Phase transition in a traffic model with passing

We investigate a traffic model in which cars either move freely with quench ed intrinsic velocities or belong to clusters formed behind slower cars. In each cluster, the next-to-leading car is allowed to pass and resume free m otion. The model undergoes a phase transition from a disordered phase for t he high passing rate to a jammed phase for the low rate. In the disordered phase, the cluster size distribution decays exponentially in the large size limit. In the jammed phase, the distribution of finite clusters is indepen dent on the passing rate, but it accounts only fora fraction of all cars; t he "excessive" cars form an infinite cluster moving with the smallest veloc ity. Mean-field equations, describing the model in the framework of Maxwell approximation, correctly predict the existence of phase transition and ade quately describe the disordered phase; properties of the jammed phase are s tudied numerically.