Wardrop Optimal Flows

Abstract

Optimal flow allocation in directed networks is often analyzed through two types of equilibria. The first, called user equilibrium, occurs when the travel times on all utilized routes are the same and shorter than every unused route. The second, called system optimum, minimizes the average travel time across all routes. These two concepts represent the optimality for individual users and for the network as a whole, respectively, and generally do not coincide. This paper introduces and examines networks where user equilibrium and system optimum are identical, termed Wardrop Optimal Networks. Moreover, we illustrate that these flows remain consistent under several important transformations as well as under uniform changes in their latency functions.