 after a certain point. On the other hand, scheme II achieves higher local connectivity values than Du’s scheme in all cases. Both scheme I and II show good performance in global connectivity and it is possible to reach 100% global connectivity with small memory usage. Moreover, scheme II has better node capture resiliency than Du et al.’s scheme with the same local connectivity value. Furthermore, communication cost of path key establishment overhead is smaller in our schemes.

References [1] F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “A survey on sensor networks,” IEEE Communications Magazine, vol. 40, no. 8, pp. 102–114, August 2002. [2] H. Chan, A. Perrig, and D. Song. Random key predistribution schemes for sensor networks. In IEEE Symposium on Research in Security and Privacy, pages 197–213, 2003. [3] W. Du, J. Deng, Y. S. Han, S. Chen, and P. Varshney. A key management scheme for wireless sensor networks using deployment knowledge. In Proceedings of IEEE INFOCOM’04, March 2004. [4] W. Du, J. Deng, Y. S. Han, and P. Varshney. A pairwise key predistribution scheme for wireless sensor networks. In Proceedings of ACM CCS’03, pages 42–51, October 2003. [5] L. Eschenauer and V. D. Gligor. A key-management scheme for distributed sensor networks. In Proceedings of the ACM CCS’02, pages 41–47, November 2002. [6] D. Liu and P. Ning. Establishing pairwise keys in distributed sensor networks. In Proceedings of ACM CCS’03, pages 52–61, October 2003. [7] D. Liu and P. Ning. Location-based pairwise key establishments for static sensor networks. In Proceedings of ACM SASN ’03, pages 72–82, October 2003. [8] S. Zhu, S. Setia, and S. Jajodia. LEAP: Efficient security mechanisms for large-scale distributed sensor networks. In Proceedings of ACM CCS’03, pages 62–72, October 2003. [9] J. Spencer, The Strange Logic of Random Graphs, Algorithms and Combinatorics 22, Springer-Verlag 2000. [10] D. Liu, P. Ning, and W. Du. Group-Based Key Pre-Distribution in Wireless Sensor Networks. In Proceedings of 2005 ACM Workshop on Wireless Security. [11] D. Huang, M. Mehta, D. Medhi, and L. Harn. Location aware Key Management Scheme for Wireless Sensor Networks. SASN’04, October 25, 2004, Washington, DC, USA. [12] R. Blom. An optimal class of symmetric key generation systems. In Proceedings of EUROCRYPT 84, 1985.

Using Auxiliary Sensors for Pairwise Key Establishment in WSN Qi Dong and Donggang Liu Department of Computer Science and Engineering The University of Texas at Arlington Box 19015, Arlington, Texas 76019-0015, USA {qi.dong,dliu}@uta.edu

Abstract. Many techniques have been developed recently for establishing pairwise keys in sensor networks. However, they are either vulnerable to a few number of compromised sensor nodes or involve expensive protocols for establishing keys. This paper introduces a much better alternative for achieving high resilience to node compromises and high efficiency in key establishment. The main idea is to deploy additional sensor nodes, called assisting nodes, to help the key establishment between sensor nodes. The proposed approach has many advantages over existing approaches. In this approach, a sensor node only needs to make a few local contacts and perform a few hash operations to setup a key with any other sensor node in the network at a very high probability. The majority of sensor nodes only need to store a single key in their memory space. Besides these benefits, it still provides high resilience to node compromises. The implementation of this approach on TelosB motes also demonstrates its feasibility for pairwise key establishment in sensor networks. Keywords: Key management, pairwise keys, sensor networks.

1

Introduction

Wireless sensor networks are ideal candidates for a wide range of applications in military and civilian operations such as health monitoring, data acquisition in hazardous environments, and target tracking. Security has been recognized as a critical requirement for many sensor applications, especially in military operations. Key management is the cornerstone to ensure the security of many network operations. As one of the most fundamental security services, pairwise key establishment enables secure node-to-node communication using cryptographic methods such as encryption and authentication. Many techniques have been developed recently to setup pairwise keys in sensor networks [1,2,3,4,5,6,7,8,9,10]. Perrig et al. developed the SNEP protocol to provide pairwise key establishment using a KDC [1]. This approach, however, introduces huge communication overhead and is vulnerable to single point failure. A number of key pre-distribution schemes were proposed to establish keys I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 251–262, 2007. c IFIP International Federation for Information Processing 2007 

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without the online KDC [2,3,4,5,6]. These approaches preload a small set of secrets into every sensor node before deployment to make sure that after deployment, every two sensor nodes can setup a shared key using their preloaded secrets. However, these approaches either require expensive protocols (e.g., path key establishment) to setup keys or are vulnerable to a small number of compromised sensor nodes. In addition, some techniques also use the sensors’ location information and assume static sensor nodes [7,8,11,10,9]. However, these two assumptions may not be true in practice. This paper presents a novel technique for pairwise key establishment in sensor networks. The main idea is to deploy additional sensor nodes, called assisting nodes, to help the key establishment between sensor nodes. Different from the nodes in traditional networks where they are mainly used for sensing and forwarding, the assisting nodes are only responsible for key management in the network, exploiting a novel dimension of using sensor nodes. The proposed approach has many advantages over existing approaches. First, it can achieve a very high probability of establishing a shared key between any two sensor nodes. Second, a sensor node only needs to make a few local contacts and perform a few hash operations to setup a key with any other sensor node in the network. Third, the majority of sensor nodes only need to store a single key in their memory space. Fourth, it does not depend on the sensors’ location information and can be used for the sensor networks with highly mobile sensor nodes. Besides these benefits, our approach still provides high resilience to node compromises. Finally, the implementation of this approach on TelosB motes [12] also demonstrates its feasibility for key establishment in sensor networks. The rest of the paper is organized as follows. Section 2 presents our pairwise key establishment protocol as well as the detailed analysis. Section 3 gives the implementation issues. Section 4 reviews related work. Section 5 concludes this paper and points out some future work.

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Pairwise Key Establishment

This section provides the technical detail as well as the analysis on how to establish pairwise keys using auxiliary sensors. In this paper, we consider the sensor networks consisting of a large number of tiny resource-constrained sensor nodes [13]. These sensor nodes can be static or highly mobile. We assume that the attacker can eavesdrop, modify, forge, replay or block any network traffic. We also assume that the attacker can compromise a few sensor nodes and learn all the secret information, including the keying materials, on those compromised nodes [14]. 2.1

Protocol Description

Typically, sensor nodes are deployed to sense the conditions in their local surroundings and report observations for various uses. However, in this paper, we exploit a new dimension of using sensor nodes and believe that it is important

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to deploy sensor nodes to facilitate certain network protocols such as key management. Hence, the main idea of our approach is to deploy additional sensor nodes, called assisting nodes, to help the pairwise key establishment between sensor nodes. The detailed protocol is presented below. Let n be the network size and m be the number of assisting sensor nodes. For convenience, we call the sensor nodes that are not assisting nodes as the regular sensor nodes. – Initialization: Before deployment, the base station generates a master key Ku for every sensor node u. The master key Ku is only known by the sensor node u and the base station. Every assisting node i will get preloaded with a hash H(Ku ||i) for every regular sensor node u, where H is a one-way hash function, and “||” denotes the concatenation operation. Hence, an assisting node will need to store n hash images. This clearly introduces considerable storage overhead at assisting sensor nodes. However, the only job of the assisting nodes is to help pairwise key establishment. As a result, they can use all their memory, including the flash memory, to store these values. Therefore, we believe that it will be feasible for an assisting node to store n hash images. For instance, the TelosB motes have 1MB flash memory and can store the hash images for a network of 128,000 sensor nodes if every hash is 8 bytes long. Additionally, research focusing on high-capacity and energyefficient storage subsystem on sensor network platforms has drawn a lot of attention, which will soon make it possible to equip a sensor node with a large flash memory [15] without increasing the cost significantly. Therefore, more and longer hash images can be stored in each assisting node for a very large sensor network. – Pairwise Key Establishment: After deployment, every regular sensor node discovers the assisting nodes in its neighborhood. When a sensor node u needs to establish a pairwise key with another node v, it will send a request to every neighbor assisting node i. The request message includes the IDs of both sensor nodes and will be protected by the key H(Ku ||i), which has been preloaded to the assisting node i. The assisting node i will serve as a KDC and generate a reply to u. This reply message includes two copies of a random key R, one is protected by H(Ku ||i) (for node u) and the other is protected by H(Kv ||i) (for node v). This procedure is similar to the Needham-Schroeder Symmetric Key Protocol[16]. After the request, u will get a random key from every neighbor assisting node. Let {R1 , ..., Rl } be the set of all these random keys. The final key Ku,v between u and v is simply the bit-wise XOR of all these keys, i.e., Ku,v = R1 ⊕ R2 ⊕ · · ·⊕ Rl . Obviously, as long as at least one random key is secure, the final key will be safe. Though our later analysis in Section 2.2 shows that even a small fraction of assisting nodes can guarantee a high probability of establishing pairwise keys using the above algorithm, it is still possible that a regular sensor node cannot find any assisting sensor node in its neighborhood since the accurate deployment of assisting nodes may not be guaranteed in some scenarios. To deal with this issue, we have supplemental key establishment, where a regular sensor node may

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discover the set of assisting nodes within a certain number of hops. This will certainly increase the chance of finding an assisting node to use. An additional benefit of doing this is to achieve better security performance. From the previous description, u derives the final key by applying XOR operations to all the random keys, which implies that the more random keys, the higher the security of the final key. – Supplemental Key Establishment: In this step, a sensor node u discovers the assisting sensor nodes that are no more than h hops away from itself. This can be easily achieved by having node u’s neighbors to help collecting the IDs of the assisting nodes around them. The neighbor nodes will broadcast the inquiry message on behalf of u, and forward u the replies from assisting nodes. Once such set is discovered, the remaining step will be similar to the pairwise key establishment discussed before. The discovery and usage of assisting nodes multiple hops away will introduce additional communication overhead since the intermediate nodes will be needed to relay the messages. However, this will only involve communication in a local area, which we believe will not be a big problem for the current generation of sensor networks. Also, the need for the supplemental key establishment will not likely be invoked frequently. 2.2

