CHINESE JOURNAL OF PHYSICS VOL. 39, NO. 5 OCTOBER 2001

Traffic Flow in a 1D Cellular Automaton Model with Open Boundaries

A. Benyoussef¹, N. Boccara^2,3, H. Chakib¹ and H. Ez-Zahraouy<sup>1,4

1</sup>Laboratoire de Magnétisme et Physique des Hautes Énergies,

Département de Physique, Faculté des Sciences,
B.P. 1014, Rabat, Morocco.
²DRECAM/SPEC, Centre d'Étude de Saclay, 91191 Gif-sur-Yvette Cedex, France.
³Department of Physics, University of Illinois, Chicago, IL 60607-7059, U.S.A.
⁴Abdus Salam International Centre For Theoretical Physics, P.O.Box 586, 34100 Trieste, Italy.
(Received February 2, 2001)

We have studied the open boundary cellular automaton models for the highway one-line traffic flow by using the mean field approximation and simulations. Our contribution focuses on the effect of braking probability (P) and a maximum velocity $(v_{\max})$ on the density, flow and average velocity of cars moving in the middle of the road. The phase diagram is presented for $v_{\max}=1$ and $v_{\max}>1$. The maximal flow phase does not occur for $v_{\max}>1$, in contrast with the case $v_{\max}=1$ where this phase appears for $p\neq 0$. The first-order transition arises at $\alpha =\beta (\alpha <\beta)$ for $v_{\max}=1\ (v_{\max}>1)$, where $\alpha$ and $\beta$ denote, respectively, the inside rate and the outside rate. The mean field approximation gives a good results in comparison with simulations for $v_{\max}>1$, while for $v_{\max}=1$, the phase diagram obtained from the simulations is predicted by the mean field approximation when $p\to 1$.

PACS. 02.50.-r - Probability theory, stochastic processes, and statistics. Brownian motion.

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