Start-Up and Acceleration Profile for Protected Left-Turn Vehicles at Signalized Intersections

The law of start-up, acceleration profile and leave-out for queuing vehicles at signal intersections is a fundamental question for the queuing theory, traffic simulation and etc in traffic engineering. This paper investigates the vehicular flow at two protected left-turns by video cameras installed at signal intersections, and checks the accuracy of speed processing software. Based on the statistical analysis and the method of curve fitting, the research team establishes the model of start-up and speed-time profile for the queuing vehicles in the protected left-turns at signal intersections. Then the leave-out time of vehicles is calculated based on the established formulas in these models, which is consistent with the observed leave-out time of vehicles by the video. The developed models proved to be accurate. The paper concludes that the queuing vehicles follow by a linear start after the green light, and the speed-time profile indicates an “S” shape from vehicles starting to reach the stable saturation flow. The speed and the queue sequence of first vehicle of saturation flow are different at different intersections, but the law of start-up of vehicles is the same: The same reaction time for the first vehicle and the same linear start-time interval for the adjacent vehicle in the queue. The relationship of leave-out time and the queue sequence of vehicle is nonlinear before the saturation flow. According to the models developed in this paper, the queue sequence of first vehicle of saturation flow and the law of leave-out time of vehicles can be calculated accurately, which is the fundamental for the queuing theory and the traffic simulation.