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A New Model for Selfish Routing

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STACS 2004 (STACS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2996))

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Abstract

In this work, we introduce and study a new model for selfish routing over non-cooperative networks that combines features from the two such best studied models, namely the KP model and the Wardrop model in an interesting way.

We consider a set of nusers, each using a mixed strategy to ship its unsplittable traffic over a network consisting of m parallel links. In a Nash equilibrium, no user can increase its Individual Cost by unilaterally deviating from its strategy. To evaluate the performance of such Nash equilibria, we introduce Quadratic Social Cost as a certain sum of Individual Costs – namely, the sum of the expectations of the squares of the incurred link latencies. This definition is unlike the KP model, where Maximum Social Cost has been defined as the maximum of Individual Costs.

We analyse the impact of our modeling assumptions on the computation of Quadratic Social Cost, on the structure of worst-case Nash equilibria, and on bounds on the Quadratic Coordination Ratio.

This work has been partially supported by the IST Program of the European Union under contract numbers IST-1999-14186 (ALCOM-FT) and IST-2001-33116 (FLAGS), and by research funds at University of Cyprus.

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References

  1. Alon, N., Azar, Y., Woeginger, G.J., Yadid, T.: Approximation Schemes for Scheduling. In: Proc. of SODA 1997, pp. 493–500 (1997)

    Google Scholar 

  2. Anshelevich, E., Dasgupta, A., Tardos, É., Wexler, T.: Near-Optimal Network Design with Selfish Agents. In: Proc. of STOC 2003, pp. 511–520 (2003)

    Google Scholar 

  3. Beckmann, M.J.: On the Theory of Traffic Flow in Networks. Traffic Quart. 21, 109–116 (1967)

    Google Scholar 

  4. Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. Yale University Press, New Haven (1956)

    Google Scholar 

  5. Braess, D.: Über ein Paradoxen aus der Verkehrsplanung. Unternehmensforschung 12, 258–268 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chandra, A.K., Wong, C.K.: Worst-case Analysis of a Placement Algorithm Related to Storage Allocation. SICOMP 4, 249–263 (1975)

    MATH  MathSciNet  Google Scholar 

  7. Altman, E., Basar, T., Jimenez, T., Shimkin, N.: Competitive Routing in Networks with Polynomial Costs. IEEE Transactions on Automatic Control 47, 92–96 (2002)

    Article  MathSciNet  Google Scholar 

  8. Cody, R.A., Coffman Jr., E.G.: Record Allocation for Minimizing Expected Retrieval Costs on Crum-Like Storage Devices. JACM 23, 103–115 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  9. Czumaj, A., Vöcking, B.: Tight Bounds for Worst-Case Equilibria. In: Proc. of SODA 2002, pp. 413–420 (2002)

    Google Scholar 

  10. Czumaj, A., Krysta, P., Vöcking, B.: Selfish Traffic Allocation for Server Farms. In: Proc. of STOC 2002, pp. 287–296 (2002)

    Google Scholar 

  11. Dafermos, S.C., Sparrow, F.T.: The Traffic Assignment Problem for a General Network. Journal of Research of the National Bureau of Standards, Series B 73B, 91–118 (1969)

    MathSciNet  Google Scholar 

  12. 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, pp. 502–513. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C.H., Shenker, S.: On a Network Creation Game. In: Proc. of PODC 2003, pp. 347–351 (2003)

    Google Scholar 

  14. 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, pp. 514–526. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  15. Feldmann, R., Gairing, M., Lücking, T., Monien, B., Rode, M.: Selfish Routing in Non-Cooperative Networks: A Survey. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 21–45. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  16. 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, pp. 123–134. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  17. Gairing, M., Lücking, T., Mavronicolas, M., Monien, B., Spirakis, P.: The Structure and Complexity of Extreme Nash Equilibria (2003) (submitted for publication)

    Google Scholar 

  18. Koutsoupias, E., Mavronicolas, M., Spirakis, P.: Approximate Equilibria and Ball Fusion. In: Proc. of SIROCCO 2002, pp. 223–235 (2002)

    Google Scholar 

  19. Koutsoupias, E., Papadimitriou, C.H.: Worst-case Equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  20. Leung, J.Y.T., Wei, W.D.: Tighter Bounds on a Heuristic for a Partition Problem. Information Processing Letters 56, 51–57 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  21. Lücking, T., Mavronicolas, M., Monien, B., Rode, M., Spirakis, P., Vrto, I.: Which is the Worst-case Nash equilibrium? In: Rovan, B., Vojtas, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 551–561. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  22. Mavronicolas, M., Spirakis, P.: The Price of Selfish Routing. In: Proc. of STOC 2001, pp. 510–519 (2001)

    Google Scholar 

  23. Nash, J.F.: Equilibrium Points in N-Person Games. Proceedings of the National Academy of Sciences 36, 48–49 (1950)

    Article  MATH  MathSciNet  Google Scholar 

  24. Nash, J.F.: Non-cooperative Games. Annals of Mathematics 54(2), 286–295 (1951)

    Article  MathSciNet  Google Scholar 

  25. Osborne, M.J., Rubinstein, A.: A Course in Game Theory. The MIT Press, Cambridge (1994)

    MATH  Google Scholar 

  26. Papadimitriou, C.H.: Algorithms, Games and the Internet. In: Proc. of STOC 2001, pp. 749–753 (2001)

    Google Scholar 

  27. Roughgarden, T.: The Price of Anarchy is Independent of the Network Topology. In: Proc. of STOC 2002, pp. 428–437 (2002)

    Google Scholar 

  28. Roughgarden, T.: Selfish Routing, Ph. D. Thesis, Department of Computer Science, Cornell University (May 2002)

    Google Scholar 

  29. Roughgarden, T., Tardos, É.: How Bad is Selfish Routing? JACM 49, 236–259 (2002)

    Article  MathSciNet  Google Scholar 

  30. Wardrop, J.G.: Some Theoretical Aspects of Road Traffic Research. In: Proceedings of the of the Institute of Civil Engineers, Pt. II, vol. 1, pp. 325–378 (1952)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Computer Science, Electrical Engineering and Mathematics, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Thomas Lücking, Burkhard Monien & Manuel Rode

  2. Department of Computer Science, University of Cyprus, P. O. Box 20537, Nicosia, CY-1678, Cyprus

    Marios Mavronicolas

Authors
  1. Thomas Lücking
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  2. Marios Mavronicolas
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  3. Burkhard Monien
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  4. Manuel Rode
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Editor information

Editors and Affiliations

  1. Universität Stuttgart, FMI, Germany

    Volker Diekert

  2. LIAFA and the University of Paris 7, Denis Diderot,  

    Michel Habib

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Lücking, T., Mavronicolas, M., Monien, B., Rode, M. (2004). A New Model for Selfish Routing. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_48

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  • DOI: https://doi.org/10.1007/978-3-540-24749-4_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21236-2

  • Online ISBN: 978-3-540-24749-4

  • eBook Packages: Springer Book Archive

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