An improved mean-field analysis of cellular automata models of single-lane vehicular traffic is proposed, well suited for models with inhomogeneous stationary states and able to capture the essential properties of phase separation, e.g. in models with slow-to-start rules.
Abstract
We propose an improved mean-field analysis of cellular automata models of single-lane vehicular traffic. By combining aspects of the Car-Oriented-Mean-Field (COMF) theory and the 2-site cluster method, which have been previously successfully applied to similar models, we aim to capture both short- and long-range correlations more accurately. In contrast to classical mean-field theories, the improved method is well suited for models with inhomogeneous stationary states and able to capture the essential properties of phase separation, e.g. in models with slow-to-start rules. The improved accuracy and new physical insights are illustrated through an application to the VDR model with $v_{\text{max}}=1$.
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