Analysis and Discussion

This subsection will present the performance analysis of the proposed scheme, focusing on the probability of establishing pairwise key, the resilience against node captures, and the overheads. For simplicity, we assume that all the n regular sensor nodes and the m assisting nodes are evenly deployed in the field. Probability of Establishing Keys: During the pairwise key establishment, a sensor node u is required to communicate with at least one assisting node in its neighborhood to setup a key with another sensor node. Let d denote the average number of one-hop neighbors of a sensor node. The probability that any assisting node i is not in the local area of the regular sensor node u can be estimated by 1 − d/(m + n). Thus, the probability that a regular sensor node fails to find any assisting node in its neighborhood can be estimated by (1 − d/(n + m))m . The probability P of establishing a pairwise key can then be estimated by P = 1 − (1 − d/(n + m))m . As d << n is usually satisfied in practice, P can be further approximated by 1 − e−dm/(n+m) . Figure 1 shows the relationship between the probability P of establishing key and the fraction of assisting nodes m n . From the figure, we can see that a small fraction (0.1) can guarantee a high probability (greater than 0.9) of establishing keys between sensor nodes. On the other hand, since P increases faster with larger number of d , the proposed scheme can achieve attractive performance in high-density networks. During the supplemental key establishment, the assisting nodes within h-hop range of u will be used. Obviously, the larger the range, the higher probability of finding the assisting nodes. Here we only analyze the situation when h = 2. From

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the above discussion, the probability that none of u’s neighbor nodes can find any assisting node can be estimated by ((1 − d/(n + m))m )d . Let P  denote the probability of establishing a pairwise key using the assisting nodes in two-hop range. Therefore, P  = P + (1 − P ) × (1 − (1 − d/(n + m))md). Figure 1 indicates that by using two-hop assisting nodes, even when the fraction of m n is as small as 0.003, the probability of establishing key is still greater than 0.9. Resilience against Node Captures: We assume that the base station will never be compromised. Thus, the master key of any non-compromised node will be always safe since the assisting nodes are only equipped with the hashes of the master key. Even if an assisting node is captured, it is computationally infeasible to get the original keys from the hashes due to the one-way property of hash functions. We also note that the sensor node derives the final key by applying XOR operation to all the random keys. The pairwise key will be secure unless all the related assisting nodes are compromised. This indicates an attractive property of our scheme: a benign assisting node can guarantee the security of the keys established in its neighborhood as long as it can communicate with the sensor nodes in its neighborhood. We then study the probability Pc of a key being compromised when a certain fraction of nodes are compromised. Assume the attacker will randomly compromise a fraction fc of sensor nodes. From our earlier analysis, Pc is equal to the probability that all the corresponding random keys are compromised. The number of assisting nodes that might provide those random keys can be estimated (m×d)/n by m×d . Figure 2 shows that our apn . Hence, Pc can be estimated by fc proach is highly resilient to the node compromise attack. It also implies that we can enhance the security of key management by deploying more assisting nodes.

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Overheads: The proposed scheme only requires a single key for every regular sensor node and n hash values for an assisting node. As we discussed before, the assisting node is only responsible for the pairwise key establishment and can use all its memory, including the flash memory, to store these hash images. The proposed scheme involves small computation overheads. A regular sensor node only need to apply a few symmetric key operations and hash operations to establish a key with any other sensor node. We note that in pairwise key establishment phase, the communication is in one-hop range. Although multi-hop communication will occur when supplemental key establishment is needed, the communication is still limited in a local area. Moreover, we have shown that in most cases, only one-hop communications are needed. As a result, the supplemental key establishment will not incur significant communication overhead for our protocol. 2.3

Comparison with Previous Schemes

This section will compare the proposed scheme with previous techniques for pairwise key establishment such as the basic probabilistic scheme [2], the q-composite scheme [3], the random pairwise keys scheme [3], the random subset assignment scheme [4], and the grid-based scheme [4]. Security Performance: We assume the network size n = 20, 000 and the average number of neighbors d = 50. For previous schemes, we assume each sensor can store 200 keys. Hence, for the grid-based scheme [4], the probability of two nodes sharing a direct key is 0.014. For the other schemes, we set P = 0.33 to make sure the network is well connected. However, from our previous analysis, our approach can always guarantee the establishment of pairwise keys at a very high probability using a small fraction of assisting nodes.

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Figure 3 shows the fraction of compromised links in the presence of compromised nodes for different schemes. The figure tells us that in terms of protecting the direct keys, our scheme can provide high resilience to node compromises, which is similar to the random subset assignment scheme and the grid-based scheme [4]. In addition, we must remember that our scheme can guarantee a much higher probability of establishing a pairwise key between two sensor nodes in a densely deployed sensor network. Note that the previous schemes need to employ expensive protocols for path key establishment when two sensor nodes cannot directly setup a pairwise key. As a result, the attacker might discover not only the direct keys but also the indirect (path) keys by compromising the intermediate nodes used in the establishment of the indirect (path) keys. On the contrary, our approach does not need to setup path keys. Even if the attacker has captured the nodes which relay the keying information, the key will not be disclosed. Figure 4 shows the fraction of compromised (direct or indirect) keys between non-compromised nodes in the presence of compromised nodes. The figure clearly shows that our scheme performs much better than other schemes. For example, when 70% sensor nodes are compromised, the fraction of compromised pairwise keys between non-compromised sensor nodes is only around 0.18. Contrarily, at least 88% keys have been exposed in the previous schemes. Additionally, our proposed scheme can guarantee that a single benign assisting node can protect the keys established in its neighborhood as long as this node can talk to the sensor nodes in its neighborhood. Overheads: In the proposed scheme, only a single master key is stored in every regular sensor node, while the previous schemes have considerable storage requirements for achieving high performance. For instance, In Figure 3 and Figure 4, the previous schemes require every node to store 200 entries to achieve

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the desire performance. In terms of the computation overhead, our proposed approach involves only a few number of symmetric key operations and hash operations. Hence, it will not incur much additional overhead. From the previous discussion, most of the communication overhead is introduced in the pairwise key establishment phase, which only requires direct communications in one-hop range. The multi-hop communication in the supplemental key establishment rarely occurs due to the high probability of finding a neighbor assisting node. On the other hand, for many previous schemes such as the grid-based scheme [4] and PIKE [6], a sensor node often needs to go through the path key establishment to setup keys with other sensor nodes. Such path key establishment could be very expensive in practice since the intermediate sensor node that can help establish the pairwise key may be located far away from the two sensor nodes that want to establish a shared key. According to the above discussion, we can clearly see that our proposed approach has significant advantages over existing schemes in terms of storage, computation and communication overheads. 2.4

Security Reinforcing Version

From our previous analysis, we note that once an assisting node is compromised, the attacker is able to discover all the random keys generated by this node. Although the actual pairwise key is combined from multiple random keys generated by different assisting nodes, it is still not desirable to let the attacker figure out the old random keys. In the following, we give a simple extension to fix this problem by updating the keys at the assisting nodes. The basic idea is to update the key at every assisting sensor node after the pairwise key establishment. In other words, the hash key at any assisting node will be changed immediately after it is used once. As a result, the attacker is not

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able to reveal any random key generated before even if the assisting sensor node is compromised at certain point. To achieve this goal, we will take the advantage of the one-way hash function H(·). We will also maintain a sequence number for every hash key shared between a regular sensor node and an assisting node. For example, initially, the hash key Hu = H(Ku ||i) and the sequence number Su = 0 will be stored in the assisting node i for the regular sensor node u before deployment. Once the assisting node i receives the request message to setup a pairwise key between u and v, i will send a random key R to one of the nodes along with the current sequence number Su and Sv via the secure links. At this time, the two copies of the random key R are protected by the hash values Hu and Hv respectively. After that, node i will replace Hu with H(Hu ) and Hv with H(Hv ), and also increase Su and Sv by 1. When the regular sensor node u receives the message from i, u will verify the authentication and confidentiality of the message using the same hash Hu , which can be computed based on Ku , i and Su . Node u can then derive the random key R for pairwise key establishment. In the protocol, node u may choose to keep track of the sequence number Su with each neighbor assisting node in its local area to reduce the overhead during the calculation of the hash key Hu . Such sequence number can certainly be used to deal with the replay attacks as well. Therefore, by employing one-way hash function, the improved approach can enhance the resilience against node captures, i.e., any compromised node will not reveal any secret about the pairwise keys established before. However, compromised assisting sensor nodes can still participate in the pairwise key establishment in the future when new nodes are added in the network. These malicious assisting nodes may disclose valuable information to adversaries. Fortunately, our scheme guarantees that as long as there are at least one benign assisting node in a given area, the final pairwise key will be still safe no matter how many sensor nodes are compromised. Based on this property, we may deploy new assisting sensor nodes to replace the old and untrustworthy ones to achieve better security during the pairwise key establishment.

3

Implementation Issues

Based on the previous analysis, we can see that our proposed pairwise key establishment approach is efficient for resource-constrained sensor nodes. In this section, we will present the implementation issues. We have implemented the prototype of the proposed scheme under TinyOS platform [17]. We use RC5 module [18] to implement the security primitives such as hash and MAC operations, assuming 8-byte long hash values and keys. This mechanism is transparent to the applications. In the protocol, the regular sensor node will first send request messages to its neighbor assisting nodes and wait for their responses. An assisting node generates the random key and send the reply message to every requesting sensor node. After the regular sensor node collects the random keys, it will combine these keys to derive the final pairwise key.

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Our scheme has been tested on the TelosB [12] motes. For the assisting nodes, the additional code space is 2598 bytes in the ROM, and the extra usage of data space in the RAM is 892 bytes. We also make use of the 1M flash memory on the chip to store the hash values of the regular nodes’ master keys. For the regular nodes that need to setup secure communication links with 50 neighbors, the additional code space in the ROM is 2102 bytes, and the extra data space in the RAM is 682 bytes. Clearly, the proposed scheme is practical for sensor networks in terms of the code size.

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Related Work

The closest related work to the techniques studied in this paper is pairwise key establishment. Many techniques have been proposed along this research direction, including the basic probabilistic scheme [2], the q-composite scheme [3], the random pairwise keys scheme [3], the two threshold-based schemes [4,5] and PIKE [6]. Additionally, the prior deployment and post deployment knowledge were also used to improve the performance of key pre-distribution in various situations [7,8,11,10]. This paper gives a better way for pairwise key establishment by exploiting a new dimension of using sensor nodes. There are many other studies on sensor network security, including broadcast authentication [1,19], tamper-resistant hardware [20], secure data aggregation [21], and vulnerabilities, attacks, and countermeasures [22]. We consider them complementary to our technique.

