Modelling Vehicular Traffic Using the Discrete Time Markovian Arrival Process

A discrete time Markovian Arrival Process which models platooned arrivals in road traffic is presented. It takes into account the bunching of traffic and correlation between headways. Several examples involving different types of probability distributions for interplatoon and intraplatoon headways, and platoon sizes are presented. An application of the MAP to a traffic signal queue is carried out and a numerical example is presented. The example confirmed the intuition that ignoring correlation in the arrival process results in the underestimation of performance measures such as the mean queue length, especially at high traffic intensities.