Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions
This paper is concerned with the modeling and mathematical analysis of vehicular traffic phenomena. We adopt a kinetic theory point of view, under which the microscopic state of each vehicle is described by: (i) position, (ii) velocity and also (iii) activity, an additional varible that we use to de...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-09-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/11/9/1093 |
| _version_ | 1811303566446428160 |
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| author | Juan Calvo Juanjo Nieto Mohamed Zagour |
| author_facet | Juan Calvo Juanjo Nieto Mohamed Zagour |
| author_sort | Juan Calvo |
| collection | DOAJ |
| description | This paper is concerned with the modeling and mathematical analysis of vehicular traffic phenomena. We adopt a kinetic theory point of view, under which the microscopic state of each vehicle is described by: (i) position, (ii) velocity and also (iii) activity, an additional varible that we use to describe the quality of the driver-vehicle micro-system. We use methods coming from game theory to describe interactions at the microscopic scale, thus constructing new models within the framework of the Kinetic Theory of Active Particles; the resulting models incorporate some of the symmetries that are commonly found in the mathematical models of the kinetic theory of gases. Short-range interactions and mean field interactions are introduced and modeled to depict velocity changes related to passing phenomena. Our main goal is twofold: (i) to use continuum-velocity variables and (ii) to introduce a non-local acceleration term modeling mean field interactions, related to, for example, the presence of tollgates or traffic highlights. |
| first_indexed | 2024-04-13T07:49:00Z |
| format | Article |
| id | doaj.art-64e3999832414edb9ebc4b8520d74fa5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T07:49:00Z |
| publishDate | 2019-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-64e3999832414edb9ebc4b8520d74fa52022-12-22T02:55:35ZengMDPI AGSymmetry2073-89942019-09-01119109310.3390/sym11091093sym11091093Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field InteractionsJuan Calvo0Juanjo Nieto1Mohamed Zagour2Departamento de Matemática Aplicada and Excellence Research Unit “Modeling Nature”, Universidad de Granada, 18071 Granada, SpainDepartamento de Matemática Aplicada and Excellence Research Unit “Modeling Nature”, Universidad de Granada, 18071 Granada, SpainEcole Supérieure de Technologie d’Essaouira, Université Cadi Ayyad, BP. 383 Essaouira, MarocThis paper is concerned with the modeling and mathematical analysis of vehicular traffic phenomena. We adopt a kinetic theory point of view, under which the microscopic state of each vehicle is described by: (i) position, (ii) velocity and also (iii) activity, an additional varible that we use to describe the quality of the driver-vehicle micro-system. We use methods coming from game theory to describe interactions at the microscopic scale, thus constructing new models within the framework of the Kinetic Theory of Active Particles; the resulting models incorporate some of the symmetries that are commonly found in the mathematical models of the kinetic theory of gases. Short-range interactions and mean field interactions are introduced and modeled to depict velocity changes related to passing phenomena. Our main goal is twofold: (i) to use continuum-velocity variables and (ii) to introduce a non-local acceleration term modeling mean field interactions, related to, for example, the presence of tollgates or traffic highlights.https://www.mdpi.com/2073-8994/11/9/1093vehicular trafficshort- and long-range interactionskinetic theory |
| spellingShingle | Juan Calvo Juanjo Nieto Mohamed Zagour Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions Symmetry vehicular traffic short- and long-range interactions kinetic theory |
| title | Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions |
| title_full | Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions |
| title_fullStr | Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions |
| title_full_unstemmed | Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions |
| title_short | Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions |
| title_sort | kinetic model for vehicular traffic with continuum velocity and mean field interactions |
| topic | vehicular traffic short- and long-range interactions kinetic theory |
| url | https://www.mdpi.com/2073-8994/11/9/1093 |
| work_keys_str_mv | AT juancalvo kineticmodelforvehiculartrafficwithcontinuumvelocityandmeanfieldinteractions AT juanjonieto kineticmodelforvehiculartrafficwithcontinuumvelocityandmeanfieldinteractions AT mohamedzagour kineticmodelforvehiculartrafficwithcontinuumvelocityandmeanfieldinteractions |