Competitive Routing over Time

  • Martin Hoefer
  • Vahab S. Mirrokni
  • Heiko Röglin
  • Shang-Hua Teng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5929)


Congestion games are a fundamental and widely studied model for selfish allocation problems like routing and load balancing. An intrinsic property of these games is that players allocate resources simultaneously and instantly. This is particularly unrealistic for many network routing scenarios, which are one of the prominent application scenarios of congestion games. In many networks, load travels along routes over time and allocation of edges happens sequentially. In this paper we consider two frameworks that enhance network congestion games with a notion of time. We propose temporal network congestion games that use coordination mechanisms — local policies that allow to sequentialize traffic on the edges. In addition, we consider congestion games with time-dependent costs, in which travel times are fixed but quality of service of transmission varies with load over time. We study existence and complexity properties of pure Nash equilibria and best-response strategies in both frameworks. In some cases our results can be used to characterize convergence for various distributed dynamics.


Nash Equilibrium Coordination Mechanism Congestion Game Potential Game Global Ranking 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ackermann, H., Röglin, H., Vöcking, B.: On the impact of combinatorial structure on congestion games. Journal of the ACM 55(6) (2008)Google Scholar
  2. 2.
    Fabrikant, A., Papadimitriou, C.H., Talwar, K.: The complexity of pure Nash equilibria. In: Proc. 36th Symp. Theory of Computing (STOC), pp. 604–612 (2004)Google Scholar
  3. 3.
    Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Roughgarden, T.: Routing Games. In: Algorithmic Game Theory, pp. 461–486. Cambridge University Press, Cambridge (2007)Google Scholar
  5. 5.
    Azar, Y., Jain, K., Mirrokni, V.S.: (Almost) optimal coordination mechanisms for unrelated machine scheduling. In: Proc. 19th Symp. Discrete Algorithms (SODA), pp. 323–332 (2008)Google Scholar
  6. 6.
    Caragiannis, I.: Efficient coordination mechanisms for unrelated machine scheduling. In: Proc. 20th Symp. Discrete Algorithms (SODA), pp. 815–824 (2009)Google Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    Immorlica, N., Li, L., Mirrokni, V.S., Schulz, A.S.: Coordination mechanisms for selfish scheduling. In: Deng, X., Ye, Y. (eds.) WINE 2005. LNCS, vol. 3828, pp. 55–69. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Vöcking, B.: Selfish Load Balancing. In: Algorithmic Game Theory, pp. 517–542. Cambridge University Press, Cambridge (2007)Google Scholar
  10. 10.
    Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proc. 37th Symp. Theory of Computing (STOC), pp. 67–73 (2005)Google Scholar
  11. 11.
    Awerbuch, B., Azar, Y., Epstein, A.: The price of routing unsplittable flow. In: Proc. 37th Symp. Theory of Computing (STOC), pp. 57–66 (2005)Google Scholar
  12. 12.
    Roughgarden, T.: Intrinsic robustness of the price of anarchy. In: Proc. 41st Symp. Theory of Computing, STOC (2009)Google Scholar
  13. 13.
    Anshelevich, E., Ukkusuri, S.: Equilibria in dynamic selfish routing. In: Proc. 2nd Intl. Symp. Algorithmic Game Theory, SAGT (2009)Google Scholar
  14. 14.
    Farzad, B., Olver, N., Vetta, A.: A priority-based model of routing. Chicago Journal of Theoretical Computer Science, Article no. 1 (2008)Google Scholar
  15. 15.
    Koch, R., Skutella, M.: Nash equilibria and the price of anarchy for flows over time. In: Proc. 2nd Intl. Symp. Algorithmic Game Theory, SAGT (2009)Google Scholar
  16. 16.
    Harks, T., Heinz, S., Pfetsch, M.: Competitive online multicommodity routing. In: Erlebach, T., Kaklamanis, C. (eds.) WAOA 2006. LNCS, vol. 4368, pp. 240–252. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  17. 17.
    Cole, R., Dodis, Y., Roughgarden, T.: Bottleneck links, variable demand, and the tragedy of the commons. In: Proc. 17th Symp. Discrete Algorithms (SODA), pp. 668–677 (2006)Google Scholar
  18. 18.
    Kleinrock, L.: Queueing Systems. Compurer Applications, vol. 2. Wiley, Chichester (1976)zbMATHGoogle Scholar
  19. 19.
    Parekh, A., Gallager, R.: A generalized processor sharing approach to flow control in integrated services networks: The single-node case. IEEE/ACM Transactions on Networking 1(3), 344–357 (1993)CrossRefGoogle Scholar
  20. 20.
    Dürr, C., Thang, N.K.: Non-clairvoyant scheduling games. In: Proc. 2nd Intl. Symp. Algorithmic Game Theory, SAGT (2009)Google Scholar
  21. 21.
    Bruno, J., Coffman Jr., E.G., Sethi, R.: Scheduling independent tasks to reduce mean finishing-time (extended abstract). SIGOPS Oper. Syst. Rev. 7(4), 102–103 (1973)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Martin Hoefer
    • 1
  • Vahab S. Mirrokni
    • 2
  • Heiko Röglin
    • 3
  • Shang-Hua Teng
    • 4
  1. 1.Department of Computer ScienceRWTH Aachen University 
  2. 2.Google Research New York 
  3. 3.Department of Quantitative EconomicsMaastricht University 
  4. 4.Computer Science DepartmentUniversity of Southern California 

Personalised recommendations