Properties of Equilibria in Competitive Routing with Several User Types

In recent years there has been a growing interest in mathematical models for routing in networks in which the decisions are taken in a non-cooperative way. Instead of a single decision maker (that may represent the network) that chooses the routes so as to maximize a global utility, one considers a number of decision makers having each its own utility to maximize by routing its own flow. This gives rise to the use of non-cooperative game theory and the Nash equilibrium concept for optimality. In the special case in which each decision maker wishes to find a minimal path for each routed object (e.g. a packet) then the solution concept is the Wardrop equilibrium. It is well known that equilibria may exhibit inefficiencies and paradoxical behaviour, such as the famous Braess paradox (in which the addition of a link to a network results in worse performance to all users). This raises the challenge for the network administrator of how to upgrade the network so that it indeed results in improved performance. We present in this paper some guidelines for that. Keywords— Computer Communication Network, Routing, Noncooperative Games, Braess Paradox.