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Conclusion and Future Work

In this paper, we developed a novel scheme to establish the pairwise keys in sensor networks. This scheme takes advantage of special nodes (the assisting nodes) in the network for key management, representing a new dimension of using sensor nodes. The analysis indicates that our scheme has significant advantages over the existing approaches. By making use of these cheap assisting nodes, we ease the burdens of other regular sensor nodes and further extend the lifetime of the whole network. Several research directions are worth investigating. We are interested in conducting a thorough evaluation in a large scale sensor network. We are particularly interested in issues on how to tolerate the communication error and delay in bad channel conditions, how to withstand the high deployment failure rate where a lot of multi-hop communication may be needed. In addition, the additional assisting nodes in the proposed scheme are only deployed to establish the pairwise keys. However, we may make further use of those nodes to defend the network against various other attacks. Acknowledgment. The authors would like to thank the anonymous reviewers for their valuable comments.

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References 1. Weis, S., Sarma, S., Rivest, R., Engels, D.: Security and privacy aspects of low-cost radio frequency identification systems.: In SPC‘03, LNCS, Vol.2802. Springer-Verlag (2003) 454 V 469 2. Ohkubo, M., Suzuki, K., Kinoshita, S.: Cryptographic Approach to Privacy-friendly Tags. In RFID Privacy Workshop. MIT (2003)

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3. Menezes, A.J., van Oorschot, P.C., Vanstone, S. A.: Handbook of Applied Cryptography. CRC Press (1997) 4. Avoine, G., Dysli, E., Oechslin, P.: Reducing time complexity in RFID systems.: In SAC‘05. LNCS, Vol. 3897. Springer-Verlag (2006) 291 V 306 5. Gaubatz, G., Kaps, J.P., Öztürk, E., Sunar, B.: State of the Art in Ultra-Low Power Public Key Cryptography for Wireless Sensor Networks.: In PerSec‘05, Kauai Island, Hawaii (2005) 6. Hoffstein, J., Silverman, J., Whyte, W.: NTRU report 012, version 2. estimated breaking times for NTRU lattices, Technical Report 12, NTRU Cryptosystems, Inc. (2003) 7. National Institute of Standards and Technology (NIST). FIPS-197: Advanced Encryption Standard, November (2001). Available online at http://www.itl.nist.gov/fipspubs/ 8. Fujistsu web site, 2006. Referenced 2006 at http://www.fujitsu.com/us/services/edevices/ microelectronics/memory/fram/ 9. Feldhofer, M., Dominikus, S., Wolkerstorfer, J.: Strong authentication for RFID systems us-ing the AES algorithm.: In CHES‘04. LNCS, Vol. 3156. Springer-Verlag (2004) 357 V 370 10. Molnar, D., Wagner, D.: Privacy and security in library RFID: Issues, practices, and architectures.: In CCS‘04. ACM Press, Washington, DC, USA (2004) 210 V 219 11. Juels, A., Weis, S.: Authenticating pervasive devices with human protocols. In CRYPTO‘05. LNCS, Vol. 3621. Springer-Verlag (2005) 293 V 308. 12. NTRU RFID data sheet, 2006. http://www.ntru.com/products/NtruRFID.pdf 13. NTRU RFID white paper, 2006. www.ntru.com/products/RFID_White_paper_FNL.pdf 14. Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: A Ring-Based Public Key Cryptosystem.: Algorithmic Number Theory (ANTS III). LNCS, Vol. 1423. Springer-Verlag, Berlin (1998) 267-288 15. Graham, N.H., Nguyen, P., Pointcheval, D., Proos, J., Silverman, J. H., Singer, A., Whyte, W.: The Impact of Decryption Failures on the Security of NTRU Encryption. In CRYPTO‘03, Santa Barbara, USA (2003) 16. Dimitriou, T.: A Lightweight RFID Protocol to protect against traceability and cloning attacks. In SecureComm‘05 59 V 66 17. Capkun, S., Hubaux, J.P.: Secure positioning of wireless devices with application to sensor networks. In INFOCOM‘05 18. Avoine, G., Oeschlin, P.: A Scalable Protocol for RFID Pseudonyms. In Persec (2004) 19. Molnar, D., Soppera, A., Wagner, D.: A Scalable, Delegatable Pseudonym Protocol Enabling Ownership Transfer of RFID Tags. Workshop on RFID and Light-Weight Crypto, July 14-15, Graz, Austria (2005) 20. Dai W.: Crypto++, a Free C++ Library for Cryptography. http://www.eskimo.com/~weidai (2004) 21. O‘Rourke, C., Sunar, B.: Achieving NTRU with Montgomery Multiplication. In IEEE Trans. on Comp., vol. 52, No. 4, April (2003) 22. Kaya, S. V., Savas, E., Levi, A., Ercetin, O.: Privacy-Aware Multi-Context RFID Infrastructure using Public Key Cryptography http://students.sabanciuniv.edu/~selimvolkan / MultiContext_RFID_Framework.pdf (November 19, 2006)

Minimum Cost Configuration of Relay and Channel Infrastructure in Heterogeneous Wireless Mesh Networks Aaron So and Ben Liang Department of Electrical and Computer Engineering University of Toronto, Toronto, Ontario, Canada M5S 3G4 {aaronso,liang}@comm.utoronto.ca

Abstract. Fixed broadband wireless access is a promising technology allowing Internet service providers to expend their customer base in sparsely populated rural areas. Because the size of the target service area is humongous, relay infrastructure is essential. Installing and maintaining this relay infrastructure is the main cost associated with such networks. Thus, we develop an optimization framework which computes the minimum number of relay stations and their corresponding channel configurations such that a pre-specified subscribers’ traffic demand can be satisfied. Since the problem is a mixed-integer program, we propose an efficient optimization algorithm to compute the optimal solution in a reasonable amount of time. Our numerical results show that by using a few relay stations in a rural community, broadband Internet access can be established in a cost effective manner. Keywords: Fixed wireless broadband Internet access, relay stations, optimal placement and channel assignment.

1 Introduction Since high wiring cost is one of the biggest factors inhibiting wired broadband Internet access in sparsely populated rural areas, broadband wireless has long held the promise of delivering a wide range of data and information services to business and residential customers quickly and cost-effectively. With the publication of a comprehensive industry standard, namely IEEE 802.16, broadband wireless is ready to unleash its full potential. The IEEE 802.16 standard requires two separate physical layer specifications because the propagation characteristics of radio waves are so different in the lowerand upper-microwave regions. The WirelessMAN-OFDM and WirelessMAN-SC specifications utilize the 2-11 GHz and 10-66 GHz spectrum respectively. Lower frequency signals can penetrate walls and deflect from obstacles, while higher frequency transmissions must meet strict line-of-sight requirements. However, the advantage of using high frequency bands is an abundance of bandwidth. This intrinsic property of IEEE 802.16 technology makes it ideal for a heterogeneous architecture. 

This research was made possible thanks to Bell Canada’s support through its Bell University Laboratories R&D program.

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For the network under investigation, we assume that there is a base station wired to the ISP core network, and this base station is assigned to serve sedentary subscribers in a particular area. Because of the size of the coverage area, the base station usually cannot serve every subscriber by single-hop communication. As a result, several relay stations (RSs) are installed in the network, for example, on the subscribers’ rooftops, to relay traffic from and to the base station. If line-of-sight communications can be established among some RSs and the base station, the bandwidth abundant high frequency spectrum is used to form a backbone network. The lower spectrum, on the other hand, is used by the base station and RSs to communicate with the subscribers and form the corresponding local network. For this architecture, the cost of the network is dominated by the installation and maintenance cost of the RSs. Under this hypothetical heterogeneous mesh networking architecture, the focus of this work is to minimize the number of RSs used in the mesh network while maintaining the prespecified uplink and downlink demands of the subscribers. Note that the above IEEE 802.16 specifications are used only as an example; the analytical framework presented in this paper is general and can be applied to mesh networks based on other types of wireless technologies. To the best of our knowledge, this work is among the first solutions to address the problem of joint relay equipment placement and channel assignment in a heterogeneous wireless mesh network. In this work, we describe a heterogeneous wireless mesh network architecture with relay infrastructure and develop an analytical framework which determines whether a network with a particular relay station placement and channel assignment can satisfy the subscribers’ demands and interference constraints. Furthermore, we propose an optimization framework which combines a heuristic with Bender’s decomposition to calculate the minimum deployment and maintenance cost of a given heterogeneous wireless mesh network. The rest of this paper is organized as follows. In Section 2, we review the related work in multihop wireless networks. In Section 3, we describe the network infrastructure and equipment capabilities. In Section 4, we define our relay station placement and channel assignment problem mathematically, and describe an optimization solution. In Section 5, we discuss the convergence time and performance of the proposed optimization algorithm. Finally, concluding remarks are given in Section 6.

2 Related Works Motivated by recent advances in ad hoc networking [1][2], wireless multihop mesh networking is now considered as the next evolutionary step for wireless data networks. To bring wireless mesh networks closer to reality, in [3], Draves et al. conducted a detailed empirical evaluation of several link-quality metrics on route computation performance in wireless mesh networks. The issue of interference management in wireless mesh networks has been discussed in several contexts. In [4], Jain et al. considered the fundamental question of how much throughput a given wireless mesh network can achieve under different interference conditions. To address operational issues, an interferenceaware channel assignment algorithm for multi-radio wireless mesh networks was proposed in [5] by Ramachandran et al.

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The problem of wireless network equipment placement has also been addressed in several works. In [6], So and Liang proposed a Lagrangian approach to computes the optimal placement of a fixed number of relay node, which relay traffic in a two-hop fashion, to improve throughput in a WLAN. In the context of community mesh networks, innovative integration techniques were developed by Begerano in [7] to minimize the number of wired access points in a mesh network to reduce wiring cost, while maintaining users’ QoS constraints. To the best of our knowledge, there is no existing work that addresses the problem of joint relay equipment placement and channel assignment in community wireless mesh networks, which is what we investigate in this work.

