A model for the formation and evolution of traffic jams F Berthelin P Degond M Delitala M Rascle

Niveau: Supérieures
A model for the formation and evolution of traffic jams F. Berthelin(1), P. Degond(2), M. Delitala(3), M. Rascle(1) (1) Laboratoire J. A. Dieudonne, U.M.R. C.N.R.S. 6621 Universite de Nice Sophia-Antipolis Parc Valrose, 06108 Nice cedex 2 - France email: , (2) MIP, UMR 5640 (CNRS-UPS-INSA) Universite Paul Sabatier 118, route de Narbonne, 31062 TOULOUSE cedex, FRANCE email: (3) Department of mathematics, Politecnico di Torino, Italy email: Abstract In this paper, we establish and analyze a traffic flow model which describes the formation and dynamics of traffic jams. It consists of a Pressureless Gas Dynamics system under a maximal constraint on the density and is derived through a singular limit of the Aw-Rascle model. From this analysis, we deduce the particular dynam- ical behaviour of clusters (or traffic jams), defined as intervals where the density limit is reached. An existence result for a generic class of initial data is proven by means of an approximation of the solution by a sequence of clusters.

• constrained pressureless


• system can


• models consist


• conservation equation


• cpgd system


• traffic


• ar model


• density constraint


• gas dynamics