  We investigate a probabilistic cellular automaton model which has been
introduced recently. This model describes single-lane traffic flow on a ring
and generalizes the asymmetric exclusion process models. We study the
equilibrium properties and calculate the so-called fundamental diagrams (flow
vs.\ density) for parallel dynamics. This is done numerically by computer
simulations of the model and by means of an improved mean-field approximation
which takes into account short-range correlations. For cars with maximum
velocity 1 the simplest non-trivial approximation gives the exact result. For
higher velocities the analytical results, obtained by iterated application of
the approximation scheme, are in excellent agreement with the numerical
simulations.
