EXACT STEADY-STATES OF DISORDERED HOPPING PARTICLE MODELS WITH PARALLEL AND ORDERED SEQUENTIAL DYNAMICS

A one-dimensional driven lattice gas with disorder in the particle hop ping probabilities is considered. It has previously been shown that in the version of the model with random sequential updating, a phase tra nsition occurs from a low-density inhomogeneous phase to a high-densit y congested phase. Here the steady states for both parallel (fully syn chronous) updating and ordered sequential updating are solved exactly. The phase transition is shown to persist in both cases with the criti cal densities being higher than that for random sequential dynamics. T he steady-state velocities are related to the fugacity of a Bose syste m suggesting a principle of minimization of velocity. A generalization of the dynamics, to the case where the hopping probabilities depend o n the number of empty sites in front of the particles, is also solved exactly in the case of parallel updating. The models have natural inte rpretations as simplistic descriptions of traffic flow. The relation t o more sophisticated traffic Bow models is discussed.