Stochastic master-equation approach to aggregation in freeway traffic

Abstract

In analogy to the usual aggregation phenomena, such as the formation of liquid droplets in a supersaturated vapor, the nucleation, growth, and condensation of car clusters are considered in a one-lane freeway traffic flow model. The clustering behavior (known as congestion) in an initially homogeneous traffic stream is described by a master equation. The construction of the stochastic equation is given as well as its relationship to other dynamical models. Numerical experiments in heavy traffic with well-explained transition probabilities show the transition from the initial free particle situation (free jet of vehicles) to the final congested cluster state, where one big aggregate of cars is formed. The results are presented analytically in dependence of the stable cluster size from car concentration and numerically as stochastic trajectories.