A model for traffic flow on a road with variable widths

We propose a model describing the traffic flow on a road with variable widths in this paper. The model, which is modified the Aw-Rascle model, is not conservative because of the source term. We obtain the elementary waves of the new traffic flow model, including rarefaction waves, shock waves, contact discontinuities and stationary waves. The Riemann problems of the system for the traffic flow are solved and some numerical results are given, which are almost the same as the theoretical ones.