3 Infrastructure and Equipment Capabilities To establish a network in a rural area, an operator needs to establish a site for the initial base station and the central office, which should have high capacity backhaul connection with the ISP core network. One cost effective backhaul solution is to lease dark fiber from electrical utilities or railroad companies. However, by using this approach, the network point of access is already fixed. Thus, the ISP does not have the freedom to choose the location of the central office and initial base station. In this work, we consider the case where the location of the base station and central office is given. Our goal is to place the minimum number of relay stations in the network such that the demands of the subscribers can be met. Since the subscriber locations are fixed and the high frequency spectrum is used, by using advanced antenna technologies and the three-dimensional space intelligently, we can effectively control interference in both the backbone and local networks. Adaptive array antenna technologies [8][9] have the ability to focus a beam very tightly toward a receiver, virtually eliminating the effects of interference. However, since such equipment is expensive, we assume that it is used only in the backbone network. For the local network, we assume a more affordable and common approach as follows [10]. Polarized directional antennas only disposes magnetic fields horizontally. When the antenna is tilted downward (or upward), beyond

Backbone Network Link Local Network Link

Base Station

Relay Station 2 Relay Station 1

High Capacity

Fiber Optic Link Relay Station 3

ISP Core Network

Fig. 1. Tilted polarized directional antenna systems

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a certain distance, the radiation will simply be absorbed into the ground (or outer space). As shown in Fig. 1, two relay stations, e.g., Relay Station 2 and 3, can use the same channel for the local network and do not interfere with each other as long as they are placed far apart from each other. However, since subscribers who use the same RS are located in the same multipath environment, they have to share the channel in a timemultiplexed fashion. In the next section, we define the problem mathematically.

4 System Model and Optimization Framework Suppose there are N subscribers and one base station in the system, and they are represented by the set V = {0, 1, ..., N }, where the base station is represented by the index 0. Let VR ⊆ V be the set of nodes where the installation of relay stations are feasible.1 We can use the set VR to form a directed-complete graph representing the backbone B network. The link weight from node i to node j, denoted Cij , represents the capacity in terms of bit per second from node i to node j using the backbone technology. The capacity between two nodes is zero if line-of-sight communication cannot be established. Similar to the backbone network, we can use the set V to form a directed-complete graph representing the local network. Within the local technology, the capacity from L . Since a link which handles local traffic has to be node i to node j is denoted by Cij L associated with the base station or a relay station, Cij = 0 if both i and j are not in the set VR . As mentioned above, two relay stations using the same channel would interfere each other’s local network operations if they are placed in each other’s interfering zones. Let N (i) be the set of nodes that interfere the operation of node i, where i ∈ VR . Moreover, when there are NC local channels available, let Λ = {1, 2, ..., NC } be the local channel set. Furthermore, for each subscriber i, there is a pre-specified uplink demand, ui , and downlink demand, di . Given the above as the input to our problem, we define the following decision variables. For discrete decision variables, let us set Xiλ = 1 if an RS which uses channel λ is installed in node i; otherwise we set Xiλ = 0. We term Xiλ the location-channel variables. Let us define the following continuous decision variables. Let fijd and fiju be the amount of downlink and uplink traffic flow from node i to node j by using the backbone technology respectively. Let hdij and huij be the amount of downlink and uplink traffic flow from node i to node j by using the local technology respectively. All input and decision variables are non-negative. Moreover, we define X01 = 1 since the base station is always present, and without loss of generality, we can also let the base station use channel 1 for its local network operation. Next, we formulate our problem as a mixed integer program. 4.1 Optimization Formulation Our goal is to find the minimum number of RSs in the system which satisfies all the demand and interference constraints. The optimization formulation is as follows: 1

Whether a subscriber site is in VR or not depends on the willingness of the subscriber and other physical conditions. Furthermore, the base station, which has index 0, is included in the set VR .

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min : X

s.t.



Xiλ

(1)

i∈VR ,λ∈Λ



i∈VR \{0}



d f0i +





hd0i =



ui

(2)

di

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i∈V \{0} u fji



hui0 =

i∈V \{0}

i∈VR \{0}

i∈V \{0}

∀ i ∈ VR \{0}

(4)

fijd

∀ i ∈ VR \{0}

(5)

huij ≥ ui

∀ i ∈ V \{0}

(6)

hdji ≥ di

∀ i ∈ V \{0}

(7)



huji



fiju

+

=

j∈V \{0}

j∈VR ,i=j



d fji −

j∈VR ,i=j

hdij =

j∈V \{0}

j∈VR ,i=j





u fi0 +



279



j∈VR ,i=j

j∈VR



j∈VR



hdij + huij

j∈V,j=i

L Cij



hdij + huji ≤ k

j∈V



+

hdji + huji



L Cji

Xiλ

≤ (1 − Xiλ )k + 1

∀ i ∈ VR , λ ∈ Λ(8)

∀ i ∈ VR

(9)

∀ i ∈ VR

(10)

λ∈Λ

Xiλ ≤ 1

λ∈Λ B fiju + fijd ≤ Cij



Xiλ

∀ i ∈ VR , j ∈ VR , i = j (11)

Xjλ

∀ i ∈ VR , j ∈ VR , i = j (12)

λ∈Λ B fiju + fijd ≤ Cij

Xiλ +





λ∈Λ

Xjλ ≤ 1

∀ i ∈ VR , λ ∈ Λ

(13)

j∈N (i)

The objective (1) minimizes the number of RSs to be installed in the network. Constraints (2) and (3) verify that the amount of traffic entering and exiting the base station equals the total uplink and downlink demands respectively. Constraints (4) and (5) verify that the amount of traffic entering each RS matches the amount of traffic exiting each RS (the conservation of flow at each RS). Constraints (6) and (7) verify that the uplink and downlink demands are met respectively. Constraints (8) and (9) work together with an arbitrary large number k. If an RS which uses channel λ is placed at node i, then Xiλ = 1, and the right hand side of constraint (8) is 1. Since local uplink and downlink traffic share the channel in a time-multiplexed fashion, constraint (8) verifies that the local traffic enters and exits through the ith RS does not exceed its capacity. If no RS is installed at node i, then Xiλ = 0 ∀λ ∈ Λ and the right hand side of constraint (8) is k + 1. Thus, constraint (8) does not impose any restriction on the traffic exiting and entering node i. However, the right hand side of constraint (9) is 0. This ensures that no

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local uplink traffic enters node i and no local downlink traffic exits node i. Constraint (10) verifies that at most one channel can be assigned to an RS. Constraints (11) and (12) work together to ensure that a positive backbone traffic between node i and j exists only if an RS is placed at node i and an RS is placed at node j. Finally, constraint (13) ensures that no two RSs which use the same channel are placed in each other’s interfering zone. 4.2 Problem Reformulation and Bender’s Decomposition Traditionally, any mixed integer problem can be solved by branch-and-bound. However, such approach is virtually intractable even for a small number of discrete variables because an exponential number of linear programs have to be solved. Given that we have a large number of continuous variables and a relatively small number of integer variables, Bender’s decomposition breaks down the problem to a sequence of small 0-1 integer problems [11] which can be solved efficiently by commercial optimization softwares such as CPLEX. In the following, we first reformulate the above analytical framework so that it can be decomposed by Bender’s method. Then, we describe the algorithm that we used to solve the RS placement and channel assignment problem. To apply Bender’s decomposition to a mixed integer program, the problem needs to be organized into the following form 2 min c1 y + c2 x

(14)

s.t. A1 y + A2 x ≥ b,

(15)

x,y

where x is a vector represents the location-channel variables Xiλ , y is a vector represents the set of continuous variables fiju , fijd , huij , hdij , c1 = 0t , c2 = 1t , and (·)t denotes vector transposition. For a fixed value of the location-channel variables x = x , problem (14) reduces to the following feasibility problem: min T (y| x)  c1 y

(16)

s.t. A1 y ≥ b − A2 x 

(17)

y

Obviously, given a particular RS placement and channel assignment, x , the resulting problem, (16)(17), may or may not be feasible. To make all location-channel variables feasible, let us introduce one positive continuous variable, v, and a very large infeasibility constant, P . We can then modify  (16)(17) by changing A1 to A1 = [A1 |1], c1 t   to c1 = [0 |P ], and y to y = y v. Then, the modified feasibility problem is the following: min T (y  | x) = c1 y  = P v 

(18)

 s.t. A1 y  ≥ b − A2 x

(19)

y

For any x  which makes (16)(17) infeasible, problem (18) (19) is still feasible, but it will suffer a very large infeasible penalty P v. 2

a = b is equivalent to a ≥ b and b ≥ a.

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Now, let us consider the dual of the modified feasibility problem (18)(19). Let u be the set of dual variables. The dual of the modified feasibility problem may now be formulated as follows: max D(u| x)  (b − A2 x )t u u

s.t. At1 u ≤ ct1 u≥0

(20) (21) (22)

Denote the optimal solutions to the linear programs (18) and (20) by y ∗ and u∗ respectively. Then, by duality theory, c1 y ∗ = (b − A2 x )t u∗

(23)

We now consider all the extreme points of the dual problem (20). Note that the extreme points are defined by the feasible region described by (21) and (22) which are independent of the location-channel variables x. Thus, the extreme points can be generated without any knowledge of the RS locations and channel assignments. Let us denote the ith extreme point by ui and total number of extreme points by p. We know from the theory of linear programming that at least one optimal solution to any linear problem occurs at an extreme point of the feasible region. Thus, the original problem can be reformulate as the following pure 0-1 problem: min c2 x + D

(24)

s.t. D ≥ (b − A2 x)t ui ∀i ∈ [1, p],

(25)

x

or equivalently, min D

(26)

x



s.t. D ≥ c2 x + (b − A2 x) u

t i

∀i ∈ [1, p].

(27)

The difficulty with problem (26) is that the number of extreme points of the dual problem is potentially very large. Thus, we do not want to enumerate all of the constraints in (27) explicitly. Also, at the optimal solution to (26), only a small subset of the constraints (27) are likely to be tight. Thus, even if we could enumerate all of them, many of them would prove to be unnecessary. On the other hand, if we solve (26) with only a subset of the constraints in (27), we will obtain a valid lower bound on the optimal value of the original objective function. Furthermore, if all of the constraints that are tight in the optimal solution to (26) happen to be in the subset of constraints that we include, then the value of the objective function (26) will exactly equal the optimal value. To generate the desired subset of extreme points, Bender’s method adds constraints to the constraint set (27) one by one [11]. When a new constraint is added, the optimal solution of (26) returns either a better (larger) lower bound value or the optimal solution to the original problem (14) if a feasible RS placement and channel assignment exists.3 3

If no feasible solution exists, the algorithm will return a very large number.

