Eur. Phys. J. B 72, 467-472 (2009)
https://doi.org/10.1140/epjb/e2009-00364-3

Bivariate time-periodic Fokker-Planck model for freeway traffic

Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany

Corresponding author: ^a flenz@mpipks-dresden.mpg.de

Received: 26 May 2009
Revised: 7 October 2009
Published online: 31 October 2009

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.