Exact results for deterministic cellular automata traffic models.
We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to a well-known lattice path counting problem. Assuming infinite lattice size and random initial configuration, the flow can be expressed in terms of generalized hypergeometric function. We show that the steady-state limit agrees with previously published results.
Fukś
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The Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, Canada M5T 3J1. hfuks@fields.utoronto.ca