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Exact solution of a cellular automaton for traffic

Item Type:Article
Title:Exact solution of a cellular automaton for traffic
Creators Name:Evans, M.R. and Rajewsky, N. and Speer, E.R.
Abstract:We present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions, e.g., cars can enter and leave a part of a highway with certain probabilities. The model studied is the asymmetric exclusion process (ASEP) with simultaneous updating of all sites. It is equivalent to a special case (v max=1) of the Nagel–Schreckenberg model for highway traffic, which has found many applications in real-time traffic simulations. The simultaneous updating induces additional strong short-range correlations compared to other updating schemes. The stationary state is written in terms of a matrix product solution. The corresponding algebra, which expresses a system-size recursion relation for the weights of the configurations, is quartic, in contrast to previous cases, in which the algebra is quadratic. We derive the phase diagram and compute various properties such as density profiles, two-point functions, and the fluctuations in the number of particles (cars) in the system. The current and the density profiles can be mapped onto the ASEP with other time-discrete updating procedures. Through use of this mapping, our results also give new results for these models.
Keywords:Asymmetric Exclusion Process, Boundary-Induced Phase Transitions, Steady State, Matrix Product Ansatz, Cellular Automaton
Source:Journal of Statistical Physics
ISSN:0022-4715
Publisher:Springer (Germany)
Volume:95
Number:1-2
Page Range:45-96
Date:April 1999
Official Publication:https://doi.org/10.1023/A:1004521326456

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