Katsuya Hasebe

Structure stability of congestion in traffic dynamics

In our previous paper, we proposed a dynamical model, whose equation of motion is expressed as a second order differential equation. This model generates traffic congestion spontaneously. In this paper we study the characteristic properties of the traffic congestion in our model, especially the organization process and the stability of the structure of congestion. It turns out that these phenomena are well described by plotting motions of vehicles in the phase space of velocity and headway. The most remarkable feature is the universality of “the hysterisis loop” in this phase space, which is observed in the final stage of the congestion organization. This loop is understood as a limit cycle of the dynamical system. This universality guarantees the stability of total cluster size.

Metastability in the formation of an experimental traffic jam

We show detailed data about the process of jam formation in a traffic experiment on a circuit without any bottlenecks. The experiment was carried out using a circular road on a flat ground. At the initial stage, vehicles are running homogeneously distributed on the circuit with the same velocity, but roughly 10 min later a traffic jam emerges spontaneously on the circuit. In the process of the jam formation, we found a homogeneous flow with large velocity is temporarily realized before a jam cluster appears. The instability of such a homogeneous flow is the key to understanding jam formation.

Instability of pedestrian flow in 2D optimal velocity model with attractive interaction

We incorporate an attractive interaction in two-dimensional optimal velocity model and investigate the stability of homogeneous flow. There exists a new type of instability and a new phase appears. We also show the behavior of the flow in each phase by numerical simulations.

Delay of vehicle motion in traffic dynamics

We demonstrate that in the Optimal Velocity Model (OVM) delay times of vehicles coming from the dynamical equation of motion of OVM explain the order of delay times observed in actual traffic flowswithout introducing explicit delay times. This implies that the explicit delay time is not important in contrast to the traditional car following models, in which the explicit delay time was thought to be essential to explain realistic traffic flow. Effective delay times in various cases are estimated: the case of a leader vehicle and its follower, a queue of vehicles controlled by traffic lights and the many-vehicle case of highway traffic flow. The remarkable result is that in most of the situation for which we can make a reasonable definition of an effective delay time, the obtained delay time is of order one second. This agrees with the observed data very well.

Quantum Space-Time

Space-time is quantized so as to obtain a four-dimensional simple cubic lattice. The covariance under Poincare transformation is guaranteed. The particles interact non-locally. The interaction region is spread so as to form a closed (Euclidean) area in the lattice of space-time.

Observation, Theory and Experiment for Freeway Traffic as Physics of Many-Body System

The importance of physical viewpoint for understanding the phenomena of freeway traffic is emphasized using the simulations of a mathematical model and the experiment. The traffic flow is understood as a many-body system of moving particles with the asymmetric interaction and the emergence of jam is the pattern formation as the phase transition of non-equilibrium system by the effect of collective motions.

Exact solutions of differential equations with delay for dissipative systems

Abstract Exact solutions of the first order differential equation with delay are derived. The equation has been introduced as a model of traffic flow. The solution describes the traveling cluster of jam, which is characterized by Jacobis elliptic function. The induced differential-difference equations are related to some soliton systems.

Instability of pedestrian flow in two-dimensional optimal velocity model

A two dimensional optimal velocity model was proposed for the study of pedestrian flow. We investigate the stability of homogeneous flow in the linear approximation and show the phase diagram of the model. We also investigate the behavior of pedestrian flow by numerical simulation in the cases of unidirectional and counter flow. From these results, we present a unified understanding of the properties of pedestrian flow and other related systems.

Optimal Velocity Model and its Applications

We review some aspects of the optimal velocity (OV) model and compare these aspects with those of other car-following models. We also show two applications of the OV model. One is an application to the intelligent transport system, especially how to suppress the emergence of traffic congestion. The other is an application to pedestrian flow. For these purposes, we propose some extensions of the OV model.

Exact Traveling Cluster Solutions of Differential Equations with Delay for a Traffic Flow Model

Exact solutions of the first order differential equation with delay are derived. The equation has been introduced as a model of traffic flow. The solution describes the traveling cluster of jam, which is characterized by Jacobi’s elliptic function. The system is related to some soliton systems.