ON THE EXISTENCE OF A VARIATIONAL PRINCIPLE FOR DETERMINISTIC CELLULAR AUTOMATON MODELS OF HIGHWAY TRAFFIC FLOW

Nino Boccara ()
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Nino Boccara: Department of Physics, University of Illinois, Chicago, USA;

International Journal of Modern Physics C (IJMPC), 2001, vol. 12, issue 02, 143-158

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.

Keywords: Cellular Automata; Interacting Particles; Highway Traffic Models; Variational Principle (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1142/S0129183101001596

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