Deterministic spontaneous appearance of traffic jams in slightly inhomogeneous traffic flow.

Abstract

This paper shows, based on numerical investigations of the kinetic model of traffic flow, what a process of a formulation of a traffic jam shows qualitatively new peculiarities seen in a slightly inhomogeneous traffic flow. A traffic jam on a highway can spontaneously appear in a deterministic way; i.e., even if fluctuations in traffic flow are negligible. This effect may be usual for a highway, where traffic flow is always slightly inhomogeneous due to entering traffic to on-ramps and leaving traffic to off-ramps. Such deterministic self-formation of traffic jams is caused by the local breakdown effect, which results in a dynamical local restructuring. Summarizing the results of this article along with two related studies, the whole possible range of density can be divided into four regions: (1) a stable state of traffic flow where any short-time perturbations fade in time; (2) a metastable state, where traffic jams can appear if localized fluctuations occur whose amplitudes exceed the critical value; (3) an unstable state where complex nonhomogeneous nonstationary structures that cover the whole road are formed; and (4) a metastable state where anticlusters and local dipole layers can be formed if localized fluctuations occur whose amplitudes exceed the critical value.