From discrete to continuous Wardrop equilibria

Carlier, Guillaume; Baillon, Jean-Bernard

Carlier, Guillaume; Baillon, Jean-Bernard (2012), From discrete to continuous Wardrop equilibria, Networks and Heterogeneous Media, 7, 2, p. 219-241. http://dx.doi.org/10.3934/nhm.2012.7.219

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00637396/fr/

Date

2012

Journal name

Networks and Heterogeneous Media

Volume

Number

Publisher

American Institute of Mathematical Science

Pages

219-241

Abstract (EN)

The notion of Wardrop equilibrium in congested networks has been very popular in congested traffic modelling since its introduction in the early 50's, it is also well-known that Wardrop equilibria may be obtained by some convex minimization problem. In this paper, in the framework of Γ-convergence theory, we analyze what happens when a cartesian network becomes very dense. The continuous model we obtain this way is very similar to the continuous model of optimal transport with congestion of Carlier, Jimenez and Santambrogio [6] except that it keeps track of the anisotropy of the network.

Subjects / Keywords

traffic congestion; Wardrop equilibria