Spatio-temporal Control for Dynamic Routing Games

  • Manjesh Kumar Hanawal
  • Eitan Altman
  • Rachid El-Azouzi
  • Balakrishna J. Prabhu
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 75)


In this paper, we study dynamic routing games where the decision of an user is spatio-temporal control. Each user ships its demand over time on a shared resource. We investigate the equilibrium of such systems and show the existence and uniqueness of equilibrium. In the second part, we study a stochastic congestion games where there is only one shared resource and the traffic is indivisible. The information structure that we consider is such that each user knows the state of its own buffer but not aware of states and the actions taken by other users. The game can be described as a game with random environment. We characterize the structure of equilibria policies using linear programming. We also study the properties of equilibrium considering another model for stochastic congestion game in which a fixed amount of divisible demand arrives each day. This demand can shipped to destination by sending some part today and remaining the next day.


Nash Equilibrium Stochastic Game Congestion Game Potential Game Delay Cost 
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.
    Haurie, A., Marcotte, P.: On the relationship between Nash-Cournot and Wardrop equilibria. Networks 15, 295–308 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Orda, A., Rom, R., Shimkin, N.: Competitive routing in multi-user environments. IEEE/ACM Trans. on Networking, 510–521 (1993)Google Scholar
  3. 3.
    Patriksson, M.: The traffic assignment problem: Models and methods. VSP, Utrecht (1994)Google Scholar
  4. 4.
    Rosenthal, R.W.: A class of games possessing pure strategy Nash equilibria. Int. J. Game Theory 2, 65–67 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Wardrop, J.G.: Some theoretical aspects of road traffic research communication networks. Proc. Inst. Civ. Eng., part 2, 1, 325–378 (1952)Google Scholar
  6. 6.
    Park, K., Sitharam, M., Chen, S.: Quality of service provision in noncooperative networks with diverse user requirements. Decis. Support Syst. 28(1-2), 101–122 (2000)CrossRefGoogle Scholar
  7. 7.
    Ayesta, U., Brun, O., Prabhu, B.J.: Price of Anarchy in Non-Cooperative Load Balancing. In: Proceedings of IEEE INFOCOM, San Diego (March 2010)Google Scholar
  8. 8.
    Cominetti, R., Correa, J.R., Stier-Moses, N.E.: The Impact of Oligopolistic Competition in Networks. Operation Reserach, INFORMS 57(6), 1421–1437 (2009)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Monderer, D., Shapley, L.S.: “Potential Games”. Games and Economic Behavior 14, 124–143 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Altman, E., Avrachenkov, K., Bonneau, N., Debbah, M., El-Azouzi, R., Sadoc Menasche, D.: Constrained Cost-Coupled Stochastic Games with Independent State Processes. Operations Research Letters 36, 160–164 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Altman, E., Basar, T., Jimenez, T., Shimkin, N.: Competitive routing in networks with polynomial cost. IEEE Trans. on Automatic Control 47, 92–96 (2002)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Nissan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory. Cambrige University Press (2009)Google Scholar
  13. 13.
    Wie, B.W., Friesz, T.L., Tobin, R.L.: Dynamic User Optimal Traffic Assignment on Congested Multidestination Networks. Transportation Research 24B(6), 431–442 (1990)MathSciNetCrossRefGoogle Scholar

Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2012

Authors and Affiliations

  • Manjesh Kumar Hanawal
    • 1
    • 2
  • Eitan Altman
    • 1
  • Rachid El-Azouzi
    • 2
  • Balakrishna J. Prabhu
    • 3
    • 4
  1. 1.Maestro group, INRIASophia AntipolisFrance
  2. 2.LIA, University of AvignonAvignonFrance
  3. 3.CNRS; LAASToulouseFrance
  4. 4.Université de Toulouse; UPS, INSA, INP, ISAE; LAASToulouseFrance

Personalised recommendations