Skip to main content
SpringerLink
Log in

Distributed topology control of wireless networks

  • Published:
Wireless Networks Aims and scope Submit manuscript

Abstract

We propose and analyaze a distributed control law that will maintain prescribed local properties of a wireless ad hoc network in the presence of node mobility, MAC layer power control and link fades. The control law uses a simple and intuitive power adaptation mechanism. We consider as an example the topology requirement of maintaining the out-degrees of each node at prescribed values and keeping the in-degree close to the out-degree. The topology objective is achieved by adapting the transmission power based only on local information. This power adaptation algorithm is analyzed using the o.d.e. approach to stochastic approximation. Simulation results verify the analysis and demonstrate its effectiveness. We also study the ability of the proposed objective to maintain connectivity. Although many heuristics are described in the literature to maintain local topological properties, the algorithm proposed in this paper is the first one that has proven convergence properties.

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. M. Benaim, Dynamics of stochastic approximations, in: Le Seminaire de Probabilites, eds. J. Azema, et al. Springer Lecture Notes in Mathematics no. 1709 (Springer Verlag, Berlin-Heidelberg, 1999) pp. 1–68.

  2. M. Benaim and M.W. Hirsch, Stochastic approximation algorithms with constant stepsize whose average is cooperative, The Annals of Applied Probability 9 (1999) 216–241.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Benveniste, M. Metivier and P. Priouret, Adaptive Algorithms and Stochastic Approximations (Springer Verlag, Berlin-Heidelberg, 1990).

    MATH  Google Scholar 

  4. V.S. Borkar, Stochastic approximations with two time scales, Systems and Control Letters 29 (1997) 291–294.

    Article  MATH  MathSciNet  Google Scholar 

  5. V.S. Borkar, Asynchronous stochastic approximation, SIAM Journal of Control and Optimization 36 (1998) 840–851.

    Article  MATH  MathSciNet  Google Scholar 

  6. V.S. Borkar and S.P. Meyn, The O.D.E. approach to convergence of stochastic approximation and reinforcement learning, SIAM Journal of Control and Optimization 38(2) (2000) 447–469.

    Article  MATH  MathSciNet  Google Scholar 

  7. M.P. Desai and D. Manjunath, On the connectivity of finite ad hoc networks, IEEE Communications Letters 10(6) (2002) 437–490.

    Article  Google Scholar 

  8. G. Foschini and Z. Miljanic, A simple distributed autonomous power control algorithm and its convergence, IEEE Transactions on Vehicular Technology 42(4) (1993).

  9. J. Gomez, A.T. Campbell, M. Naghshineh and C. Bisdikian, Conserving transmission power in wireless ad hoc networks, in: Proceedings of Ninth IEEE Conference on Network Protocols (ICNP) (2001).

  10. P. Gupta and P.R. Kumar, Critical power for asymptotic connectivity in wireless networks, in: Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming, eds W.M. McEneaney, G. Yin and Q. Zhang (Birkhüser, Boston, 1998).

    Google Scholar 

  11. M.W. Hirsch, Systems of differential equations that are competitive or cooperative II: Convergence almost everywhere, SIAM Journal of Mathematical Analysis 16 (1985) 423–439.

    Article  MATH  MathSciNet  Google Scholar 

  12. T. Hou and V. Li, Transmission range control in multihop packet radio networks, IEEE Transactions Communications 34 (1986) 38–44.

    Article  Google Scholar 

  13. D.B. Johnson, D.A. Maltz, Y.-C. Hu and J.G. Jetcheva, The dynamic source routing protocol (DSR) for mobile ad hoc networks, Internet Draft: draft-ietf-manet-dsr-07.txt (21 February 2002).

  14. V. Kawadia and P.R. Kumar, Power control and clustering in ad hoc networks, in: Proceedings of IEEE INFOCOM (2003).

  15. V. Kawadia and P.R. Kumar, Power control in ad hoc networks, To appear in IEEE Journal on Selected Areas in Communications, Preprint available from http://black1.csl.uiuc.edu/∼prkumar.

  16. L. Kleinrock and J.A. Silvester, Optimum transmission radii in packet radio networks or why six is a magic number, in: Proceedings of the National Telecommunications Conference, Birmingham, Alabama (1978) pp. 04.3.1–5.

  17. H.J. Kushner and G.G. Yin, Stochastic Approximation Algorithms and Applications (Springer Verlag, New York, 1997).

    MATH  Google Scholar 

  18. L. Li, J.Y. Halpern, V. Bahl, Y.M. Wang and R. Wattenhofer, Analysis of a cone-based distributed topology control algorithm for wireless multihop networks, in: Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC), Newport, RI (2001) pp. 264–273.

