@misc{10481/57667,
year = {2019},
month = {9},
url = {http://hdl.handle.net/10481/57667},
abstract = {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.},
organization = {J.C. and J.N. are partially supported by Junta de Andalucía Project P12-FQM-954 and MINECO
Project RTI2018-098850-B-I00. J.C. is supported by Universidad de Granada (“Plan propio de investigación,
programa 9”) through FEDER funds. M.Z. was supported by CNRST (Morocco), project “Modèles Mathématiques
appliqués à l’environnement, à l’imagerie médicale et aux biosystèmes”.},
publisher = {MDPI},
keywords = {Vehicular traffic},
keywords = {Short range interactions},
keywords = {Long range interactions},
keywords = {Kinetic theory},
title = {Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions},
doi = {10.3390/sym11091093},
author = {Calvo Yagüe, Juan and Nieto Muñoz, Juan José and Zagour, Mohamed},
}