An extended queueing model for vehicles at signalized intersections considering the platoon correlated arrivals

The unpredictability and randomness of traffic arrivals are key contributors to the large variability in the delays experienced by vehicles at signalized intersections. Vehicles traveling between signalized intersections in the urban road networks typically move in platoons due to the fact that they are released at the upstream signalized intersections; however, most traffic queueing models ignore the feature of correlations in traffic flows. To fill this gap, this paper proposes a more flexible traffic queueing model for vehicles at signalized intersections by explicitly taking into account the platoon size and headway correlations between vehicles in a platoon, which can well incorporate a wide range of arrival processes. We derive the time-dependent joint distribution of queue length, arrival phase, and signal state, which can be used to achieve a more complete quantitative analysis of the dynamics of the vehicle queueing process over the signal state. Mean queue performance metrics, such as mean queue length and mean delay, are obtained. Traffic load intensity and the queue length of vehicles at any given stage within a signal cycle are also analytically determined. The various queueing performance metrics obtained in this study can provide a good understanding of the queueing process of vehicles arriving at signalized intersections in the platoon correlated arrivals. Our results in numerical experiments confirm that the feature of correlations in traffic flows cannot be ignored in traffic flow modeling because, given the same traffic volume, the queueing process of vehicles at signalized intersections will be further determined by arrival modes, platoon sizes, and correlated arrival characteristics.