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

A Traffic-Flow Model with Constraints for the Modeling of Traffic Jams F. Berthelin? P. Degond† V. Le Blanc‡ S. Moutari? M. Rascle? J. Royer Abstract 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. Key words. Traffic flow models, Second order models, Constraints, Riemann problem, Weak solutions. AMS Subject Classification: 35L60, 35L65, 35L67 1 Introduction During the past fifty years, a wide range of models of vehicular traffic flow has been developed. Roughly speaking, three important classes of approaches are commonly used to model traffic phenomena.

• maximal density


• traffic flow


• phenomena such


• somc model


• traffic complex


• traffic jams


• no invariant


• using invariant rectangles