Wardrop equilibria : rigorous derivation of continuous limits from general networks models
Provides a theoretical foundation for modeling traffic flow in dense networks, relevant to applied mathematics and transportation engineering.
The authors rigorously derive continuous limits of Wardrop equilibria from general dense networks in R^d, extending previous results from two-dimensional cartesian networks to arbitrary network topologies.
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.