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...

A kinetic clustering of cars is analyzed using a limiting procedure and a reductive perturbation method. By using the limiting procedure, the difference–difference equation to describe the clustering is obtained. We derive the coarse-grained equation describing the hydrodynamic mode, using the...

We study the bus delay and the passenger behaviour on a bus route by the use of the bus route model. The time-headway model of the bus route is extended to take into account the passengers on buses. The bus delay relates with the number of passengers on buses. It is shown that the dynamical...

In this paper, we consider a time-headway model, introduced in Ref. [Physica A 296 (2001) 320], for buses on a bus route. By including a simple no-passing rule, we are able to enumerate and study the unstable modes of a homogeneous system. We then discuss the application of the model to...