General phase transition models for vehicular traffic with point constraints on the flow

We generalize the phase transition model studied in [R. Colombo. Hyperbolic phase transition in traffic flow.\ SIAM J.\ Appl.\ Math., 63(2):708-721, 2002], that describes the evolution of vehicular traffic along a one-lane road. Two different phases are taken into account, according to whether the traffic is low or heavy. The model is given by a scalar conservation law in the \emph{free-flow} phase and by a system of two conservation laws in the \emph{congested} phase. In particular, we study the resulting Riemann problems in the case a local point constraint on the flux of the solutions is enforced.