Propagation of perturbations in dense traffic flow: a model and its implications

A model of the evolution of speed perturbations in dense traffic flow is presented in this work. Traffic volume is assumed to be at capacity and a given vehicle undergoes a temporary speed drop. This speed drop may propagate through the traffic flow until it is either dissipated or causes the stoppage of the traffic flow. The two events are random and occur with a certain probability. The proposed model leads to a set of recurrence equations for the speed drop and its duration. The simulation of those equations allows the estimation of the normalization probability, that is, the probability that the perturbation vanishes. An analytical approximation for the normalization probability is also proposed. The approximation is based on a result from Brownian motion theory. The agreement with the simulation results is fairly good given the simplicity of the approximation. The model and its analytical approximation allows one to conjecture which could be the most important parameters that determine the evolution of the perturbation. The implications of this conjecture are commented and the assumptions of the model are contrasted with related work.