ODE-PDE Models in Traffic Flow Dynamics

We present two frameworks for the description of traffic flow. First, we consider the coupling of a micro- and a macroscopic models, the former consisting in a system of ordinary differential equations and the latter in the usual LWR conservation law. Then, inspired by this model, we consider a macroscopic model where some trajectories are known thanks to, for instance, GPS measurement devices. The result is a new traffic model able to take into account real time data, or, in other words, that encodes these data.