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Zbl 1161.82324
Alperovich, Timur; Sopasakis, Alexandros
Stochastic description of traffic flow. (English)
[J] J. Stat. Phys. 133, No. 6, 1083-1105 (2008). ISSN 0022-4715; ISSN 1572-9613/e

Summary: 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.

MSC 2000:: *82C20 Dynamic lattice systems
90B20 Highway traffic
82C80 Numerical methods of time-dependent statistical mechanics
60J10 Markov chains with discrete parameter

Keywords: multi-lane traffic flow; anisotropic look-ahead rule; Markov Chain; Spin-flip dynamics; spin-exchange dynamics; Arrhenius potential; kinetic Monte Carlo

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