Analytical approaches to CA for traffic flow: Approximations and exact solutions

Details Analytical approaches to CA for traffic flow: Approximations and exact solutions Analytical approaches to CA for traffic flow: Approximations and exact solutions

1997-11-27

arxiv.org/abs/cond-mat/9711296v1

Physics

Condensed Matter

Statistical Mechanics

15 pages, 10 postscript figures, to be published in the Proceedings of the conference "Traffic and Granular Flow '97", Duisbur

Scientific paper

Cellular automata have turned out to be important tools for the simulation of traffic flow. They are designed for an efficient impletmentation on the computer, but hard to treat analytically. Here we discuss several approaches for an analytical description of the Nagel-Schreckenberg (NaSch) model and its variants. These methods yield the exact solution for the special case $\vm=1$ of the NaSch model and are good approximations for higher values of the velocity ($\vm > 1$). We discuss the validity of these approximations and the conclusions for the underlying physics that can be drawn from the success or failure of the approximation.

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