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On The Existence Of A Variational Principle For Deterministic Cellular Automaton Models Of Highway Traffic Flow

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  • NINO BOCCARA

    (Department of Physics, University of Illinois, Chicago, USA;
    DRECAM/SPEC, CE Saclay, 91191 Gif-sur-Yvette Cedex, France)

Abstract

It is shown that a variety of deterministic cellular automaton models of highway traffic flow obey a variational principle which states that, for a given car density, the average car flow is a nondecreasing function of time. This result is established for systems whose configurations exhibits local jams of a given structure. If local jams have a different structure, it is shown that either the variational principle may still apply to systems evolving according to some particular rules, or it could apply under a weaker form to systems whose asymptotic average car flow is a well-defined function of car density. To establish these results, it has been necessary to characterize among all number-conserving cellular automaton rules which ones may reasonably be considered as acceptable traffic rules. Various notions such as free-moving phase, perfect and defective tiles, and local jam play an important role in the discussion. Many illustrative examples are given.

Suggested Citation

  • Nino Boccara, 2001. "On The Existence Of A Variational Principle For Deterministic Cellular Automaton Models Of Highway Traffic Flow," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 143-158.
    • Handle: RePEc:wsi:ijmpcx:v:12:y:2001:i:02:n:s0129183101001596
    DOI: 10.1142/S0129183101001596
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    Cited by:

    1. Yuan, Weifeng & Tan, Kang Hai, 2011. "A model for simulation of crowd behaviour in the evacuation from a smoke-filled compartment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4210-4218.

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