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On the existence of a variational principle for deterministic cellular automaton models of highway traffic flow

Nino Boccara
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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 non-decreasing 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.

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Nino Boccara. 2000-05-15. On the existence of a variational principle for deterministic cellular automaton models of highway traffic flow. https://doi.org/10.1142/s0129183101001596

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