Multicommodity flows on road networks

Abstract

In this paper, we discuss the multicommodity flow for vehicular traffic on road networks. To model the traffic, we use the “Aw-Rascle” multiclass macroscopic model. We describe a solution to the Riemann problem at junctions with a criterion of maximization of the total flux, taking into account the destination path of the vehicles. At such a junction, the actual distribution depends on the demands and the supplies on the incoming and outgoing roads, respectively. Furthermore, this new distribution scheme captures efficiently key merging characteristics of the traffic and in contrast to M. Herty, S. Moutari and M. Rascle, Networks and Heterogeneous Media, 1, 275-294, 2006, leads to an easy computational model to solve approximately the homogenization problem described in M. Herty, S. Moutari and M. Rascle, Networks and Heterogeneous Media, 1, 275-294, 2006, (M. Herty and M. Rascle, SIAM J. Math. Anal., 38(2), 595-616, 2006). Furthermore, we deduce the equivalent distribution scheme for the LWR multiclass model in M. Garavello and B. Piccoli, Commun. Math. Sci., 3, 261-283, 2005, and we compare the results with those obtained with the “Aw-Rascle” multiclass model for the same initial conditions.