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Optimal transportation with traffic congestion and Wardrop equilibria

Santambrogio, Filippo; Jimenez, Chloé; Carlier, Guillaume (2008), Optimal transportation with traffic congestion and Wardrop equilibria, SIAM Journal on Control and Optimization, 47, 3, p. 1330-1350. http://dx.doi.org/10.1137/060672832

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Type
Article accepté pour publication ou publié
Date
2008
Journal name
SIAM Journal on Control and Optimization
Volume
47
Number
3
Pages
1330-1350
Publication identifier
Metadata
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Author(s)
Santambrogio, Filippo
Jimenez, Chloé
Carlier, Guillaume
Abstract (EN)
In the classical Monge–Kantorovich problem, the transportation cost depends only 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 variant is a continuous version of a well-known traffic problem on networks that is studied both in economics and in operational research. The interest of this problem is in its relations with traffic equilibria of Wardrop type. What we prove in the paper is exactly the existence and the variational characterization of equilibria in a continuous space setting.
Subjects / Keywords
Wardrop equilibria; traffic congestion; optimal transportation