  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.
