Stochastic modeling and simulation of traffic flow: asymmetric single exclusion process with Arrhenius look-ahead dynamics

Research output: Contribution to journalArticle


A novel traffic flow model based on stochastic microscopic dynamics is introduced and analyzed. Vehicles advance based on the energy profile of their surrounding traffic implementing the "look-ahead" rule and following an underlying asymmetric exclusion process with Arrhenius spin-exchange dynamics. Monte Carlo simulations produce numerical solutions of the microscopic traffic model. Fluctuations play an important role in profiling observationally documented but, at the simulation level, elusive traffic phenomena. Furthermore, based on scaling and limit arguments we obtain a macroscopic description of this microscopic dynamics formulation which up to leading term of the expansions takes the form of integrodifferential Burgers or higher-order dispersive partial differential equations. We outline connections and comparisons of the hierarchical models presented here (microscopic, macroscopic) with other well-known traffic flow models.


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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics


  • traffic flow, Monte Carlo simulations, look-ahead stochastic Arrhenius microscopic dynamics
Original languageEnglish
Pages (from-to)921-944
JournalSIAM Journal on Applied Mathematics
Issue number3
Publication statusPublished - 2006
Publication categoryResearch
Externally publishedYes