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...

We study the dynamical behavior of shuttle buses on a route where N buses shuttle between an origin and a destination repeatedly. We present the dynamic model of shuttle buses to take into account the speed control depending on time headway between buses. The model is described by N-dimensional...

We study the dynamical behavior of counter traffic flow through a sequence of signals (traffic lights) controlled by a phase shift. There are two lanes for the counter traffic flow: the first lane is for east-bound vehicles and the second lane is for west-bound vehicles. The green-wave strategy...

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 dynamical behavior of a cyclic bus on a circular route with many bus stops, when the cyclic bus passes some bus stops without stopping to retrieve the delay. The recurrent time (one period) is described in terms of a piecewise nonlinear map. It is found that the cyclic bus exhibits...

We study the traffic states and jamming transitions induced by a bus (slow car) in a two-lane traffic of cars. We use the dynamic model which is an extended one of the optimal velocity model to take into account the lane changing. The fundamental (flow-density) diagram is presented. 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...