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.