Kinetic clustering and jamming transitions in a car-following model for bus route

The car-following model of traffic is extended to mimic bus behavior in the bus route. We study the phase transitions and bunching in the bus route model by both simulation and linear stability analysis. It is found that the jamming transitions among an inhomogeneous bunching phase, the homogeneous free traffic, the coexisting phase, and the homogeneous congested traffic phase occur with increasing density. It is shown that the transition lines obtained from simulation are consistent with those from the linear stability analysis.