On the microscopic modeling of vehicular traffic on general networks

Abstract

We introduce a formalism to deal with the microscopic modeling of vehicular traffic on a road network. Traffic on each road is unidirectional, and the dynamics of each vehicle is described by a follow-the-leader model. From a mathematical point of view, this amounts to defining a system of ODEs on an arbitrary network. A general existence and uniqueness result is provided, while priorities at junctions are shown to hinder the stability of solutions. We investigate the occurrence of the Braess paradox in a time-dependent setting within this model. The emergence of Nash equilibria in a nonstationary situation results in the appearance of Braess-type paradoxes, and this is supported by numerical simulations.