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Cellular Automata For Traffic Flow: Analytical Results

Andreas Schadschneider·Michael Schreckenberg
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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 $\vm =1$ 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 $n$-cluster approach our results for $\vm >1$ are in excellent agreement with numerical simulations. We also present a modified cellular automaton which is closely related to a two-dimensional dimer model.

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Andreas Schadschneider, Michael Schreckenberg. 1995-11-07. Cellular Automata For Traffic Flow: Analytical Results. https://arxiv.org/abs/cond-mat/9511037

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