A new model for selfish routing

Abstract

In this work, we introduce and study a new model for selfish routing over non-cooperative networks that combines features from the two such best studied models, namely the KP model and the Wardrop model in an interesting way. We consider a set of n users, each using a mixed strategy to ship its unsplittable traffic over a network consisting of m parallel links. In a Nash equilibrium, no user can increase its Individual Cost by unilaterally deviating from its strategy. To evaluate the performance of such Nash equilibria, we introduce Quadratic Social Cost as a certain sum of Individual Costs - namely, the sum of the expectations of the squares of the incurred link latencies. This definition is unlike the KP model, where Maximum Social Cost has been defined as the maximum of Individual Costs. We analyse the impact of our modeling assumptions on the computation of Quadratic Social Cost, on the structure of worst-case Nash equilibria, and on bounds on the Quadratic Coordination Ratio. © Springer-Verlag 2004.