Abstract
We develop a mathematical model within a game theoretical framework to capture the flow control problem for variable rate traffic at a bottleneck node. In this context, we also address various issues such as pricing and allocation of a single resource among a given number of users. We obtain a distributed, end-to-end flow control using cost functions defined as the difference between particular pricing and utility functions. We prove the existence and uniqueness of a Nash equilibrium for two different utility functions. The paper also discusses three distributed update algorithms, parallel, random and gradient update, which are shown to be globally stable under explicitly derived conditions. The convergence properties and robustness of each algorithm are studied through extensive simulations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Altman E., Başar T., Jimenez T. and Shimkin N., “Competitive routing in networks with polynomial costs,” IEEE Transactions on Automatic Control, vol. 47(1), pp. 92–96, January 2002.
Altman E. and Başar T., “Multi-user rate-based flow control,” IEEE Transactions on Communications, vol. 46(7), pp. 940–949, July 1998.
Orda A., Rom R. and Shimkin N., “Competitive routing in multiuser communication networks,” IEEE/ACM Transactions on Networking, vol. 1, pp. 510–521, October 1993.
Douligeris C. and Mazumdar R., “A game theoretic perspective to flow control in telecommunication networks,” Journal of the Franklin Institute, vol. 329, pp. 383–402, March 1992.
Başar T. and Olsder G. J., Dynamic Noncooperative Game Theory. 2nd edn. Philadelphia, PA: SIAM, 1999.
Korilis Y. A. and Lazar A., “On the existence of equilibria in noncooperative optimal flow control,” Journal of the ACM, vol. 42, pp. 584–613, May 1995.
Hsiao M. T. and Lazar A., “Optimal decentralized flow control of markovian queueing networks with multiple controllers,” Performance Evaluation, vol. 13, pp. 181–204, 1991.
Bertsekas D. and Gallager R., Data Networks. 2nd edn. Upper Saddle River, NJ: Prentice Hall, 1992.
Alpcan T. and Başar T., “A game-theoretic framework for congestion control in general topology networks,” in Proc. of the 41st IEEE Conference on Decision and Control, Las Vegas, NV, December 2002, pp. 1218–1224.
Alpcan T. and Başar T., “A utility-based congestion control scheme for internet-style networks with delay,” in Proc. IEEE Infocom, San Francisco, CA, April 2003.
Alpcan T., Başar T. and Tempo R., “Randomized algorithms for stability and robustness analysis of high speed communication networks,” in Proc. of IEEE Conference on Control Applications (CCA), Istanbul, Turkey, June 2003, pp. 397–403.
Alpcan T. and Başar T., “Global stability analysis of an end-to-end congestion control scheme for general topology networks with delay,” in Proc. of the 42nd IEEE Conference on Decision and Control, Maui, HI, December 2003, pp. 1092–1097.
Shenker S., “Fundamental design issues for the future internet,” IEEE Journal on Selected Areas in Communications, vol. 13, no. 7, pp. 1176–1188, September 1995.
Bertsekas D., Nonlinear Programming, 2nd edn. Belmont, MA: Athena Scientific, 1999.
Maheswaran R. T. and Başar T., “Multi-user flow control as a Nash game: Performance of various algorithms,” in Proc. of the 37th IEEE Conference on Decision and Control, December 1998, pp. 1090–1095.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Birkhäuser Boston
About this chapter
Cite this chapter
Alpcan, T., Başar, T. (2005). Distributed Algorithms for Nash Equilibria of Flow Control Games. In: Nowak, A.S., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 7. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4429-6_26
Download citation
DOI: https://doi.org/10.1007/0-8176-4429-6_26
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4362-1
Online ISBN: 978-0-8176-4429-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)