1999/02/28 by Henryk Fuks · 2 citations
Physics and Astronomy · #comp-gas #cond-mat #nlin.CG
paper · pdf · doi:10.1103/physreve.60.197
published as Phys. Rev. E 60 197-202 (1999) · 13 pages, 4 figures
arxiv created 1999/11/02 · arxiv updated 2009/11/30
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.