Marios Mavronicolas
Paul Spirakis
ABSTRACT
We study the problem of routing traffic through a congested network. We focus on the simplest case of a network consisting of m parallel links. We assume a collection of n network users, each employing a mixed strategy which is a probability distribution over links, to control the shipping of its own assigned traffic. Given a capacity for each link specifying the rate at which the link processes traffic, the objective is to route traffic so that the maximum expected latency over all links is minimized. We consider both uniform and non-uniform link capacities.
How much decrease in global performace is necessary due to the absence of some central authority to regulate network traffic and implement an optimal assignment of traffic to links? We investigate this fundamental question in the context of Nash equilibria for such a system, where each network user selfishly routes its traffic only on those links available to it that minimize its expected latency cost, given the network congestion caused by the other users. We use the coordination ratio, defined by Koutsoupias and Papadimitriou [25] as the ratio of the maximum (over all links) expected latency in the worst possible Nash equlibrium, over the least possible maximum latency had global regulation been available, as a measure of the cost of lack of coordination among the network users.
- 1.E. Altman, "Flow Control Using the Theory of Zero-Sum Markov Games," IEEE Transactions on Automatic Control, Vol. 39, pp. 814-818, April 1994.Google Scholar
Cross Ref
- 2.E. Altman, T. Basar, T. Jimenez and N. Shimkin, "Competitive Routing in Networks with Polynomial Cost," Proceedings of the 19th IEEE Conference on Computer Communications (IEEE INFOCOM 2000), March 2000.Google Scholar
- 3.D. Angluin and L. G. Valiant, "Fast Probabilistic Algorithms for Hamiltonian Circuits and Matchings," Journal of Computer and System Sciences, Vol. 18, pp. 155-193, 1979.Google ScholarCross Ref
- 4.G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela and M. Protasi, Complexity and Approximation - Combinatorial Optimization Problems and Their Approximability Properties, Springer, 1999. Google ScholarDigital Library
- 5.Y. Azar, A. Z. Broder, A. R. Karlin and E. Upfal, Balanced Allocations, Proceedings of the 26th Annual ACM Symposium on the Theory of Computing, pp. 593-602, May 1994. Google ScholarDigital Library
- 6.T. Basar and G. J. Olsder, Dynamic Noncooperative Game Theory, SIAM Series in Classics in Applied Mathematics, Philadelphia, 1999.Google Scholar
- 7.A. Borodin and R. El-Yaniv, Online Computation and Competitive Analysis, Cambridge University Press, 1998. Google ScholarDigital Library
- 8.J. J. Carrahan, P. A. Russo, K. Kitami and R. Kung, "Intelligent Network Overview," IEEE Communications Magazine, Vol. 31, pp. 30-36, March 1993.Google ScholarDigital Library
- 9.H. Chernoff, "A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the Sum of Observations," Annals of Mathematical Statistics, Vol. 23, pp. 493-509, 1952.Google ScholarCross Ref
- 10.S. Deering and R. Hinden, Internet Protocol Version 6 Specifacation, Internet Draft, IETF, March 1995.Google Scholar
- 11.P. Dubey, "Inefficiency of Nash Equilibria," Mathematics of Operations Research, Vol. 11, No. 1, pp. 1-8, February 1986. Google ScholarDigital Library
- 12.A. A. Economides and J. A. Silvester, "Multi-objective Routing in Integrated Services Networks: A Game Theory Approach," Proceedings of the IEEE Conference on Computer Communications (IEEE INFOCOM 1991), pp. 1220-1225, 1991.Google Scholar
- 13.J. Feigenbaum, C. Papadimitriou and S. Shenker, "Sharing the Cost of Multicast Transactions," Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, pp. 218-227, Portland, Oregon, May 2000. Google ScholarDigital Library
- 14.G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, Oxford Science Publications, Second Edition, 1992.Google Scholar
- 15.M. Habib, C. McDiarmid, J. Ramirez-Alfonsin and B. Reed (eds.), Probabilistic Methods in Algorithmic Discrete Mathematics, Vol. 16 in Algorithms and Combinatorics, Springer, 1998.Google Scholar
- 16.M.-T. T. Hsiao and A. A. Lazar, "Optimal Decentralized Flow Control of Markovian Queueing Networks with Multiple Controllers," Performance Evaluation, Vol. 13, No. 3, pp. 181-204, 1991. Google ScholarDigital Library
- 17.N. L. Johnson and S. Kotz, Urn Models and Their Applications, John Wiley & Sons, 1977.Google Scholar
