An Integral Equation for the Semi-Poisson Headway Distribution Model

The semi-Poisson headway distribution model introduced by Buckley [“Road Traffic Headway Distributions,” Proc. Australian Road Research Board 1, 153–183 (1962); “A semi-Poisson Model of Traffic Flow,” Trans. Sci. 2, 107–133 (1968)] involves the decomposition of the headway distribution into components which can be regarded as corresponding to “free” and “constrained” vehicles. This model is reformulated here in order to derive an integral equation by means of which the components can be calculated directly from the observed headway distribution, thereby avoiding an arbitrary parametric representation of the constrained distribution component. The model is applied to traffic observations under high flow conditions from a British and an American freeway. The model results are interpreted as an indication of whether the freeway lane is operating at its maximum possible capacity. It is found that one lane of the British freeway had a flow very near the maximum given by the model, but the greatest observed flow on the American freeway was still less than the calculated maximum.