Extensions and amplifications of a traffic model of Aw and Rascle

In a recent paper Aw and Rascle [SIAM J. Appl. Math., 60 (2000), pp. 916 938] 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 the 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.