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4.3 Modified Bender’s Method By using the original Bender’s method, at each iteration, one needs to solve a small pure 0-1 minimization problem. Even though this approach makes the problem manageable, it could be time consuming and potentially require a large amount of time to compute. The purpose of finding the solution of (26) at each iteration is to find an appropriate extreme point to add to the constraint set (27). Instead of performing the minimization (26) at each iteration, we propose to use a heuristic to find a decent extreme point at each iteration, and only perform minimization (26) when the extreme point generated by the heuristic is invalid. To further reduce the run time of the Bender’s method, we propose to use the results generated by each iteration to reduce the solution space. If a feasible RS placement and channel assignment exists, the optimal solution must be an integer which equals the minimum number of required  relay stations. To take advantage of this observation, we add the constraint, Ll ≤ i∈VR ,λ∈Λ Xiλ ≤ Lu , to the problem, where the minimum number of required relay stations must be greater than or equal to Ll and smaller than or equal to Lu . We initialize Ll = −∞ and Lu = ∞. We update Lu whenever a new (smaller) upper bound is found, and we update Ll whenever the lower bound, which is computed by the minimization of (26), increases by more than 1. Fig. 2 presents a flow chart of the modified Bender’s decomposition approach to solve the RS placement and channel assignment problem.

Empty constraint set (27) and an arbitrary RS placement and channel assignment xˆ incumbent upper bound = ’

Solve the modified feasibility problem (20) (21) (22) and obtain extreme point u t and upper bound= c 2 xˆ  (b  A2 xˆ ) u STOP YES if upper bound < incumbent upper bound incumbent upper bound = upper bound

Lu

¬incumbent upper bound ¼

lower bound • incumbent upper bound?

NO

xˆ

xˆ '

Add new constraint

D' t c2 x  (b  A2 x)t u to constraint set (27)

Solve updated problem (26)(27) and obtain a potential lower bound and a new RS placement and channel assignment xˆ ' by heuristic.

NO

lower bound • incumbent upper bound?

Solve updated problem (26)(27) and obtain a lower bound and a new RS placement and channel assignment xˆ ' by optimization. YES

Ll

ªlower bound º

Fig. 2. Flowchart of the modified Bender’s decomposition approach for solving the RS placement and channel assignment problem

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We begin by using an empty constraint set (27), and we add new constraints to it iteratively. By using the RS locations and channel assignments, x , generated by the previous iteration4, we solve the modified feasibility problem (20). When this problem is solved, we obtain an extreme point u. From this, we obtain the minimum infeasibility penalty for the RS placement and channel assignment, x , suggested by the previous iteration. The sum of the infeasibility penalty and the cost of the RSs constitute an  + (b − A2 x )t u. upper bound of the problem. That is to say the upper bound = c2 x We keep the best (lowest) upper bound found so far and save it as the incumbent upper bound. The newly generated extreme point is then used to add a new constraint, D ≥ c2 x + (b − A2 x)t u, to the constraint set (27). In the original Bender’s method, one solves the updated problem (26) and obtain a lower bound value and a new RS placement and channel assignment x  . In this work, we propose to use a simple heuris5 tic to generate decent values of x  , and we only perform minimization if the lower bound value generated by the heuristic is higher than or equal to the incumbent upper bound. Otherwise we set x  = x  and generate another extreme point.6 If the lower bound generated by the minimization and the incumbent upper bound are equal, we stop. Otherwise, we set x =x  and go back to the beginning of the iterative phase.

5 Numerical Analysis In this section, we present numerical results based on a hypothetical IEEE 802.16 network. A link capacity model, similar to that in [6], is used to determine the operational bit rate between any pair of nodes. The optimal RS placement and channel assignment in a typical rural environment will be derived by the proposed modified Bender’s decomposition method. By using the proposed optimization framework, we evaluate the cost of deploying a heterogeneous wireless mesh network with relay stations in a sparse rural area. The cost of the network is the minimum number of RSs required. We set the infeasibility constant P to 1000. For the backbone network, a 20MHz spectrum is occupied, and the IEEE 802.16 WirelessMAN-SC technology is used. For the local network, we use the IEEE 802.16 WirelessMAN-OFDM technology and a 20MHz spectrum as well. As shown in Fig. 4, the subscribers are distributed in a 12km × 12km rural area, and the base station and central office are located at node 0, where they can be connected to the ISP core network via the fiber optic network of the railroad company, which is assumed to be underutilized. According to the IEEE 802.16 WirelessMAN-OFDM specifications, channel bandwidth can be adjusted dynamically. However, the bandwidth occupied by each channel is vendor specific. In this work, as an example of illustration, we assume that the local network spectrum is divided into three channels.7 Each RS or base station has a 4km 4 5 6

7

For the first iteration, we use an arbitrary RS placement and channel assignment. In our numerical result, we use a simple descent algorithm. Problem (26) is a small pure 0-1 minimization problem. This problem can be solved to optimality in a reasonable amount of time by any commercial optimization softwares if the number of integer variables is not too large (e.g. less than 1000). The link rate of one channel is one third of the original 20MHz channel.

A. So and B. Liang 5

x 10

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Fig. 4. Network configuration of a heterogeneous wireless mesh network

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interference zone. In other words, if a base station or RS using a particular channel is placed in one location, another RS which uses the same channel cannot be placed within a 4km radius of the former base station or RS. Among the 58 nodes, we assume the ISP has access to 50 of them for the installation of RSs. Furthermore, we set the uplink and downlink demand of each subscriber to 1Mbps, and 2Mbps respectively. As mentioned in Section 4.2, the original version of Bender’s decomposition method requires solving a small pure 0-1 optimization problem in each iteration, which potentially takes a very long time to perform. In the modified version as shown in Fig.2, we have integrated a classic descent algorithm [12] to reduce the runtime of the Bender’s method. The convergence of the original and modified Bender’s decomposition methods are shown in Fig. 3, and the resulting configuration of the network is shown in Fig. 4. It takes about 22 hours for the modified version of the Bender’s decomposition method to converge to the optimal value, while in the same amount of time, the gap between the upper bound and the lower bound generated by the original method is still very large. Even though the extreme points generated by the heuristic at some iterations are not the desired extreme points, the heuristic can rapidly generate a set of useful extreme points which leads to faster convergence than the original approach.

6 Conclusion In this work, we investigate the optimal placement and channel assignment of wireless relay stations to minimize the operational cost of a wireless mesh network. We have presented a heterogeneous wireless mesh network architecture which uses relay stations to form a backbone and a local network. Furthermore, we have developed an analytical model to investigate whether a particular RS placement and channel assignment can satisfy the user demands and interference constraints. We use Bender’s decomposition to compute the optimal number of RSs and their corresponding placement and channel assignment which minimize the operational cost of a heterogeneous wireless mesh network. Furthermore, we integrate heuristics in the algorithm to reduce the runtime of the Bender’s decomposition method. Given a set of network parameters, the proposed framework and optimization technique can offer significant run time advantages, when used by network designers to compute the optimal placement and channel assignment of relay stations and to provide design guidelines on the network setup and maintenance cost estimations.

References 1. Perkins, C.E., ed.: Ad Hoc Networking. Addison-Wesley Longman (2001) 2. Haas, Z., Deng, J., Liang, B., Papadimitratos, P., Sajama, S.: Wiley Encyclopedia of Telecommunications. John Wiley & Sons (2002) 3. Draves, R., Padhye, J., Zill, B.: Comparison of routing metrics for multi-hop wireless networks. In: Proc. of ACM SIGCOMM, Portland, OR, U.S.A. (Sept. 2004) 4. Jain, K., Padhye, J., Padmanabhan, V.N., Qiu, L.: Impact of interference on multi-hop wireless network performance. In: Proc. of ACM MOBICOM, San Diego, CA, U.S.A. (Sept. 2003) 66–80

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5. Ramachandran, K., Belding, E., Almeroth, K., Buddhikot, M.: Interference-aware channel assignment in multi-radio wireless mesh networks. In: Proc. of IEEE INFOCOM, Barcelona, Spain (April 2006) 6. So, A., Liang, B.: A Lagrangian approach for the optimal placement of wireless relay nodes in wireless local area networks. In: Proc. of the International IFIP-TC6 Networking Conference, Coimbra, Portugal (May 2006) 160–172 (extended version in press, to appear in the IEEE Transactions on Mobile Computing) 7. Bejerano, Y.: Efficient integration of multihop wireless and wired networks with QoS constraints. IEEE Transactions on Networking 12(6) (Dec. 2004) 1064– 1078 8. Glapa, S.: Navigating the harsh realities of broadband wireless network economics. Technical report, ArrayComm, Inc. (2004) 9. Beaton, M.: Unwiring broadband, technology white paper. Technical report, Navini Networks (2002) 10. D. Sweeney, ed.: WiMax Operatos’s Manual, Building 802.16 Wireless Networks. 2 edn. Apress (2005) 11. Martin, R.K.: Large Scale Linear and Integer Programming. 1 edn. Kluwer Academic Publishers (1999) 12. Wolsey, L.: Integer Programming. 1 edn. Wiley (1998)

Optimization Models for the Radio Planning of Wireless Mesh Networks Edoardo Amaldi, Antonio Capone, Matteo Cesana, and Federico Malucelli Politecnico di Milano, Dipartimento Elettronica ed Informazione, Milano, Italy {amaldi,capone,cesana,malucell}@elet.polimi.it

Abstract. In this paper we propose novel optimization models for the planning of Wireless Mesh Networks whose objective is to minimize the network installation cost, while providing full coverage to wireless mesh clients. Our mixed integer linear programming models aim at selecting the number and positions of mesh routers and access points, while taking into account in an accurate way traffic routing, interference, rate adaptation, and channel assignment. We provide the optimal solutions of the proposed problem formulations on a set of realistic-size instances and discuss the effect of different parameters on the characteristics of the planned networks.

