Structure and parameters of clusters in traffic flow

The nonlinear theory of the cluster effect in a traffic flow B. S. Kerner and P. Konh\"auser, Phys. Rev. E 48, 2335 (1993), i.e., the effect of the appearance of a region of high density and low average velocity of vehicles in an initially homogeneous flow, is presented. The structures of a stationary moving cluster are derived. It is found that the density, the average velocities of vehicles inside and outside the cluster, and also the velocity of the cluster are the characteristic parameters of the traffic flow. The dependencies of the cluster structure and parameters on the density of vehicles in the initially homogeneous flow and on the length of the road are investigated. It is found that the cluster can appear within regions of density of vehicles which correspond to a stable homogeneous flow. It is shown that an appearance of a localized perturbation, having a finite amplitude, in the stable homogeneous flow can lead to a self-formation of a local cluster of vehicles which is surrounded by the homogeneous traffic flow. The parameters of the local cluster do not depend on the amplitude of this perturbation but only on the parameters of the flow.