Extensions and amplifications of a traffic model of Aw and Rascle (Q2783731)

The author extents a traffic flow model on a uni-directional highway by allowing drivers to attempt travel at the maximum allowable speed. In particular, he modifies the equation \(\alpha_t+u \alpha_x=0\) for driver's velocity reserve \(\alpha=u-v(\rho)\) \((u\) is car velocity, \(v(\rho)\) is maximum allowable speed for traffic density \(\rho)\). Right-hand side is added and the equation becomes \(\alpha_t+ u\alpha_x= -\alpha/ \delta\), where \(\delta\) can be interpreted as a relaxation or adjustment time. Then the author defines and investigates computational algorithm for solving Lagrangian reformulation of the problem. Estimates for suggested downwind integration scheme show that the scheme is stable and well behaved. The author presents also some interesting numerical simulations.