Cellular Automata For Traffic Flow: Analytical Results
Abstract
We use analytical methods to investigate cellular automata for traffic flow. Two different mean-field approaches are presented, which we call site-oriented and car-oriented, respectively. The car-oriented mean-field theory yields the exact fundamental diagram for the model with maximum velocity whereas in the site-oriented approach one has to take into account correlations between nearest-neighbour sites. Going beyond mean-field using the so-called -cluster approach our results for are in excellent agreement with numerical simulations. We also present a modified cellular automaton which is closely related to a two-dimensional dimer model.
Keywords
Cite
@article{arxiv.cond-mat/9511037,
title = {Cellular Automata For Traffic Flow: Analytical Results},
author = {Andreas Schadschneider and Michael Schreckenberg},
journal= {arXiv preprint arXiv:cond-mat/9511037},
year = {2007}
}
Comments
Latex, uses mprocl.tex macro-package (available from xxx.lanl.gov), 5 pages with 4 ps-figures to appear in the proceedings of the workshop "Traffic and Granular Flow"