Bivariate time-periodic Fokker-Planck model for freeway traffic

Abstract

Recorded data of the density of cars and their speed from a German motorway are modeled by a bivariate Fokker-Planck equation. In order to cope with the evident diurnal variation, we assume a 24 h-periodicity in the drift and diffusion coefficients of this equation. After fitting these and smoothing them by polynomials, we validate the model by comparison of the empirical densities and densities generated by the model dynamics. We show that the time dependence of the drift field is related to a saddle-node bifurcation due to which the congested traffic state becomes stable. The separatrix between the basins of attraction is used to define flowing and jamming traffic during rush hours and characterizes the traffic dynamics together with the fixed points and the centre manifold. © 2009 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.