  19. R. Mathar and J. Mattfeldt, Analyzing routing strategy NFP in multihop packet radio network on a line, IEEE Transactions on Communications 43(2–4) (1995) 977–988.

    Article  Google Scholar 

  20. J.P. Monks, V. Bhargavan and M.W. Hwu, A power controlled mutiple access protocol for wireless packet networks, in: Proceedings of IEEE INFOCOM (2001) pp. 219–228.

  21. S. Narayanaswamy, V. Kawadia, R.S. Sreenivas and P.R. Kumar, Power control in ad hoc networks: Theory, architecture, algorithm and implementation of the COMPOW protocol, in: Proceedings of European Wireless 2002. Next Generation Wireless Networks: Technologies, Protocols, Services and Applications, Florence, Italy (2002) pp. 156–162.

  22. J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970).

    MATH  Google Scholar 

  23. R. Ramanathan and R. Rosalie-Hain, Topology control of multihop wireless networks using transmit power adjustment, in: Proceedings of the IEEE INFOCOM (2000) pp. 404–413.

  24. V. Rodoplu and T.H. Meng, Minimum energy mobile wireless networks, IEEE Journal on Selected Areas in Communications 17(8) (1999).

  25. S. Singh and C.S. Raghavendra, Power efficient MAC protocol for multihop radio networks, in: Proceedings of the IEEE International Symposium on Personal, Indoor and Mobile Radio Communincations (1998) pp. 153–157.

  26. H.L. Smith, Monotone Dynamical Systems (American Math. Society, Providence, R.I., 1995).

  27. H. Takagi and L. Kleinrock, Optimal transmission ranges for randomly distributed packet radio terminals, IEEE Transactions on Communications 32 (1984) 246–257.

    Article  Google Scholar 

  28. R. Wattenhofer, L. Li, P. Bahl and Y.-M. Wang, Distributed topology for power efficient operation in multihop wireless ad hoc networks, in: Proceedings of IEEE INFOCOM (2001).

  29. F. Xue and P.R. Kumar, The number of neighbors needed for connectivity of wireless networks, Wireless Networks 10(2) (2004) 169–181.

    Article  Google Scholar 

  30. F. Xue and P.R. Kumar, On the θ-coverage and connectivity of large random networks, Preprint (2005).

Download references

Author information

Authors and Affiliations

  1. School of Technology & Computer Science, Tata Inst. of Fundamental Research, Homi Bhabha Road, Mumbai, 400 005, India

    Vivek S. Borkar

  2. Department of Electrical Engineering, Indian Institute of Technology, Powai, Mumbai, 400 076, India

    D. Manjunath

Authors
  1. Vivek S. Borkar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Manjunath
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Manjunath.

Additional information

Vivek S. Borkar got his B. Tech. (Elec. Engg.) from Indian Institute of Technology, Mumbai, in 1976, M. S. (Systems and Control) from Case Western Reserve Uni. in 1977 and Ph.D. (Elec. Engg. and Comp. Sci.) from Uni. of California, Berkeley. He was with Uni. of Twente (1980–81), TIFR Centre, Bangalore (1982–89), Indian Inst. of Science (1989–99), and has been with School of Technology and Computer Science, Tata Inst. of Fundamental Research, Mumbai, since April 1999. His research interests include stochastic optimization and applications.

D. Manjunath received his B.E. from Mysore University, M.S. from Indian Institute of Technology, Madras and Ph.D. from Rensselaer Polytechnic Inst, Troy NY in 1986, 1989 and 1993 respectively. He has been a summer intern in the Corporate R & D Center of GE (1990), a visiting faculty in the Computer and Information Sciences Dept. of the University of Delaware (1992-93), a post doctoral fellow in the Computer Science Dept. of the University of Toronto (1993–84) and on the Electrical Engineering faculty of the Indian Inst. of Technology, Kanpur (1994–98).He has been with the Elec Enggg. Dept. of Indian Inst. of Technology, Bombay in Mumbai since July 1998 where he is now an Associate Professor. His research interests are in the areas of communication networks, performance analysis of systems, queueing systems and multimedia communications.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borkar, V.S., Manjunath, D. Distributed topology control of wireless networks. Wireless Netw 14, 671–682 (2008). https://doi.org/10.1007/s11276-006-0008-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11276-006-0008-3

Keywords

Search

Navigation