Exact stationary state for a deterministic high speed traffic model with open boundaries
Abstract
An exact solution for a high speed deterministic traffic model with open boundaries and synchronous update rule is presented. Because of the strong correlations in the model, the qualitative structure of the stationary state can be described for general values of the maximum speed. It is shown in the case of v_{\rm max}=2 that a detailed analysis of this structure leads to an exact solution. Explicit expressions for the stationary state probabilities are given in terms of products of 24\times 24 matrices. From this solution an exact expression for the correlation length is derived.