Stochastic description of traffic flow

Research output: Contribution to journalArticle


We propose a traffic model based on microscopic stochastic dynamics. We built a Markov chain equipped with an Arrhenius interaction law. The resulting stochastic process is comprised of both spin-flip and spin-exchange dynamics which models vehicles exiting, entering and interacting in a two-dimensional lattice environment corresponding to a multi-lane highway. The process is further equipped with a novel look-ahead type, anisotropic interaction potential which allows drivers/vehicles to ascertain local fluctuations and advance to new cells forward or sideways. The resulting vehicular traffic model is simulated via kinetic Monte Carlo and examined under both, typical and extreme traffic flow scenarios. The model is shown to correctly predict both qualitative as well as quantitative traffic observables for any highway geometry. Furthermore it also captures interesting multi-scale phenomena in traffic flows after a simulated accident which lead to oscillatory, dissipating, traffic waves with different periods per lane.


External organisations
  • University of North Carolina at Charlotte
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics


  • Multi-lane traffic flow - Anisotropic look-ahead rule - Markov Chain - Spin-flip/spin-exchange dynamics - Arrhenius potential - Kinetic Monte Carlo
Original languageEnglish
Pages (from-to)1083-1105
JournalJournal of Statistical Physics
Issue number6
Publication statusPublished - 2008
Publication categoryResearch
Externally publishedYes