A stochastic wave propagation model

We introduce in this paper gap time, the time taken for a following vehicle to travel at its current speed the distance between its head position and the position of the rear of its leading vehicle, as a fundamental parameter for modeling some prominent features of congested traffic, namely the scatter of the fundamental diagram and the growth and decay of traffic disturbances on highways. In the model, traffic waves propagate in a stochastic manner and their speeds are determined by the relative differences between gap times and the reaction times of drivers. The scatter on the fundamental diagram and the growth and decay of perturbations are explained by random fluctuations of gap time and random transitions of traffic states on the fundamental diagram, respectively. Empirical data are used to validate the model and the evaluation shows close correspondence between model predictions and field observations. (c) 2008 Elsevier Ltd. All rights reserved.