Why Does Traffic Jam Acts Universally?

Abstract

The theoretical reason for the existence of universal features of traffic jams forming in various places and with different number of cars on highways is provided using exact solutions of a mathematical model for traffic flow, the Optimal Velocity (OV) model. The OV model well reproduces real traffic data of jams in several aspects, such as the critical density of jam formation, the velocity of a jam cluster, etc. where each value is almost universal. The OV model with Heaviside step function as OV-function has essentially the same properties as a realistic OV model. Recently, we have obtained exact solutions of jam flow in the model for an arbitrary number of cars N > 3 and car-density. In the solutions, the dependence on N and the density are exponentially reduced for \(N \rightarrow \infty \). This means that the properties of jams with more than about ten cars are almost the same as that of an infinite jam. This result is originated in the fact that the model is built mathematically based on the concept that traffic flow is a non-equilibrium dissipative system. This explains the universality of jam flow.