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EnglishIn 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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| Data di pubblicazione: | 2017 | |
| Titolo: | General phase transition models for vehicular traffic with point constraints on the flow | |
| Autori: | Dal santo, E.; Rosini, M. D.; Dymski, N.; Benyahia, M. | |
| Rivista: | MATHEMATICAL METHODS IN THE APPLIED SCIENCES | |
| Keywords: | Aw-Rascle-Zhang model; Conservation laws; Lighthill-Whitham-Richards model; Phase transitions; Riemann problem; Unilateral point constraint; Vehicular traffic; Mathematics (all); Engineering (all) | |
| Abstract in inglese: | 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. | |
| Digital Object Identifier (DOI): | 10.1002/mma.4478 | |
| Handle: | http://hdl.handle.net/11392/2380969 | |
| Appare nelle tipologie: | 03.1 Articolo su rivista |
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