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.

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<p style='text-indent:20px;'>This work is devoted to the study of the wave interactions of an improved Aw-Rascle-Zhang model with a non-genuinely nonlinear field. The wave interactions between single elementary waves involving the composite wave are analyzed by reviewing the Riemann solutions. Due to the non-genuinely nonlinear field, some new phenomena are found. The rarefaction waves may penetrate the shock waves. As a contact discontinuity interacts with the composite waves, there appear the compression waves which change to a contact discontinuity, then to rarefaction waves. Using the single wave interaction results, we construct the weak solutions of this model with three piecewise constant states. Finally, we give some intuitions to eliminate the "phantom traffic jam".</p>