1

Introduction

The network devices composing Wireless Mesh Networks (WMNs) [1] are of three types: Mesh Routers (MRs), Mesh Access Points (MAPs) and Mesh Clients (MCs). The functionality of both the MRs and the MAPs is twofold: they act as classical access points towards the MCs, whereas they have the capability to set up a Wireless Distribution System (WDS) by connecting to other mesh routers or access points through point to point wireless links. Both MRs and MAPs are often fixed and electrically powered devices. Furthermore, the MAPs are geared with some kind of broadband wired connectivity (LAN, ADSL, fiber, etc.) and act as gateways toward the wired backbone. MCs are users terminals connected to the network through MAPs or MRs. Several parameters concur to the determination of a general wireless mesh network effectiveness including the number of radio interfaces for each device, the number of available radio channels, the access mechanism, the routing strategies and the specific wireless technology used to implement the mesh paradigm. All these parameters are de facto degrees of freedom the network designer can exploit to deploy an effective WMN, thus optimization criteria are needed for the tuning of such parameters. To this end, many works have appeared in the literature with the purpose of providing optimized protocols for WMNs. So et al. propose in [2] a multichannel MAC protocol in the case single interface transceivers are used, whereas reference [3] analyzes those networks where even multiple radio interface per wireless node can be used adapting the channel access protocol. Das et al. propose two I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 287–298, 2007. c IFIP International Federation for Information Processing 2007 

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Integer-Linear programming models to solve the fixed channel assignment problem with multiple radio interfaces [4], whilst [5] and [6] address the problems of channel assignment and routing jointly, providing different formulations to the optimization problem. The most of the previously published work assumes a given network topology, i.e., the general approach tends to optimize the channel assignment and/or the routing assuming given positions for the MRs and the MAPs. On the other hand, the purpose of the present work is to model the radio planning problem of WMNs, providing quantitative methods to optimize number, positions and coordination of MRs and MAPs and the overall topology of the network. The problem of planning WMNs differs from that of planning other wireless access networks, such as cellular systems [7] or WLANs [8]. In the latter cases, network planning involves selecting the locations in which to install the base stations or access points, setting their configuration parameters (emission power, antenna height, tilt, azimuth, etc.), and assigning channels so as to cover the service area and to guarantee enough capacity to each cell [9]. In the case of WMNs, each candidate site can host either MAPs or MRs, which have different installation costs. Roughly speaking, MAPs are more expensive than MRs since they must be directly connected to the wired backbone and might be more powerful than MRs in terms of both processing and transmission capabilities. Moreover, the traffic to/from the wired backbone has to be routed on a path connecting the MR to one MAP at least. In this context, capacity limits of radio links among MRs and between MRs and MAPs play a key role since the traffic routed on a link must not exceed its capacity. The resulting network design problem must simultaneously consider the radio coverage of users, like in classical radio planning for wireless access networks [9], and the traffic routing, like in the design of wired networks [10]. Very few previous works consider the problem of planning WMNs or, more in general, fixed multi-hop wireless network. The main attempt to address the problem appears in [11] where the focus is on locating internet transit access points (MAPs in the terminology adopted in this paper) in wireless neighborhood network. Heuristic solutions and a lower bound are provided. Since the positions of all the other nodes (MRs) is given and such nodes are also the only traffic ending points in the network, the problem considered in [11] is actually a subproblem of that proposed in this paper since the coverage part is not included. Moreover, the interference model is based on the number of hops crossed by flows, while the model considered in this paper is a fluidic version [12] of the protocol interference model [14]. The problem in [11] was originally proposed in [13] where, on the other hand, a time division multiple access is assumed and the slot scheduling optimization is included in the model. In this work we propose an optimization model for the problem of planning WMNs based on mathematical programming which takes into account both the local and the multihop connectivity requirements. The problem is NP-hard but it can be solved to the optimum for realistic size instances. We provide

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optimal solutions for a set of synthetic instances and discuss the effect of different parameters on the characteristics of the solution. Our work is organized as follows: Section 2 gives the formulation of the proposed model and comments on its main features, whilst Section 3 reports numerical results. Concluding remarks are given in Section 4.

2

Wireless MESH Network Planning

For the sake of simplicity, we define a basic version of the model for the WMN planning problem neglecting interference, adaptive modulation and multiple channels, and then we extend it step-by-step. Let us consider the network description presented in Figure 1. Similarly to the coverage problems commonly considered for wireless access networks [9], let S = {1, . . . , m} denote the set of CSs and I = {1, . . . , n} the set of TPs. A special node N represents the wired backbone network. The cost associated to installing a MR in CS j is denoted by cj , while the additional cost required to install a MAP in CS j is denoted by pj , j ∈ S. The total cost for installing a MAP in CS j is therefore given by (cj + pj ). Traffic generated by TP i is given by parameter di , i ∈ I. The traffic capacity of the wireless link between CSs j and l is denoted by ujl , j, l ∈ S, while the capacity of the radio access interface of CS j is denoted by vj , j ∈ S. The sequence Si of CSs that can cover TP i is calculated for all TPs considering a non increasing order of (i) (i) (i) received signal strength, Si = {j1 , j2 , . . . , jLi }, i ∈ I. According to TPs and CSs location and propagation information the connectivity parameters can be calculated. Let aij , i ∈ I, j ∈ S, be the coverage parameters:  1 if a MAP or MR in CS j cover TP i aij = 0 otherwise, and bjl , j, l ∈ S, the wireless connectivity parameters:  1 if CS j and l can be connected with a link bjl = 0 otherwise.

N wjN zj

j yjl

Wired backbone

MAP MR TP

l xij i

Fig. 1. WMN planning problem description

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Decision variables of the problem include TP assignment variables xij , i ∈ I, j ∈ S:  1 if TP i is assigned to CS j xij = 0 otherwise, installation variables zj , j ∈ S:  1 if a MAP or a MR is installed in CS j zj = 0 otherwise, wired backbone connection variables wjN , j ∈ S (if zj = 1, wjN denote if j is connected to the wired network N , i.e. if it is a MAP or a MR):  1 if a MAP is installed in CS j wjN = 0 otherwise, wireless connection variables yjl , j, l ∈ S:  1 if there is a wireless link between CS j and l yjl = 0 otherwise, and finally flow variables fjl which denote the traffic flow routed on link (j, l), where the special variable fjN denotes the traffic flow on the wired link between MAP j and the backbone network. Given the above parameters and variables, the WMN planning problem can be stated as follows:  (cj zj + pj wjN ) (1) min j∈S



s.t.

xij = 1

∀i ∈ I

(2)

j∈S



xij ≤ zj aij ∀i ∈ I, ∀j ∈ S  di xij + (flj − fjl ) − fjN = 0

i∈I

(3) ∀j ∈ S

(4)

l∈S

flj + fjl ≤ ujl yjl  di xij ≤ vj

∀j, l ∈ S

(5)

∀j ∈ S

(6)

∀j ∈ S

(7)

∀j, l ∈ S

(8)

i∈I

fjN ≤ M wjN yjl ≤ zj , yjl ≤ zl yjl ≤ bjl zj (i) + 

Li  h=+1

xij (i) ≤ 1 h

∀j, l ∈ S ∀ = 1, . . . , Li − 1, ∀i ∈ I

xij , zj , yjl , wjN ∈ {0, 1}

∀i ∈ I, ∀j, l ∈ S

(9) (10) (11)

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The objective function (1) accounts for the total cost of the networks including installation costs cj and costs related to the connection of MAP to the wired backbone pj . If for some practical reason only a MR and not a MAP can be installed in CS j, the corresponding variable wjN is set to zero. Constraints (2) provide full coverage of all TPs, while constraints (3) are coherence constraints assuring respectively that a TP i can be assigned to CS j only if a device (MAP or MR) is installed in j and if i is within the coverage set of j. Constraints (4) define the flow balance in node j. These constraints are the same as those adopted for classical multicommodity flow problems. The term  assigned TPs, l∈S flj is the total traffic i∈I di xij is the total traffic related to received by j from neighboring nodes, l∈S fjl is the total traffic transmitted by j to neighboring nodes, and fjN is the traffic transmitted to the wired backbone. Even if these constraints assume that traffic from TPs is transmitted to the devices to which they are assigned and that this traffic is finally delivered by the network to the wired backbone, without loss of generality we can assume that di accounts for the sum of traffic in the uplink (from TPs to the WMN) and in the downlink (from WMN to the TPs) since radio resources are shared in the two directions. Constraints (5) impose that the total flow on the link between device j and l does not exceed the capacity of the link itself (ujl ). Constraints (6) impose for all the MCs’ traffic serviced by a network device (MAP or MR) not to exceed the capacity of the wireless link used for the access, whilst constraints (7) forces the flow between device j and the wired backbone to zero if device j is not a MAP. The parameter M is used to limit the capacity of the installed MAP. Constraints (8) and (9) defines the existence of a wireless link between CS j and CS l, depending on the installation of nodes in j and l and wireless connectivity parameters bjl . The constraints expressed by (10) force the assignment of a TP to the best CS in which a MAP or MR is installed according to a proper sorting criteria (such as the received signal strength), whilst constraints (11) defines the decision variables of the model to assume binary values only. Obviously, the above model is NP-hard since it includes the set covering and the multi-commodity flow problems as special cases. The model defined above considers fixed transmission rates for both the wireless access interface and for the wireless distribution system, and it will be referred to as Fixed Rate Model (FRM) throughout the paper. The FRM can be easily extended to endorse transmission rate adaptation. As to the wireless distribution system, the rate adaptation can be accounted directly in the variables ujl . Rate adaptation in the wireless access network can be accounted in the model with a slight modifications of constraints (6). We consider several concentric regions centered in each CS, assigning to each region a maximum rate value. All the TPs falling in one of these regions can communicate with the node in the CS using the specific rate of the region. Formally, we can define the set of regions for a given CS j Rjk = 1, ..., K and the set Ijk ⊂ I containing all the TPs falling in region k of CS j. Such sets can be determined for each CS j using the incidence variable akij which is equal to

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1 if TP i falls within region k of the CS j and to zero otherwise. Each of these regions of a given CS j is assigned a maximum capacity defined by variable vjk . Using such definitions, the FRM can be extended to the case of rate adaptation in the wireless access part of the network by substituting the constraints (6) with the following new constraints:   i∈Ijk di xij ≤ 1 ∀j ∈ S (12) vjk k∈R j

The new defined model with constraints (12) will be referred to as Rate Adaptation Model (RAM) throughout the paper. Both the FRM and the RAM do not consider the effect of the interference on the access capacity and on the capacity of wireless links connecting mesh nodes. However, in practical cases we must take into account interference effect. We focus here on the case of IEEE 802.11 and assume that all MAPs and MRs share the same radio channel for the access part and use another shared channel for the backbone links. Since now the access capacity is shared by all mesh nodes, we can take into account interference quite easily modifying constraints (12) and considering not only the TPs assigned to the node in CS j but all TPs in the coverage range:   i∈Ijk di ≤ 1 ∀j ∈ S (13) zj vjk k∈R j

The interference limiting effect on the wireless link capacities is more difficult to account for, since it depends on the network topology and the multiple access protocol. Considering the protocol interference model proposed in [14], we can define sets of links that cannot be active simultaneously. These sets depend on the specific multiple access protocol considered. In the case of CSMA/CA, adopted by IEEE 802.11, each set Cjl considers a link (j, l) and includes all links that are one and two hops away in the mesh-network graph (links connecting j and l to their neighbors and their neighbors to the neighbors of their neighbors). To each set we can associate a constraint on the flows crossing its links: yjl

 (k,h)∈Cjl

fkh ≤1 ukh

∀j, l ∈ S

(14)

Obviously, by describing the capacity limitation due to set Cjl with the constraint on flows crossing its links, we make an approximation since we pass from a discrete model to a fluidic one [12]. The effect of this approximation and the one due to traffic dynamics can be accounted by properly reducing capacity values ukh . We estimated through simulation of IEEE 802.11 multi-hop networks that a reduction of 5% is sufficient to achieve consistent results. Replacing constraints (5) with (14) and (6) with (13) we get a new model referred to in the paper as Interference Aware Model (IAM). Note that the nonlinear constraints (14) can be easily linearized.

