A second order model for vehicular traffics with local point constraints on the flow

B Andreianov (1, 2) , Carlotta Donadello (2) , Massimiliano D. Rosini (3)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
3 ICM

In this paper we present a second order model based on the Aw, Rascle, Zhang model (ARZ) for vehicular traffics subject to point constraints on the flow, its motivation being, for instance, the modeling of traffic lights along a road. We first introduce a definition of entropy solution by choosing a family of entropy pairs analogous to the Kruzhkov entropy pairs for scalar conservation laws; then we apply the wave-front tracking method to prove existence and a priori bounds for the entropy solutions of constrained Cauchy problem for ARZ with initial data of bounded variation and piecewise constant constraints. The case of solutions attaining values at the vacuum is considered. We construct an explicit example to describe some qualitative features of the solutions.

Mots clés: Wave-front tracking approximations; Traffic modeling; Hyperbolic systems of PDEs with constraints; Aw-Rascle-Zhang model

Domaines: Equations aux dérivées partielles [math.AP]

B Andreianov, Carlotta Donadello, Massimiliano D. Rosini. A second order model for vehicular traffics with local point constraints on the flow. 2015. ⟨hal-01146116⟩