Kinetic Theory Methods in Traffic Flow
A.R. Méndez [1], R.M. Velasco [2]

[1] Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana - Cuajimalpa, [2] Departamento de Fisica, Universidad Autonoma Metropolitana - Iztapalapa

Abstract: Similarly to the treatment of dilute gases, kinetic methods are formulated to study unidirectional freeway traffic. From these it is possible to construct fluid-dynamic equations which not only have the advantage of having fewer adjustable parameters than the heuristic models, but also allow for a more formal inclusion of finer effects. In this work we compare the two principal approaches within the microscopic formalisms and present advances in the modeling of the synchronization phenomena, the phase transition between free flow and traffic jams.