Developing an Aw-Rascle model of traffic flow

A traffic flow model is established based on the car following principle with a maximal constraint on the density-velocity relationship. The model develops the Aw-Rascle model and amends some nonphysical features. Moreover, we construct the solutions of the Riemann problem for the model. The Riemann solutions provide a more reasonable invariant region and show the phase-transition phenomena.