We study the traffic states and jams induced by a slowdown of vehicles in a single lane highway. We use an extended one of the optimal velocity model to take into account the slowdown in a section of highway. The fundamental (flow-density) diagram is calculated. The flow (current) increases...

We study the traffic states and jams induced by a slowdown of vehicles in a single-lane highway. The two-stage optimal velocity model is used in which the optimal velocity function has two turning points. The fundamental (flow-density) diagrams are calculated. At low density, the flow (current)...

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...

A mean-field model is presented to mimic the pedestrian channel flow with a bottleneck. The pedestrian flow is described by the mean-field rate equation on the square lattice. The dynamical transition from the free flow to the choking flow is studied by carrying out a numerical simulation for...

We study the effect of gravitational force upon traffic flow on a highway with sag, uphill, and downhill. We extend the optimal velocity model to take into account the gravitational force which acts on vehicles as an external force. We study the traffic states and jamming transitions induced by...

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...

We study the behavior of a recurrent bus on a circular route with many bus stops. We present the basic model determining the recurrent time (one period) on each bus stop. The recurrent times on M bus stops are given by M simultaneous nonlinear equations. It is found that the dynamical phase...

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...