The asymptotic steady states of deterministic one-dimensional traffic flow models

The asymptotic steady state of deterministic Nagel-Schreckenberg (NS) traffic flow cellular automaton (CA) model for high-velocity cars (upsilon(max) = M > 1) is studied. It is shown that the fundamental diagram, i.e., the relationship between the average car velocity and the car density, of the NS model in which the velocity of a car may increase by at most one unit per time step is exactly the same as that of the Fukui-Ishibashi (FI) traffic flow CA model in which a car may increase its velocity abruptly from zero to M or the maximum velocity allowed by the empty spacings ahead in one time step. This implies that for both gradual and abrupt accelerations, the self-organization of cars gives the same asymptotic behavior in one-dimensional traffic flow models. (C) 2000 Elsevier Science B.V. All rights reserved.