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Relaying in mobile ad hoc networks: The Brownian motion mobility model

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Abstract

Mobile ad hoc networks are characterized by a lack of a fixed infrastructure and by node mobility. In these networks data transfer can be improved by using mobile nodes as relay nodes. As a result, transmission power and the movement pattern of the nodes have a key impact on the performance. In this work we focus on the impact of node mobility through the analysis of a simple one-dimensional ad hoc network topology. Nodes move in adjacent segments with reflecting boundaries according to Brownian motions. Communications (or relays) between nodes can occur only when they are within transmission range of each other. We determine the expected time to relay a message and compute the probability density function of relaying locations. We also provide an approximation formula for the expected relay time between any pair of mobiles.

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Authors and Affiliations

  1. INRIA, 2004 route des Lucioles, 06902, Sophia Antipolis, France

    R. Groenevelt, E. Altman & P. Nain

Authors
  1. R. Groenevelt
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  2. E. Altman
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  3. P. Nain
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Corresponding author

Correspondence to P. Nain.

Additional information

Robin Groenevelt received a M.Sc. in Business Mathematics and Computer Science (1998) and a M.Sc. in Mathematics (2000) from the Vrije Universiteit, Amsterdam. From 1999–2001 he worked as a consultant in the Center for Applied Mathematics at the Rabobank in the Netherlands. In 2005 he obtained his Ph.D. in Computer Science at INRIA (Sophia Antipolis), where he worked on the modeling and performance analysis of mobile ad hoc networks. In 2004–2005 he held a teaching/research position at the University of Nice-Sophia Antipolis. Since September 2005 he has been working as a researcher in the R & D Techlabs of Accenture in Sophia Antipolis, France.

Philippe Nain received the Maîtrise Es-Sciences in Mathematics in 1978, the Diplôme d’Etudes Approfondies in Statistics in 1979, and the Doctorat de 3ème cycle specializing in Modeling of Computer Systems in 1981 from the University of Paris XI, Orsay, France. In 1987 he received the Doctorat d’Etat in Applied Mathematics from the University Pierre and Marie Curie, Paris, France. Since december 1981 he has been with INRIA where he is currently the head of the research project Maestro devoted to the modeling of computer systems and telecommunications networks. He has held visiting appointments at the University of Massachusetts (1993–94), at the University of Maryland (1987) and at North Carolina State University (1988). His research interests include modeling and performance evaluation of communication networks. He is an Associate Editor of IEEE/AC Transaction Networking, Performance Evaluation and Operations Research Letters, and was an Associate Editor of IEEE Transactions on Automatic Control. He was a co-program chair of the ACM Sigmetrics 2000 conference, the general chair of the Performance 2005 conference, and he is a member of IFIP WG 7.3.

E. Altman received the B.Sc. degree in electrical engineering (1984), the B.A. degree in physics (1984) and the Ph.D. degree in electrical engineering (1990), all from the Technion-Israel Institute, Haifa. In (1990) he further received his B.Mus. degree in music composition in Tel-Aviv university. Since 1990, he has been with INRIA (National research institute in informatics and control) in Sophia-Antipolis, France. His current research interests include performance evaluation and control of telecommunication networks and in particular congestion control, wireless communications and networking games. He is in the editorial board of several scientific journals: Stochastic Models, JEDC, COMNET, SIAM SICON and WINET. He has been the (co)chairman of the program committee of several international conferences and workshops (on game theory, networking games and mobile networks). More informaion can be found at http://www.inria.fr/mistral/personnel/Eitan.Altman/me.html

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Groenevelt, R., Altman, E. & Nain, P. Relaying in mobile ad hoc networks: The Brownian motion mobility model. Wireless Netw 12, 561–571 (2006). https://doi.org/10.1007/s11276-006-6535-0

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  • DOI: https://doi.org/10.1007/s11276-006-6535-0

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