Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions Calvo Yagüe, Juan Nieto Muñoz, Juan José Zagour, Mohamed Vehicular traffic Short range interactions Long range interactions Kinetic theory 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. 2019-11-04T10:30:18Z 2019-11-04T10:30:18Z 2019-09-02 info:eu-repo/semantics/article Calvo, J.; Nieto, J.; Zagour, M. Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions. Symmetry 2019, 11, 1093. [doi:10.3390/sym11091093] http://hdl.handle.net/10481/57667 10.3390/sym11091093 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España MDPI