Constrained traffic equilibrium in routing

Abstract

We study noncooperative routing in which each user is faced with a multicriterion optimization problem, formulated as the minimization of one criterion subject to constraints on others. We address the questions of existence and uniqueness of equilibrium. We show that equilibria indeed exist but uniqueness may be destroyed due to the multicriteria nature of the problem. We obtain uniqueness in some weaker sense under appropriate conditions: we show that the link utilizations are uniquely determined at equilibrium. We further study the normalized constrained equilibrium and apply it to pricing.