A macroscopic traffic model with phase transitions and local point constraints on the flow

Mohamed Benyahia; Massimiliano D. Rosini; Mohamed Benyahia; Massimiliano D. Rosini

doi:10.3934/nhm.2017013

Networks and Heterogeneous Media

2017, Volume 12, Issue 2: 297-317. doi: 10.3934/nhm.2017013

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A macroscopic traffic model with phase transitions and local point constraints on the flow

Mohamed Benyahia ^{1
,},
Massimiliano D. Rosini ^{2
,
,}

1.
Gran Sasso Science Institute, Viale F. Crispi 7,67100 L'Aquila, Italy
2.
Instytut Matematyki, Uniwersytet Marii Curie-Skłodowskiej, Plac Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

Received: 01 November 2016 Revised: 01 January 2017
Primary: 35L65, 90B20; Secondary: 82C26

In this paper we present a macroscopic phase transition model with a local point constraint on the flow. Its motivation is, for instance, the modelling of the evolution of vehicular traffic along a road with pointlike inhomogeneities characterized by limited capacity, such as speed bumps, traffic lights, construction sites, toll booths, etc. The model accounts for two different phases, according to whether the traffic is low or heavy. Away from the inhomogeneities of the road the traffic is described by a first order model in the free-flow phase and by a second order model in the congested phase. To model the effects of the inhomogeneities we propose two Riemann solvers satisfying the point constraints on the flow.
- Conservation laws,
- phase transitions,
- Lighthill-Whitham-Richards model,
- Aw-Rascle-Zhang model,
- unilateral constraint,
- Riemann problem
Citation: Mohamed Benyahia, Massimiliano D. Rosini. A macroscopic traffic model with phase transitions and local point constraints on the flow[J]. Networks and Heterogeneous Media, 2017, 12(2): 297-317. doi: 10.3934/nhm.2017013

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Abstract

In this paper we present a macroscopic phase transition model with a local point constraint on the flow. Its motivation is, for instance, the modelling of the evolution of vehicular traffic along a road with pointlike inhomogeneities characterized by limited capacity, such as speed bumps, traffic lights, construction sites, toll booths, etc. The model accounts for two different phases, according to whether the traffic is low or heavy. Away from the inhomogeneities of the road the traffic is described by a first order model in the free-flow phase and by a second order model in the congested phase. To model the effects of the inhomogeneities we propose two Riemann solvers satisfying the point constraints on the flow.

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