Non-cooperative routing in loss networks

The paper studies routing in loss networks in the framework of a non-cooperative game with selfish users. Two solution concepts are considered: the Nash equilibrium, corresponding to the case of a finite number of agents (such as service providers) that take routing decisions, and the Wardrop equilibrium, in which routing decisions are taken by a very large number of individual users. We show that these equilibria do not fall into the standard frameworks of non-cooperative routing games. As a result, we show that uniqueness of equilibria or even of utilizations at equilibria may fail even in the case of simple topology of parallel links. However, we show that some of the problems disappear in the case in which the bandwidth required by all connections is the same. For the special case of a parallel link topology, we obtain some surprisingly simple way of solving the equilibrium for both cases of Wardrop as well as Nash equilibrium.

[1]  Eitan Altman,et al.  Equilibria for multiclass routing in multi-agent networks , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[2]  F. Kelly,et al.  Braess's paradox in a loss network , 1997, Journal of Applied Probability.

[3]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[4]  Eitan Altman,et al.  Braess-like paradoxes of nash equilibria for load balancing in distributed computer systems , 1998 .

[5]  Ariel Orda,et al.  Competitive routing in multi-user communication networks , 1993, IEEE INFOCOM '93 The Conference on Computer Communications, Proceedings.

[6]  Ariel Orda,et al.  Competitive routing in multiuser communication networks , 1993, TNET.

[7]  Ariel Orda,et al.  Avoiding the Braess paradox in non-cooperative networks , 1999, Journal of Applied Probability.

[8]  Piyush Gupta,et al.  A system and traffic dependent adaptive routing algorithm for ad hoc networks , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[9]  Ariel Orda,et al.  Incentive compatible pricing strategies for QoS routing , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[10]  A. C. Pigou.  Economics of welfare , 1920 .

[11]  Peter Marbach,et al.  Priority service and max-min fairness , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[12]  Keith W. Ross,et al.  Multiservice Loss Models for Broadband Telecommunication Networks , 1997 .

[13]  J. Goodman.  Note on Existence and Uniqueness of Equilibrium Points for Concave N-Person Games , 1965 .

[14]  Hisao Kameda,et al.  Effects of symmetry on Braess-like paradoxes in distributed computer systems-a numerical study , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[15]  Eitan Altman,et al.  Braess-like paradoxes in distributed computer systems , 2000, IEEE Trans. Autom. Control..

[16]  Dietrich Braess,et al.  Über ein Paradoxon aus der Verkehrsplanung , 1968, Unternehmensforschung.

[17]  K. R. Krishnan.  The convexity of loss rate in an Erland loss system and sojourn in an Erlang delay system with respect to arrival and service rates , 1990, IEEE Trans. Commun..

[18]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[19]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[20]  S. Zachary,et al.  Loss networks , 2009, 0903.0640.

[21]  Alain Haurie,et al.  On the relationship between Nash - Cournot and Wardrop equilibria , 1983, Networks.