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Garden of Eden states in traffic models

Andreas Schadschneider·Michael Schreckenberg
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Abstract

We investigate the allowed configurations in the stationary state of the cellular automaton model for single-lane traffic. It is found that certain states in the configuration space can not be reached if one uses parallel dynamics. These so-called Garden of Eden (GoE) states do not exist for random-sequential dynamics and are responsible for the strong short-ranged correlations found in parallel dynamics. By eliminating the GoE states we obtain a simple and effective approximative description of the model. For $v_{max}=1$ the exact solution is recovered. For $v_{max}=2$ this elimination leads to much higher values of the flux compared to the mean-field result which are in good agreement with Monte Carlo simulations.

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Andreas Schadschneider, Michael Schreckenberg. 1998-01-08. Garden of Eden states in traffic models. https://arxiv.org/abs/cond-mat/9801061

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