  A recently introduced cellular automaton model for the description of traffic
flow is investigated. It generalises asymmetric exclusion models which have
attracted a lot of interest in the past. We calculate the so-called fundamental
diagram (flow vs.\ density) for parallel dynamics using an improved mean-field
approximation which takes into account short-range correlations. For maximum
velocity 1 we find that the simplest non-trivial of these approximations gives
already the exact result. For higher velocities our results are in excellent
agreement with numerical data.
