Four headway models of increasing generality are considered from three points of view. We discuss (i) the value of the models for use as arrival processes in stochastic model building, (ii) some traffic situations where it is known from theoretical considerations, that the models are appropriate, and (iii) empirical evidence to support the models. It is shown that the two most general models have a sound rationale from viewpoints (ii) and (iii) and thus offer a realistic arrival assumption for stochastic modelling. Also, it is shown in two worked problems that these general models do not lead to mathematical difficulties when used as arrival processes. We conclude that these models offer a balanced compromise between realism and tractability for the stochastic model builder.
Abstract