The price of selfish routing

  • Authors:

  • Marios Mavronicolas;Paul Spirakis

  • Affiliations:

  • Dept. of Computer Science, University of Cyprus, Nicosia CY-1678, Cyprus;Dept. of Computer Engineering and Informatics, University of Patras, & Computer Technology Institute, 261 10 Patras, Greece

  • Venue:
  • STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
  • Year:
  • 2001

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Abstract

We study the problem of routing traffic through a congested network. We focus on the simplest case of a network consisting of m parallel links. We assume a collection of n network users, each employing a mixed strategy which is a probability distribution over links, to control the shipping of its own assigned traffic. Given a capacity for each link specifying the rate at which the link processes traffic, the objective is to route traffic so that the maximum expected latency over all links is minimized. We consider both uniform and non-uniform link capacities.How much decrease in global performace is necessary due to the absence of some central authority to regulate network traffic and implement an optimal assignment of traffic to links? We investigate this fundamental question in the context of Nash equilibria for such a system, where each network user selfishly routes its traffic only on those links available to it that minimize its expected latency cost, given the network congestion caused by the other users. We use the coordination ratio, defined by Koutsoupias and Papadimitriou [25] as the ratio of the maximum (over all links) expected latency in the worst possible Nash equlibrium, over the least possible maximum latency had global regulation been available, as a measure of the cost of lack of coordination among the network users.