Road traffic headway distributions

The importance of the study of road traffic headways is discussed and a review is made of the literature relating to their probability distribution. A semi random model of traffic flow is postulated and hence a probability density function and moment generating function for headways is derived. This probability density function and certain other functions are compared with a limited amount of headway frequency data observed on an American freeway under conditions of high flow, and it is concluded that the empirical data is consistent with the semi random model. The model is shown to be related to various other theories of road traffic, and amenable to simulation on a digital electronic computer. The occurrence of negatively auto correlated headways for road traffic at very high volumes is reported and its possible importance discussed. A headway probability function is derived for a varying random model which is postulated for road traffic under certain conditions, and for air traffic (A).