The Riemann problem for a Two-Phase model for road traffic with fixed or moving constraints

We define two Riemann solvers for the Two-Phase traffic model proposed in [1], given by a system of two conservation laws with Lipschitz continuous flow, under fixed and moving constraints. From the traffic point of view this situation corresponds to the study of vehicular flow with fixed constraints as, for instance, a traffic light, a toll gate or a construction site. On the other hand, the presence of a slow moving large vehicle, like a bus, corresponds to the case of a moving constraint. In the latter case, we have to consider a mixed system where the conservation laws are coupled with an ordinary differential equation describing the trajectory of the large vehicle.