Effect of car acceleration on traffic flow in 1D stochastic CA model

The one-dimensional (1D) asymmetric simple-exclusion model with parallel update (the deterministic cellular automaton (CA) 184) is extended to take into account acceleration of cars. Velocity and acceleration are assigned to each particle (car). The acceleration of a car is determined by the dynamical equation of motion. The stochastic cellular automaton model mimics the traffic flow on a highway. In congested traffic flow, the properties of traffic jams are studied by computer simulation. The dependence of the propagating velocity of traffic jams upon car acceleration is shown. Also, a simple mean-field theory is given for the congested traffic flow. It is found that the propagating velocity of a traffic jam obtained from simulation agrees with the analytical result for not small values of car acceleration.