Skip to main content
SpringerLink
Log in

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

  • Published:
Wireless Networks Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Bansal and Z. Liu. Capacity, delay and mobility in wireless ad-hoc networks. In Proc. of IEEE Infocom Conf., San Francisco, March-April 2003.

  2. C. Bettstetter, G. Resta, and P. Santi. The node distribution of the random waypoint mobility model for wireless ad hoc networks. IEEE Transactions on Mobile Computing, 2(3), July-September 2003.

  3. D. Cox and H. Miller. The Theory of Stochastic Processes. Chapman & Hall, London, UK, 1965.

    MATH  Google Scholar 

  4. I. Gradshteyn and I. Ryzhik. Tables of Integrals, Series, and Products. Academic Press, Inc. (London) Ltd., fourth edition, 1983.

    Google Scholar 

  5. R. Groenevelt. Stochastic Models for Mobile Ad Hoc Networks. PhD thesis, INRIA, Sophia Antipolis, France, April 2005.

  6. R. Groenevelt, E. Altman, and P. Nain. Relaying in mobile ad hoc networks. In Proc. of Workshop on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt'04), UK, March 2004.

  7. M. Grossglauser and D. Tse. Mobility increases the capacity of ad-hoc wireless networks. ACM/IEEE Transactions in Networking, 10(4):477–486, August 2002.

    Article  Google Scholar 

  8. D. Nain, N. Petigara, and H. Bakakrishnan. Integrated routing and storage for messaging applications in mobile ad hoc networks. In Proc. of Workshop on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt'03), Sophia Antipolis, France, March 2003. To appear in MONET.

  9. S. Redner. A Guide to First-Passage Processes. Cambridge University Press, 2001.

  10. G. Sharma and R. R. Mazumdar. Delay and capacity trade-offs for wireless ad hoc networks with random mobility. Submitted for publication, October 2003.

  11. T. Small and Z. Haas. The shared wireless infostation model—a new ad hoc networking paradigm (or where there is a whale, there is a way). In Proc. of ACM International Symposium on Mobile Ad Hoc Networking and Computing (Mobihoc), Annapolis, Maryland, USA, June 2003.

  12. V. Syrotiuk and C. Colbourn. Routing in mobile aerial networks. In Proc. of Workshop on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt'03), Sophia Antipolis, France, March 2003.

  13. G. Weiss. Aspects and Applications of the Random Walk. Random Materials and Processes. Elsevier Science B.V, North Holland, Amsterdam, The Netherlands, 1994.

    Google Scholar 

  14. J. Yoon, M. Liu, and B. Noble. Random waypoint considered harmful. In Proc. of IEEE Infocom Conf., San Francisco, March-April 2003.

Download references

Author information

Authors and Affiliations

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

    R. Groenevelt, E. Altman & P. Nain

Authors
  1. R. Groenevelt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Altman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Nain
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Published:

  • Issue Date:

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

Keywords

Search

Navigation