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

摘要

We generalize the phase transition model studied in [R. Colombo. Hyperbolicphase 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. Twodifferent phases are taken into account, according to whether the traffic islow 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 problemsin the case a local point constraint on the flux of the solutions is enforced.