- 18.R. Karp, E. Koutsoupias, C. H. Papadimitriou and S. Shenker, "Optimization Problems in Congestion Control," Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, October 2000. Google ScholarDigital Library
- 19.V. F. Kolchin, V. P. Chistiakov and B. A. Sevastianov, Random Allocations, V. H. Winston, New York, 1978.Google Scholar
- 20.Y. Korilis and A. Lazar, "On the Existence of Equilibria in Noncooperative Optimal Flow Control," Journal of the ACM, Vol. 42, No. 3, pp. 584-613, 1995. Google ScholarDigital Library
- 21.Y. A. Korilis, A. A. Lazar and A. Orda, "Architecting Noncooperative Networks," IEEE Journal on Selected Areas in Communications, Vol. 13, No. 7, pp. 1241-1251, 1995. Google ScholarDigital Library
- 22.Y. Korilis, A. A. Lazar and A. Orda, "Achieving Network Optima Using Stackelberg Routing Strategies," IEEE/ACM Transactions on Networking, Vol. 5, No. 1, pp. 161-173, February 1997. Google ScholarDigital Library
- 23.Y. A. Korilis, A. A. Lazar and A. Orda, "Capacity Allocation under Noncooperative Routing," IEEE Transactions on Automatic Control, Vol. 42, No. 3, pp. 309-325, 1997.Google ScholarCross Ref
- 24.Y. A. Korilis, A. A. Lazar and A. Orda, "Avoiding the Braess Paradox in Non-Cooperative Networks," Journal of Applied Probability, Vol. 36, pp. 211-222, 1999.Google ScholarCross Ref
- 25.E. Koutsoupias and C. H. Papadimitriou, "Worst-case Equilibria," Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, G. Meinel and S. Tison eds., pp. 404-413, Vol. 1563, Lecture Notes in Computer Science, Springer-Verlag, Trier, Germany, March 1999. Google ScholarDigital Library
- 26.A. A. Lazar, A. Orda and D. E. Pendarakis, "Virtual Path Bandwidth Allocation in Multi-User Networks," IEEE/ACM Transactions on Networking, Vol. 5, pp. 861-871, December 1997. Google ScholarDigital Library
- 27.L. Libman and A. Orda, "The Designer's Perspective to Atomic Noncooperative Networks," IEEE/ACM Transactions on Networking, Vol. 7, No. 6, pp. 875-884, December 1999. Google ScholarDigital Library
- 28.M. Mavronicolas, A. Mouskos and P. Spirakis, "The Cost of Lack of Coordination in Distributed Network Routing," unpublished manuscript, April 2000.Google Scholar
- 29.R. D. McKelvey and A. McLennan, "Computation of Equilibria in Finite Games," in Handbook of Computational Economics, Vol. 1, pp. 87-142, 1996.Google ScholarCross Ref
- 30.R. Motwani and P. Raghavan, Randomized Algorithms, Cambridge University Press, 1995. Google ScholarDigital Library
- 31.J. F. Nash, "Non-cooperative Games," Annals of Mathematics, Vol. 54, No. 2, pp. 286-295, 1951.Google ScholarCross Ref
- 32.A. Orda, R. Rom and N. Shimkin, "Competitive Routing in Multiuser Communication Networks," IEEE/ACM Transactions on Networking, Vol. 1, pp. 510-521, October 1993. Google ScholarDigital Library
- 33.M. J. Osborne and A. Rubinstein, A Course in Game Theory, The MIT Press, 1994.Google Scholar
- 34.G. Owen, Game Theory, Third Edition, Academic Press, 1995.Google Scholar
- 35.C. H. Papadimitriou and M. Yannakakis, "On the Approximability ofTrade-offs and Optimal Access of Web Sources," Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, October 2000. Google ScholarDigital Library
- 36.T. Roughgarden and E. Tardos, "How Bad is Selfish Routing?" Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, October 2000. Google ScholarDigital Library
- 37.Z. Zhang and C. Douligeris, "Convergence of Synchronous and Asynchronous Greedy Algorithms in a Multiclass Telecommunications Environment," IEEE Transactions on Computers, Vol. 40, pp. 1277-1281, August 1992.Google Scholar
Index Terms
- The price of selfish routing
Recommendations
The Price of Selfish Routing
We study the problem of routing traffic through a congested network. We focus on the simplest case of a network consisting of m parallel links. We assume a collection of n network users; each user employs a mixed strategy, which is a probability ...
Routing selfish unsplittable traffic
We consider general resource assignment games involving selfish users/agents in which users compete for resources and try to be assigned to those which maximize their own benefits (e.g., try to route their traffic through links which minimize the ...
How much can taxes help selfish routing?
EC '03: Proceedings of the 4th ACM conference on Electronic commerceWe study economic incentives for influencing selfish behavior in networks. We consider a model of selfish routing in which the latency experienced by network traffic on an edge of the network is a function of the edge congestion, and network users are ...
Comments