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

Roméo Hatchi (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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 Γ-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.

Mots clés: traffic congestion; Wardrop equilibrium; Γ-convergence; generalized curves

Domaines: Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Roméo Hatchi. Wardrop equilibria : rigorous derivation of continuous limits from general networks models. 2015. ⟨hal-01169660⟩