Exact limiting solutions for certain deterministic traffic rules
Cellular Automata and Lattice Gases
2007-05-23 v1
Abstract
We analyze the steady-state flow as a function of the initial density for a class of deterministic cellular automata rules (``traffic rules'') with periodic boundary conditions [H. Fuks and N. Boccara, Int. J. Mod. Phys. C 9, 1 (1998)]. We are able to predict from simple considerations the observed, unexpected cutoff of the average flow at unity. We also present an efficient algorithm for determining the exact final flow from a given finite initial state. We analyze the behavior of this algorithm in the infinite limit to obtain for R_m,k an exact polynomial equation maximally of 2(m+k)th degree in the flow and density.
Cite
@article{arxiv.nlin/0105045,
title = {Exact limiting solutions for certain deterministic traffic rules},
author = {Janne V. Kujala and Tuomas J. Lukka},
journal= {arXiv preprint arXiv:nlin/0105045},
year = {2007}
}
Comments
25 pages, 8 figures