Structure stability of congestion in traffic dynamics

Abstract

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.