Optimal transportation with traffic congestion and Wardrop equilibria

TL;DR

This paper extends classical optimal transportation models to include traffic congestion effects, establishing existence and characterization of equilibria in a continuous setting, thus bridging transportation theory and game theory.

Contribution

It introduces a congestion-aware variant of the Monge-Kantorovich problem and proves existence and characterization of Wardrop equilibria in continuous spaces.

Findings

Existence of minimizers for the congestion-including transportation problem

Characterization of Wardrop equilibria in a continuous framework

Application to continuous space transportation models

Abstract

In the classical Monge-Kantorovich problem, the transportation cost only depends on the amount of mass sent from sources to destinations and not on the paths followed by this mass. Thus, it does not allow for congestion effects. Using the notion of traffic intensity, we propose a variant taking into account congestion. This leads to an optimization problem posed on a set of probability measures on a suitable paths space. We establish existence of minimizers and give a characterization. As an application, we obtain existence and variational characterization of equilibria of Wardrop type in a continuous space setting.