The European Physical Journal B

, Volume 72, Issue 3, pp 467–472 | Cite as

Bivariate time-periodic Fokker-Planck model for freeway traffic

  • F. Lenz
  • D. Herde
  • A. Riegert
  • H. Kantz
Open Access
Interdisciplinary Physics


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.


Diffusion Tensor Langevin Equation Centre Manifold Stable Fixed Point Explicit Time Dependence 
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Copyright information

© The Author(s) 2009

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.Max Planck Institute for the Physics of Complex SystemsDresdenGermany

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