We present different frameworks for the description of traffic flow. First, we discuss models based on the coupling of systems of different types. In particular we consider a 2-phase model, where a scalar conservation law is coupled with a 2 x 2 system. Then, we present a coupled micro-macro description, the former consisting of a system of ordinary differential equations and the latter being the usual LWR conservation law. Inspired by the above cases, we consider a macroscopic model where a sample of the trajectories are known thanks, for instance, to 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.
This is a joint research with Rinaldo M. Colombo (University of Brescia).