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Game-Theoretic Analysis of Internet Switching with Selfish Users

  • Alex Kesselman
  • Stefano Leonardi
  • Vincenzo Bonifaci
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3828)

Abstract

We consider the problem of Internet switching, where traffic is generated by selfish users. We study a packetized (TCP-like) traffic model, which is more realistic than the widely used fluid model. We assume that routers have First-In-First-Out (FIFO) buffers of bounded capacity managed by the drop-tail policy. The utility of each user depends on its transmission rate and the congestion level. Since selfish users try to maximize their own utility disregarding the system objectives, we study Nash equilibria that correspond to a steady state of the system. We quantify the degradation in the network performance called the price of anarchy resulting from such selfish behavior. We show that for a single bottleneck buffer, the price of anarchy is proportional to the number of users. Then we propose a simple modification of the Random Early Detection (RED) drop policy, which reduces the price of anarchy to a constant.

Keywords

Nash Equilibrium Queue Length Congestion Control Exponential Weighted Moving Average Random Early Detection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Akella, A., Karp, R., Papadimitrou, C., Seshan, S., Shenker, S.: Selfish behavior and stability of the Internet: A game-theoretic analysis of TCP. In: Proceedings of ACM SIGCOMM 2002 (2002)Google Scholar
  2. 2.
    Altman, E., Basar, T., Jimenez, T., Shimkin, N.: Routing into two parallel links: Game-Theoretic Distributed Algorithms. Special Issue of Journal of Parallel and Distributed Computing on Routing in Computer and Communication Networks 61(9), 1367–1381 (2001)zbMATHGoogle Scholar
  3. 3.
    Bertsekas, D., Gallager, R.: Data Networks. Prentice-Hall, Englewood Cliffs (1987)Google Scholar
  4. 4.
    Boulogne, T., Altman, E., Pourtallier, O.: On the convergence to Nash equilibrium in problems of distributed computing. Annals of Operation research (2002)Google Scholar
  5. 5.
    Christodoulou, G., Koutsoupias, E., Nanavati, A.: Coordination Mechanisms. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 345–357. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Czumaj, A., Krysta, P., Vocking, B.: Selfish traffic allocation for server farms. In: Proceedings of STOC 2002 (2002)Google Scholar
  7. 7.
    Czumaj, A., Vocking, B.: Tight bounds on worst case equilibria. In: Proceedings of SODA 2002 (2002)Google Scholar
  8. 8.
    Douligeris, C., Mazumdar, R.: On Pareto optimal flow control in an integrated environment. In: Proceedings of the 25th Allerton Conference on Communication, Control and Computing (1987)Google Scholar
  9. 9.
    Dutta, D., Goel, A., Heidemann, J.: Oblivious AQM and Nash Equilibria. In: Proceedings of INFOCOM 2003 (2003)Google Scholar
  10. 10.
    Even-Dar, E., Kesselman, A., Mansour, Y.: Convergence Time to Nash Equilibria. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Feldmann, R., Gairing, M., Lücking, T., Monien, B., Rode, M.: Nashification and the Coordination Ratio for a Selfish Routing Game. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    Florian, M., Hearn, D.: Network Equilibrium Models and Algorithms. In: Ball, M.O., et al. (eds.) Network Routing. Handbooks in RO and MS, pp. 485–550. Elsevier, Amsterdam (1995)CrossRefGoogle Scholar
  13. 13.
    Floyd, S., Jacobson, V.: Random Early Detection for Congestion Avoidance. IEEE/ACM Transactions on Networking (August 1993)Google Scholar
  14. 14.
    Fotakis, D., Kontogiannis, S., Koutsoupias, E., Mavronicolas, M., Spirakis, P.: The Structure and Complexity of Nash Equilibria for a Selfish Routing Game. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, p. 123. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Fudenberg, D., Levine, D.: The theory of learning in games. MIT Press, Cambridge (1998)zbMATHGoogle Scholar
  16. 16.
    Gao, X., Jain, K., Schulman, L.J.: Fair and efficient router congestion control. In: Proceedings of SODA 2004, pp. 1050–1059 (2004)Google Scholar
  17. 17.
    Garg, R., Kamra, A., Khurana, V.: A Game-Theoretic Approach Towards Congestion Control in Communication Networks. ACM SIGCOMM Computer Communications Review 32(3), 47–61 (2002)CrossRefGoogle Scholar
  18. 18.
    Gibbens, R., Kelly, F.: Resource pricing and the evolution of congestion control. Automatica 35, 1969–1985 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Jacobson, V.: Congestion Avoidance and Control. In: Proceedings of ACM SIGCOMM 1998 (1988)Google Scholar
  20. 20.
    Kelly, F., Maulloo, A., Tan, D.: Rate control in communication networks: shadow prices, proportional fairness and stability. Journal of the Operational Research Society 49, 237–252 (1998)zbMATHGoogle Scholar
  21. 21.
    Korilis, Y.A., Lazar, A.A.: On the Existence of Equilibria in Noncooperative Optimal Flow Control. Journal of the ACM 42, 584–613 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Koutsoupias, E., Papadimitriou, C.H.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, p. 404. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  23. 23.
    La, R.J., Anantharam, V.: Optimal Routing Control: Game Theoretic Approach. In: Proceedings of the 36rd IEEE Conference on Decision and Control, pp. 2910–2915 (1997)Google Scholar
  24. 24.
    Nash, J.F.: Non-cooperative games. Annals of Mathematics 54, 286–295 (1951)CrossRefMathSciNetGoogle Scholar
  25. 25.
    Orda, A., Rom, N., Shimkin, N.: Competitive routing in multi-user communication networks. IEEE/ACM Transaction on Networking 1, 614–627 (1993)CrossRefGoogle Scholar
  26. 26.
    Pan, R., Prabhakar, B., Psounis, K.: CHOKe – a stateless active queue management scheme for approximating fair bandwidth allocation. In: Proceedings of INFOCOM 2000, pp. 942–951 (2000)Google Scholar
  27. 27.
    Qiu, L., Yang, Y.R., Zhang, Y., Shenker, S.: On Selfish Routing in Internet-Like Environments. In: Proceedings of ACM SIGCOMM 2003 (2003)Google Scholar
  28. 28.
    Roughgarden, T., Tardos, E.: How Bad is Selfish Routing? Journal of the ACM 49(2), 236–259 (2002)CrossRefMathSciNetGoogle Scholar
  29. 29.
    Shenker, S.: Making greed work in networks a game-theoretic analysis of switch service disciplines. IEEE/ACM Transactions on Networking 3, 819–831 (1995)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Alex Kesselman
    • 1
  • Stefano Leonardi
    • 2
  • Vincenzo Bonifaci
    • 2
  1. 1.Max Planck Institut für InformatikSaarbrückenGermany
  2. 2.Dipartimento di Informatica e SistemisticaUniversita’ di Roma ”La Sapienza”RomaItaly

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