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...

We study the unidirectional flow of mobile objects through obstacles on a square lattice. Two models are presented: one is the lattice gas model consisting of translational particles and the other is that of turning particles. Fundamental diagrams for the two models are presented. The traffic...

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...

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...

We study the freezing transition in the counter flow of pedestrians within the channel numerically and analytically. We present the mean-field approximation (MFA) model for the pedestrian counter flow. The model is described in terms of a couple of nonlinear difference equations. The...

A two-lane traffic model is presented to investigate traffic jams induced by a car accident. The model is an extension one of the optimal velocity model taking into account lane changing in the open flow. We study the jammed states and the fine structures of jams. It is shown that there are two...

The effect of partition line on the pedestrian counter flow is investigated under the open boundaries by using the lattice-gas model of biased random walkers. There are two types of walkers without the back step: the one is the walker going to the right and the other is the walker going to the...