Dynamic Cesaro-Wardrop equilibration in networks

We analyze a routing scheme for a broad class of networks which converges (in the Cesaro sense) with probability one to the set of approximate Cesaro-Wardrop equilibria, an extension of the notion of a Wardrop equilibrium. The network model allows for wireline networks where delays are caused by flows on links, as well as wireless networks, a primary motivation for us, where delays are caused by other flows in the vicinity of nodes. The routing algorithm is distributed, using only the local information about observed delays by the nodes, and is moreover impervious to clock offsets at nodes. The scheme is also fully asynchronous, since different iterates have their own counters and the orders of packets and their acknowledgments may be scrambled. Finally, the scheme is adaptive to the traffic patterns in the network. The demonstration of convergence in a fully dynamic context involves the treatment of two-time scale distributed asynchronous stochastic iterations. Using an ordinary differential equation approach, the invariant measures are identified. Due to a randomization feature in the algorithm, a direct stochastic analysis shows that the algorithm avoids non-Wardrop equilibria. Finally, some comments on the existence, uniqueness, stability, and other properties of Wardrop equilibria are made.

[1]  Piyush Gupta.  Design and Performance Analysis of Wireless Networks , 2000 .

[2]  William H. Sandholm,et al.  Evolutionary Implementation and Congestion Pricing , 2002 .

[3]  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).

[4]  Harold J. Kushner,et al.  Stochastic Approximation Algorithms and Applications , 1997, Applications of Mathematics.

[5]  V. Borkar.  Stochastic approximation with two time scales , 1997 .

[6]  P. Marcotte,et al.  A game-theoretic approach to network equilibrium , 1986 .

[7]  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).

[8]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

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

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

[11]  Fernando Vega-Redondo,et al.  Evolution, Games, and Economic Behaviour , 1996 .

[12]  G. Sell.  Topological dynamics and ordinary differential equations , 1971 .

[13]  S. Ethier,et al.  Markov Processes: Characterization and Convergence , 2005 .

[14]  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.

[15]  Hisao Kameda,et al.  A case where a paradox like Braess's occurs in the Nash equilibrium but does not occur in the Wardrop equilibrium - a situation of load balancing in distributed computer systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[16]  Tamer Basar,et al.  Analysis of Recursive Stochastic Algorithms , 2001 .

[17]  Jörgen W. Weibull,et al.  Evolutionary Game Theory , 1996 .

[18]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

[19]  D. Hearn,et al.  Chapter 6 Network equilibrium models and algorithms , 1995 .

[20]  Yishay Mansour,et al.  Nash Convergence of Gradient Dynamics in General-Sum Games , 2000, UAI.

[21]  John K. Antonio,et al.  Distributed iterative aggregation algorithms for box-constrained minimization problems and optimal routing in data networks , 1989 .

[22]  H. Young.  Individual Strategy and Social Structure , 2020 .

[23]  Ariel Orda,et al.  Incentive Compatible Pricing Strategies for QoS Routing , 1999, INFOCOM 1999.

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

[25]  Manuela M. Veloso,et al.  Multiagent learning using a variable learning rate , 2002, Artif. Intell..

[26]  Jaume Barceló,et al.  Dynamic traffic assignment: Considerations on some deterministic modelling approaches , 1995, Ann. Oper. Res..

[27]  William H. Sandholm,et al.  Potential Games with Continuous Player Sets , 2001, J. Econ. Theory.

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

[29]  W. Tsai.  Convergence of gradient projection routing methods in an asynchronous stochastic quasi-static virtual circuit network , 1989 .

[30]  J G Wardrop,et al.  CORRESPONDENCE. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .

[31]  V. Borkar.  Probability Theory: An Advanced Course , 1995 .