The Riemann problem for a Two-Phase model for road traffic with fixed or moving constraints
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 constraint...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2020062?viewType=HTML |
| _version_ | 1818649935917088768 |
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| author | Francesca Marcellini |
| author_facet | Francesca Marcellini |
| author_sort | Francesca Marcellini |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T01:42:14Z |
| format | Article |
| id | doaj.art-760a8224babd4a8e90e7f37deda06f3b |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-17T01:42:14Z |
| publishDate | 2020-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-760a8224babd4a8e90e7f37deda06f3b2022-12-21T22:08:18ZengAIMS PressMathematical Biosciences and Engineering1551-00182020-01-011721218123210.3934/mbe.2020062The Riemann problem for a Two-Phase model for road traffic with fixed or moving constraintsFrancesca Marcellini 0INdAM Unit, Department of Information Engineering, University of Brescia, Via Branze 38, I-25123, Brescia, ItalyWe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2020062?viewType=HTMLhyperbolic systems of conservation lawscontinuum traffic modelsevolution problemsunilateral flux constraintsmoving bottlenecks |
| spellingShingle | Francesca Marcellini The Riemann problem for a Two-Phase model for road traffic with fixed or moving constraints Mathematical Biosciences and Engineering hyperbolic systems of conservation laws continuum traffic models evolution problems unilateral flux constraints moving bottlenecks |
| title | The Riemann problem for a Two-Phase model for road traffic with fixed or moving constraints |
| title_full | The Riemann problem for a Two-Phase model for road traffic with fixed or moving constraints |
| title_fullStr | The Riemann problem for a Two-Phase model for road traffic with fixed or moving constraints |
| title_full_unstemmed | The Riemann problem for a Two-Phase model for road traffic with fixed or moving constraints |
| title_short | The Riemann problem for a Two-Phase model for road traffic with fixed or moving constraints |
| title_sort | riemann problem for a two phase model for road traffic with fixed or moving constraints |
| topic | hyperbolic systems of conservation laws continuum traffic models evolution problems unilateral flux constraints moving bottlenecks |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2020062?viewType=HTML |
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