A Traffic-Flow Model with Constraints for the Modeling of Traffic Jams

Recently, Berthelin et al [5] introduced a traffic flow model describing the formation and the dynamics of traffic jams. This model which consists of a Constrained Pressureless Gas Dynamics system assumes that the maximal density constraint is independent of the velocity. However, in practice, the distribution of vehicles on a highway depends on their velocity. In this paper we propose a more realistic model namely the Second Order Model with Constraint (SOMC model), derived from the Aw & Rascle model [1] abd which takes into this feature. Moreover, when the maximal density constraint is saturated, the SOMC model “relaxes” to the Lighthill & Whitham model [17]. We prove an existence result of weak solutions for this model by means of cluster dynamics in order to construct a sequence of approximations and we solve completely the associated Riemann problem.