Systems of conservation laws with discontinuous fluxes and applications to traffic

In this paper we study 2 × 2 systems of conservation laws with discontinuous fluxes arising in vehicular traffic modeling. The main goal is to introduce an appropriate notion of solution. To this aim we consider physically reasonable microscopic follow-the-leader models. Macroscopic Riemann solvers are then obtained as many particle limits. This approach leads us to develop six models. We propose a unified way to describe such models, which highlights their common property of maximizing the density flow across the interface under appropriate physical restrictions depending on the case at hand.