Wardrop equilibria : rigorous derivation of continuous limits from general networks models

TL;DR

This paper rigorously derives continuous models of Wardrop equilibria from dense network traffic models in R^d using Γ-convergence, extending previous results from Cartesian to general networks.

Contribution

It extends the derivation of continuous Wardrop equilibrium models from dense network models to general networks in R^d using generalized curves.

Findings

Derived continuous minimization problems on measures on curves.

Extended the framework from Cartesian to general networks.

Provided rigorous Γ-convergence analysis for dense network limits.

Abstract

The concept of Wardrop equilibrium plays an important role in congested traffic problems since its introduction in the early 50's. As shown in [2], when we work in two-dimensional cartesian and increasingly dense networks, passing to the limit by {\Gamma}-convergence, we obtain continuous minimization problems posed on measures on curves. Here we study the case of general networks in R d which become very dense. We use the notion of generalized curves and extend the results of the cartesian model.