Cumulative Flow Diagram Estimation and Prediction Based on Sampled Vehicle Trajectories at Signalized Intersections

Although considerable methods have been developed for the performance evaluation of signalized intersections using sampled vehicle trajectories, most of them aim at estimating a single parameter and cannot describe the entire arrival-departure process of the traffic flow. This significantly constrains the application of these methods for a comprehensive evaluation and efficient optimization of signalized intersections. In this paper, we propose a cumulative flow diagram (CFD) estimation and prediction method using sampled vehicle trajectories. It can be used to calculate multiple performance measures--traffic volume, queue length, average delay, and total delay--based on the estimated CFD for the current signal timing plan. Concurrently, it can be further employed for signal control optimization based on the predicted CFDs for candidate signal timing plans. The core idea of the proposed method is to generate the cumulative arrival curve based on the arrival characteristics of the sampled vehicles, and then fit the queue leaving points to obtain the cumulative departure curve. Thereby, given the current or any candidate signal timing plan, we can estimate or predict the CFDs by updating the sampled vehicle arrivals. The proposed method is evaluated using both simulation and empirical data. The simulation results yield that the average estimation error of the four performance measures is 10.3% under a real-world level penetration rate of 10%. Meanwhile, similar accuracies are achieved for the CFD prediction. The empirical results show that under a penetration rate of 8.6%, the estimation errors of the traffic volume and queue length are 2.7% and 3.3%, respectively.