A 2-Phase Traffic Model Based on a Speed Bound

We extend the classical Lighthill–Whitham–Richards (LWR) traffic model allowing different maximal speeds for different vehicles. Then we add a uniform bound on the traffic speed. The result, presented in this paper, is a new macroscopic model displaying two phases based on a nonsmooth 2×2 system of conservation laws. This model is compared with other models of the same type in the current literature, as well as with a kinetic one. Moreover, we establish a rigorous connection between a microscopic follow-the-leader model based on ordinary differential equations and this macroscopic continuum model.