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The Riemann problem for a Two-Phase model for road traffic with fixed or moving constraints

INdAM Unit, Department of Information Engineering, University of Brescia, Via Branze 38, I-25123, Brescia, Italy

Special Issues: Mathematical Modeling with Measures

We define two Riemann solvers for the Two-Phase traffic model proposed in [1], given by a system of two conservation laws with Lipschitz continuous flow, under fixed and moving constraints. From the traffic point of view this situation corresponds to the study of vehicular flow with fixed constraints as, for instance, a traffic light, a toll gate or a construction site. On the other hand, the presence of a slow moving large vehicle, like a bus, corresponds to the case of a moving constraint. In the latter case, we have to consider a mixed system where the conservation laws are coupled with an ordinary differential equation describing the trajectory of the large vehicle.
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Keywords hyperbolic systems of conservation laws; continuum traffic models; evolution problems; unilateral flux constraints; moving bottlenecks

Citation: Francesca Marcellini. The Riemann problem for a Two-Phase model for road traffic with fixed or moving constraints. Mathematical Biosciences and Engineering, 2020, 17(2): 1218-1232. doi: 10.3934/mbe.2020062


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