A stochastic dynamic model for vehicle time headways

In the existing literature, vehicle time headway is usually modelled by a univariate statistical distribution, without involving any interaction among the surrounding vehicles. This paper develops a stochastic time headway model to capture drivers’ dynamic interaction with the surrounding vehicles, with consideration of the overall traffic environment and individual drivers’ travelling variation, termed gamma auto-regressive mixture (GARM) model for time headways. The proposed GARM model consists of three components, i.e. (a) a mixture model that probabilistically sorts vehicles into different groups based on their travelling behaviour; (b) a dynamic relationship that characterises how the time headway of a vehicle is related to its lead vehicles; and (c) a non-Gaussian statistical distribution, gamma distribution, that describes the variation of individual headways. The GARM model is then applied at two sites to test serial independence hypothesis. The statistical tests show strong evidence that for tightly-spaced traffic, time headways exhibit serial correlations.