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As a matter of fact, FRMT/RAM and IAM can be considered extreme cases with respect to interference, corresponding respectively to those scenarios where enough channels and radio interfaces are available in the mesh nodes so that interference can be neglected, and to those scenarios where only one channel is available for the mesh backbone. In all the other intermediate scenarios, channel assignment to mesh nodes must be included in the optimization model. The extension of the model to the multiple channels case is quite straightforward and, due to length constraints, here we just outline the modifications needed. Let us assume that a set F of Q channels is available and that each mesh node is equipped with B radio cards. New installation variables zjq (q ∈ F, j ∈ S) must be considered which are equal to one if a mesh node is installed in j and q are extended is assigned channel q, and to zero otherwise. Also link variables yjl q . In the to include the channel used by link (j, l), as well as flow variables fjl objective function we replace variable zj with new variable tj which is equal to 1 if a mesh node is installed in j. Constraints are easily modified to include the new dimension related to channels. In particular, constraints (3)-(5) are replaced with the following:  q zj aij ∀i ∈ I, ∀j ∈ S (15) xij ≤ q∈F



di xij +

i∈I

   q q flj − fjl − fjN = 0

∀j ∈ S

(16)

l∈S,q∈F q yjl

 (k,h)∈Cjl

q fkh ≤1 ukh

∀j, l ∈ S, ∀q ∈ F.

(17)

To limit to B the maximum number of channels assigned to a mesh node a new set of constraints must be added:  q zj ≤ B ∀j ∈ S, (18) q∈F

and to define new variables tj we add: tj ≤ zjq ∀j ∈ S, ∀q ∈ F.

(19)

The new model will be referred to as Multi-Channel Model (MCM).

3

Numerical Results

In this section we test the sensitivity of the models proposed in previous section to different parameters like the number of candidate sites, the traffic demands from the MCs and the installation costs. To this end, we have implemented a generator of WMN topologies which considers specific parameter settings and makes some assumptions on propagation and device features. Obviously, these assumptions do not affect the proposed model which is general and can be applied to any problem instance. The generator considers a square area with edge L = 1000 m,

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and it randomly draws the position of m CSs and of n = 100 TPs. The coverage area of a mesh node is assumed to be a circular coverage region with radius RA = 100 m. Only feasible instances where each TP is covered by at least one CS are considered. The wireless range of wireless backbone links is RB = 250 m, while the capacities of the access links,vj and backbone links, ujl , are both set to 54 Mb/s for all j and l. The capacity of links connecting MAPs to the wired network is M = 128 Mb/s, while the ratio between the cost of a MR and a MAP is β (β = 1/10 unless otherwise specified). All the results commented hereafter are the optimal solutions of the considered instances obtained formalizing the model in AMPL [16] and solving it with CPLEX [15] using workstations equipped with a AMD Athlon (TM) processor with CPUs operating at 1.2GHz, and with 1024Mbyte of RAM. 3.1

Fixed Rate Model

Once assigned the number and the positions of either CS and TP, the quality of the deployed WMN and consequently the overall installation cost depends on two parameters: the traffic demand d of the MCs and the ratio between the MR and MAP installation costs β. In this section we analyze the sensitivity of the proposed model to these parameters.

(a) d=600Kb/s

(b) d=3Mb/s

Fig. 2. Sample WMNs planned by the FRM with increasing traffic demands of the MCs and finite capacity of the installed MAPs (M = 128M b/s). Standard setting of the topological parameters.

Effect of the Traffic Demands. Figure 2 reports an example of the planned networks when applying the FRM to the same instance with two different requirements on the end user traffic, d = 600Kb/s and d = 3M b/s for all MCs. Table 1 analyze the characteristics of the solutions of the FRM when varying the number of candidate sites. The results presented are obtained averaging each point on 10 instances of network topology. For each couple (m, d) the tables

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Table 1. Solutions provided by the FRM d=600Kb/s

d=3Mb/s

MAP MR Links Time (s) MAP MR Links Time (s) m=30 2.25 23.75 21.50

0.4

23.65 20.20

0.63

m=40 1.45

22.55

1.43

3.40 23.75 21.00

10.93

m=50 1.25 24.15 22.9

4.69

3.25 23.95 21.55

32.88

24

4

report the number of installed MRs, the number of installed MAPs, the number of wireless links of the WDS and the processing time to get the optimal solution. Two main results come from the observation of the table: first, the very same effect of traffic increase observed in Figure 2 is evident also on averaged results, in fact the number of installed MAPs increases when increasing the traffic demands. Second, for a given traffic value, increasing the number of CS to 50 augments the probability for a MC to be connected to a MAP through a multi hop wireless path, therefore the model tends to install less MAPs and more MRs. On the other side, if the number of CS is lower (30), the model installs more MAPs since not all the MCs can be connected to the installed MAPs through multi hop wireless paths. In other words, with high m the solution space is bigger and the model favors those solutions providing connectivity which have a lower impact on the network cost, i.e., those installing more MRs than MAPs. Effect of the Cost Parameter. The number of installed MAPs and MRs intuitively depends on the installation cost ratio between a simple wireless router and a mesh access point. Table 2. Solutions provided by the FRM when varying the installation cost ratio β. Number of CS m = 30. d=600Kb/s β

d=3Mb/s

MAP MR Links MAP MR Links

1/10 2.10 23.40 21.30

3.80 23.30 20.20

1/7

2.40 24.00 21.60

4.10 23.80 20.10

1/5

2.40 24.30 22.70

4.10 23.80 20.10

1/3

2.40 24.30 21.60

4.10 23.80 20.10

1/2

2.80 23.60 20.80

4.20 23.60 19.60

Table 2 reports the characteristics of the solutions when varying the parameter β for different values of the offered traffic d. The results reported in the table shows that if the cost for installing a MAP decreases with respect to the cost of MRs, the proposed model tends to install more MAPs. However, the differences observed with different cost ratios are much smaller than what one could expect.

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E. Amaldi et al. Table 3. Quality of the solutions provided by the RAM d=200Kb/s

d=600Kb/s

MAP MR Links Time (s) MAP MR Links Time (s) m=30 2.80 23.80 21.00

2.24

2.80 25.40 22.60

2.24

m=40 1.70 24.60 22.90

9.66

1.70 26.00 24.30

13.25

m=50 1.20 24.40 23.20

46.83

1.20 26.10 24.90

61.37

The reason is that in the considered scenario the optimization process is driven mainly by the capacity constraints. We obtained results (not shown here) with a bigger difference in the number of installed MAPs by letting higher capacity for the links connecting MAPs (setting high values to parameter M ). 3.2

Rate Adaptation Model

In real wireless networks, the capacity of a given wireless link depends on the distance between transmitter and receiver. The RAM endorses this fact by defining three capacity regions around a MR (and MAP) and assigning the link between MC and MR (or MAP) an increasing capacity when getting nearer to the MR (or MAP) location. The rate values vik = v k ∀j adopted to obtain numerical results emulates IEEE 802.11g transmission and depends on the distance r: 0m ≤ r ≤ 30m v k = 36M b/s, 30m < r ≤ 60m v k = 18M b/s, 60m < r ≤ 100m v k = 2M b/s. The behavior of the RAM is similar to the one of the FRM in terms of sensitivity to the model parameters. Table 3 summarizes the characteristics of the solutions of the RAM when varying the number of candidate sites. The traffic offered by the MCs is lower with respect to the one used to test the FRM since the link rates are in the average lower then those in the FTR case. As a result, we observed that higher values of d may lead to unfeasible instances. The results obtained highlight a behavior of the RAM very similar to the one already observed for the FRM in the same configuration. 3.3

Interference Aware Model

The IAM considers the impact of the interference on the access capacity, through constraints (14), and the capacities wireless links, through constraints (13). Table 4 reports the results obtained with the IAM for the special case in which rate adaptation is not included. The parameter settings are the same adopted for the FRM and therefore results in Table 4 can be directly compared with those reported in Table 1. Sets Cjl have been obtained considering the IEEE 802.11 multiple access scheme. We observe that the number of MAPs installed is remarkably higher and the number of links lower with respect to the FRM case. This is due to the capacity reduction of wireless links that favors solutions where MRs and MAPs are interconnected through paths with a small number of hops. In fact, with short paths between MRs and MAPs the effect of interference is weaker. Obviously, short paths

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Table 4. Solutions provided by the IAM without rate adaptation d=600Kb/s

d=3Mb/s

MAP MR Links Time (s) MAP MR Links Time (s) m=30 3.40 22.20 19.40

4.37

8.50 22.00 14.20

4.16

m=40 2.50 23.10 20.90

258.09

7.80 22.50 16.10

53.98

m=50 2.30 23.40 21.60 1,706.63

7.70 23.40 17.80 1,345.32

Table 5. Solutions provided by the MCM without rate adaptation d=600Kb/s

d=3Mb/s

MAP MR Links Time (s) MAP MR Links Time (s) m=30 2.25 23.75 21.60

2.99

4.00 23.65 20.55

9.79

m=40 1.45 24.00 22.60

73.43

3.40 23.75 21.30

141.18

m=50 1.25 24.05 22.85

393.38

3.30 23.65 21.35

673.52

require a higher number of MAPs. Another relevant difference between the FRM and the IAM results is the computation time which is much higher for IAM in most of the cases. As expected this is due to the structure of constraints (13) which involve several flow variables simultaneously. A similar behavior can be observed considering the results (not shown here) obtained with IAM and rate adaptation. 3.4

Multiple Channel Model

The MCM adds to the planning problem the channel assignment to multi-radio devices. Table 5 reports the numerical results obtained by the MCM when considering Q = 11 channels and B = 3 radio interfaces, which are typical values for the IEEE 802.11a technology. We observe that the results are not very different from those obtained with the FRM (see Table 1) in terms of installed MAPs, MRs and links. On the other side, the computation complexity of MCM is much higher than the one of the other models: considering a constraints of four hours on the computation time, we are able to obtain the optimum solution (reported in the table) only in the 80% of the instances. Therefore, the MCM should be adopted when planning multi-channel/multi-radio WMNs only in case the number of available channels and interfaces is very limited. In the other cases the FRM/RAM models can be safely used for planning the network and frequency assignment can be optimized in a second phase [4].

