General phase transition models for vehicular traffic with point constraints on the flow |
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Authors: | E Dal Santo M D Rosini N Dymski M Benyahia |
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Institution: | 1. Instytut Matematyki, Uniwersytet Marii Curie‐Sk?odowskiej, Lublin, Poland;2. Inria Sophia Antipolis ‐ Méditerranée, Université C?te d'Azur, Inria, CNRS, LJAD, Sophia‐Antipolis, France;3. Gran Sasso Science Institute, L'Aquila, Italy |
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Abstract: | In this paper, we present a general phase transition model 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 free‐flow phase and by a system of 2 conservation laws in the congested phase. The free‐flow phase is described by a one‐dimensional fundamental diagram corresponding to a Newell‐Daganzo type flux. The congestion phase is described by a two‐dimensional fundamental diagram obtained by perturbing a general fundamental flux. In particular, we study the resulting Riemann problems in the case a local point constraint on the flow of the solutions is enforced. |
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Keywords: | conservation laws phase transitions Lighthill‐Whitham‐Richards model Aw‐Rascle‐Zhang model vehicular traffic unilateral point constraint Riemann problem |
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