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Stochastic Description of Traffic Flow

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Abstract

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.

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Authors and Affiliations

  1. Univ. of Massachusetts at Amherst, 710 North Pleasant Street, Amherst, MA, 01003, USA

    Timur Alperovich

  2. Dept. of Math. & Stat., Univ. of North Carolina at Charlotte, 2101 University City Blvd., Charlotte, NC, 28223, USA

    Alexandros Sopasakis

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  1. Timur Alperovich
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  2. Alexandros Sopasakis
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Correspondence to Alexandros Sopasakis.

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Alperovich, T., Sopasakis, A. Stochastic Description of Traffic Flow. J Stat Phys 133, 1083–1105 (2008). https://doi.org/10.1007/s10955-008-9652-6

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  • DOI: https://doi.org/10.1007/s10955-008-9652-6

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