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...

The effect of accelerating stepwise on the jamming transition is investigated in the extended car-following model. The optimal velocity function is modified to take into account accelerating stepwise vehicles. It is shown that the multiple phase transitions occur on varying the car density. The...

Phase transition and critical phenomenon are investigated in high-dimensional traffic flow numerically and analytically. The two-dimensional lattice traffic model is extended to the three- and d-dimensional traffic flows. It is shown that the phase transition among the freely moving phase, the...

Traffic flows on crossing roads with an information board installed at the intersection have been simulated by a cellular automaton model. In the model, drivers have to enter the road with a shorter trip-time indicated on the information board, by making a turn at the intersection if necessary....

We present the thermodynamic theory describing the phase transition and critical phenomenon in traffic flow. We derive the time-dependent Ginzburg–Landau (TDGL) equation through the modified Korteweg–de Vries (KdV) equation from the car following model, using the perturbation method. We find...

Continuum models of traffic are proposed to describe the jamming transition in traffic flow on a highway. They are the simplified versions of the hydrodynamic model of traffic. Two continuum models are presented: one is described by the partial differential equations and the other is the...

Phase transitions and critical phenomena are investigated in the two-dimensional traffic flow on the triangular lattice numerically and analytically. The two-dimensional traffic model on the square lattice is extended to the traffic flow on the triangular lattice where the three roads cross on a...

Recent empirical observations show that traffic flow is related to various phase transitions, especially at bottlenecks. This paper studies traffic flow induced by an on-ramp in the Nagel–Schreckenberg model. It is shown that when considering the situation that vehicles on main road and...

In this paper, we study the phase transition from free flow to synchronized flow. We carry out the simulations under the speed limit condition with a car-following model, the “full velocity difference model.” We find that the transition is second-order if the speed limit region is long and...

A power-law model of traffic is proposed to extend the optimal velocity model of traffic. The phase transition and critical phenomenon are investigated by computer simulation. It is shown that the phase transition among the freely moving phase, the coexisting phase, and the homogeneous congested...