In a recent paper [1] Aw and Rascle introduced a new model of traffic on a uni-directional highway. Here the author studies an extension of this model, one which accounts for drivers attempting to travel at their maximum allowable speed. The author looks at a Lagrangian reformulation of this problem; a formulation that leads to an effective computational algorithm for solving the resulting system. He also investigates approximation scheme introduced by Dafermos [5] for scalar conservation laws and demonstrates that this Dafermos scheme works well on this 2 x 2 system.
['J. M. Greenberg']
Extensions and amplifications of a traffic model of Aw and Rascle