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

摘要

It is shown that a variety of deterministic cellular automaton models ofhighway traffic flow obey a variational principle which states that, for agiven car density, the average car flow is a non-decreasing function of time.This result is established for systems whose configurations exhibits local jamsof a given structure. If local jams have a different structure, it is shownthat either the variational principle may still apply to systems evolvingaccording to some particular rules, or it could apply under a weaker form tosystems whose asymptotic average car flow is a well-defined function of cardensity. To establish these results it has been necessary to characterize amongall number-conserving cellular automaton rules which ones may reasonably beconsidered as acceptable traffic rules. Various notions such as free-movingphase, perfect and defective tiles, and local jam play an important role in thediscussion. Many illustrative examples are given.