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Open AccessArticle

Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions

Departamento de Matemática Aplicada and Excellence Research Unit “Modeling Nature”, Universidad de Granada, 18071 Granada, Spain
Ecole Supérieure de Technologie d’Essaouira, Université Cadi Ayyad, BP. 383 Essaouira, Maroc
Author to whom correspondence should be addressed.
To the memory of Abdelghani Bellouquid.
Symmetry 2019, 11(9), 1093;
Received: 29 July 2019 / Revised: 19 August 2019 / Accepted: 22 August 2019 / Published: 2 September 2019
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. View Full-Text
Keywords: vehicular traffic; short- and long-range interactions; kinetic theory vehicular traffic; short- and long-range interactions; kinetic theory
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Calvo, J.; Nieto, J.; Zagour, M. Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions. Symmetry 2019, 11, 1093.

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