A macroscopic traffic model with phase transitions and local point constraints on the flow

In this paper we present a macroscopic phase transition model with a local point constraint on the flow. Its motivation is, for instance, the modelling of the evolution of vehicular traffic along a road with pointlike inhomogeneities characterized by limited capacity, such as speed bumps, traffic lights, construction sites, toll booths, etc. The model accounts for two different phases, according to whether the traffic is low or heavy. Away from the inhomogeneities of the road the traffic is described by a first order model in the free-flow phase and by a second order model in the congested phase. To model the effects of the inhomogeneities we propose two Riemann solvers satisfying the point constraints on the flow.