Distribution models for start-up lost time and effective departure flow rate

Due to its importance, lots of investigations had been carried out in the last four decades to study the relationship between phase duration and vehicle departure amount. In this paper, we aim to build appropriate distribution models for start-up lost time and effective departure flow rate, by considering their relations with the frequently mentioned departure headway distributions. The motivation behind is that distribution models could provide richer information than the conventional mean value models and thus better serve the need of traffic simulation and signal timing planning. To reach this goal, we first check empirical data collected in Beijing, China. Tests show that the departure headways at each position in a discharging queue are very weakly dependent or almost independent. Based on this new finding, two distribution models are proposed for start-up lost time and effective flow rate, respectively. We also examine the dependences of departure headways that are generated by three popular traffic simulation software: VISSIM, PARAMICS and TransModeler. Results suggest that in VISSIM, the departure headways at different positions are almost deterministically dependent and may not be in accordance with empirical observations. Finally, we discuss how the dependence of departure headways may influence traffic simulation and signal timing planning.