4

Conclusion

In this paper we proposed an optimization model based on mathematical programming whose objective function is the minimization of the overall network

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installation cost while taking into account the coverage of the end users, the wireless connectivity in the wireless distribution system and the management of the traffic flows. Technology dependent issues such as rate adaptation and interference effect have been considered. To test the quality of the solutions provided by the model, we generated synthetic instances of WMNs and solved them to the optimum using AMPL/CPLEX varying several network parameters. The numerical results we gathered show that the model is able to capture the effect on the network configuration of all these parameters, providing a promising framework for the planning of WMNs.

References 1. I.F. Akyildiz, X. Wang, I. Kiyon, A Survey on Wireless Mesh Networks, IEEE Com. Mag., Sept. 2005, Vol. 43, No. 9, pp. 23–30. 2. J. So, N. Vaidya, Multi-Channel MAC for ad hoc Networks: Handling MultiChannel Hidden Terminals using a Single Transceiver, ACM MOBIHOC 2004, pp. 222-233. 3. A. Adya et al., A Multi-Radio Unification Protocol for IEEE 802.11 Wireless Networks, IEEE BROADNETS 2004, pp. 344–354. 4. A.K. Das, H.M.K. Alazemi, R. Vijayakumar, S. Roy, Optimization models for fixed channel assignment in wireless mesh networks with multiple radios, IEEE SECON 2005, pp. 463–474. 5. M. Alicherry, R. Bhatia, L. E. Li, Multi-radio, multi-channel communication: Joint channel assignment and routing for throughput optimization in multi-radio wireless mesh networks, ACM MOBICOM 2005, pp. 58–72. 6. A. Raniwala, K. Gopalan, and T. C. Chiueh, Centralized channel assignment and routing algorithms for multichannel wireless mesh networks, ACM MC2R, Apr. 2004, Vol. 8, No. 2, pp. 50–65. 7. E. Amaldi, A. Capone, F. Malucelli, Planning UMTS Base Station Location: Optimization Models with Power Control and Algorithms, IEEE Trans. on Wireless Comm., Sept. 2003, Vol. 2, No. 5, pp. 939–952. 8. S. Bosio, A. Capone, M. Cesana, Radio Planning of Wireless Local Area Networks, ACM/IEEE Trans. on Net., to appear. 9. E. Amaldi, A. Capone, F. Malucelli, C. Mannino, Optimization Problems and Models for Planning Cellular Networks, in Handbook of Optimization in Telecommunications, Kluver Academic Publishers, 2006. 10. M. Pioro, D. Medhi, Routing, Flow, and Capacity Design in Communication and Computer Networks, Morgan Kaufmann Publishers, 2004. 11. R. Chandra, L. Qiu, K. Jain, M. Mahdian, Optimizing the placement of integration points in multi-hop wireless networks, IEEE ICNP 2004, pp. 271–282. 12. M. Kodialam, T. Nandagopal, Characterizing the Capacity Region in Multi-Radio Multi-Channel Wireless Mesh Networks, ACM Mobicom 2005, pp. 73–87. 13. Y. Bejerano, Efficient integration of multi-hop wireless and wired networks with QoS constraints, ACM MOBICOM 2002, pp. 215–226. 14. P. Gupta and P.R Kumar, The capacity of wireless networks, IEEE Trans. on Inf. Theory, Mar. 2000, Vol. 46, No. 2, pp. 388–404. 15. ILOG CPLEX 8.0 user’s manual, 2002. 16. R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL, A modeling language for mathematical programming, 1993.

Interference-Aware Multicasting in Wireless Mesh Networks Sudheendra Murthy1 , Abhishek Goswami2 , and Arunabha Sen1 1

School of Computing and Informatics, Arizona State University, Tempe, AZ 85287 [email protected],[email protected] 2 Mobile Devices Software, Motorola [email protected]

Abstract. Multicasting is one of the most important applications in Wireless Ad hoc Networks and the currently emerging Wireless Mesh Networks. In such networks, interference due to the shared wireless medium is a prime factor in determining the data rate achievable by a multicast application. In this research work, we present an interferenceaware multicast routing algorithm that takes into account the effects of interference to determine the maximum bandwidth multicast structure. We characterize the problem of computing maximum bandwidth multicast structure as a graph problem of finding minimum degree weakly induced subgraph in a graph subject to the connectivity and interference constraints. We establish the intractability of the problem and provide efficient heuristic that performs close to the optimal in most of the cases. We also present the design of a more practical distributed algorithm. The simulation results demonstrate the benefits of our heuristic over Shortest Path Tree and Minimum Steiner Tree approximation algorithms. Keywords: Wireless Mesh Network, Minimum Interference Multicast, Weakly Induced Connected Subgraph, NP-Complete.

1

Introduction

Research in Wireless Mesh Networks (WMNs) has gained tremendous momentum recently as a result of its commercial deployment in many US cities including Seattle, Philadelphia, Tempe [1]. WMNs are increasingly being used to provide cost effective and reliable Internet connectivity to residents and businesses in these cities. These WMNs consist of a set of wireless routers (access points) to which the end users connect, a set of wireless routers that act as forwarding nodes and a set of gateway routers that provide connectivity to the Internet. Data from the end users is routed in the WMN towards the gateway routers and to the Internet. 

This research was supported in part by ARO grant W911NF-06-1-0354. The information reported here does not reflect the position or the policy of the federal government.

I.F. Akyildiz et al. (Eds.): NETWORKING 2007, LNCS 4479, pp. 299–310, 2007. c IFIP International Federation for Information Processing 2007 

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The widespread deployment of WMNs has fueled research work in providing better support to multimedia applications like real-time video transport and Voice over the Internet (VoIP) services. Common to many of these applications is the need for a multicast framework that facilitates efficient distribution of datagrams to a cohort of hosts. Multicasting results in bandwidth savings as compared to multiple unicast sessions. Early efforts in providing multicast support in WMNs ignored to consider the interference effects of the shared wireless medium in which the mesh routers operate. Interference is an important factor that dictates the bandwidth available for the multicast transmission. The mesh routers are usually equipped with IEEE 802.11 a/b/g interfaces. Interference in the context of this paper refers to the bandwidth sharing effect between nodes operating in close range caused due to the CSMA/CA nature of 802.11. In this paper, we present a novel multicast framework that considers the effects of interference and constructs a multicast structure that provides maximum bandwidth to the applications. Our objective is to identify multicast forwarding group nodes whose transmission induces least amount of interference. To the best of our knowledge, this is the first paper that proposes such a framework. The main contributions of this work are as follows. 1. We provide a novel formulation of the interference-aware multicasting problem as a graph problem of finding weakly induced subgraph in a graph representing the mesh routers. 2. We prove the NP-completeness of the problem, thereby establishing its intractable nature. 3. We provide an Integer Linear Program technique of optimally solving this problem. 4. We provide a centralized heuristic algorithm that performs close to the optimal and describe a distributed implementation of the algorithm. We compare the performance of the proposed heuristic with the optimal, shortest path solution and minimum Steiner tree solution. The road map for rest of the paper is as follows. In section 2, we introduce the required notation and give the formal problem definition. The complexity analysis of the problem is provided in section 3. The Integer Linear Program formulation to obtain the optimal solution is provided in section 4. The centralized heuristic and the design of its distributed extension are provided in section 5. Section 6 presents the evaluation of our heuristics. Section 7 reviews the related work in this area, while section 8 concludes the paper.

2 2.1

Problem Formulation Wireless Transmission and Interference Model

We assume uniform transmission range RT and interference range RI for all the routers in the WMN. We represent a WMN by a directed potential communication graph G(V, E) in which the vertices represent the mesh routers. Denote

Interference-Aware Multicasting in Wireless Mesh Networks

7 1

RT 2

7

2 3 4

6

1

RI 2

Fig. 1. A Potential Communication Graph G(V, E) with transmission radius RT

7

2

2 6 3

5

301

4

5

1

6 3 4

Fig. 2. Potential Interference Graph H(V, F ) with interference radius RI =1.5RT

5

Fig. 3. SH , the subgraph weakly induced by the vertex set S = {3, 6, 7} on the graph of figure 2

the Euclidean distance between routers u and v by dist(u, v). Two directed edges {(u, v), (v, u)} ∈ E if dist(u, v) ≤ RT and implies that mesh router u can communicate directly with mesh router v. We assume that each router is equipped with one radio and all routers operate on the same channel. Any of the mesh routers can be the source node in the multicast tree. However in many applications, the multicast source comes from the wired network and hence, the multicast source is a gateway mesh router. An access point router becomes a receiver of the multicast structure if there is at least one end-user connected to the access point who wants to receive this multicast stream. We assume a 802.11 CSMA/CA medium access control scheme1 . Thus, a transmission between two nodes may prevent all nodes within the transmission range of the sender from transmitting due to carrier sensing. We assume that the interference range RI is q × RT with q ≥ 1. We model the co-channel interference of the WMN with the help of a directed potential interference graph. A directed potential interference graph is represented by H(V, F ) in which the vertex set corresponds to the mesh routers. Two directed edges {(u, v), (v, u)} ∈ F if dist(u, v) ≤ RI . A directed edge (u, v) in the potential interference graph implies that the transmission of router u can cause interference at router v. Figure 1 shows a sample potential communication graph with 7 mesh routers. The circles around the routers are drawn with radius RT /2 and hence two intersecting circles implies that the two routers are within the transmission range of each other. Figure 2 shows the corresponding potential interference graph with RI =1.5RT . Since RT ≤ RI , the potential communication graph is always a subgraph of the potential interference graph. This interference model is different from the frequently used conflict graph representation of interference in a WMN. In the conflict graph representation, a vertex vij is in the vertex set of the conflict graph if (i, j) is an edge in the potential communication graph. There exists an edge between two vertices vij and vkl in the conflict graph if min (dist(i, k), dist(i, l), dist(j, k), dist(j, l)) 1

Although we consider the standard 802.11 protocol without RTS/CTS, our techniques can be applied to RTS/CTS 802.11 en