Shock Wave Approach for Estimating Queue Length at Signalized Intersections by Fusing Data from Point and Mobile Sensors

With the growth in traffic sensing data, the measurement of levels of service such as queue length at intersections in real time has been receiving considerable attention. This paper examines how to estimate real-time cycle-by-cycle queue length at signalized intersections by using the data of an upstream point sensor and the traveling trajectory of a probe vehicle observed by a mobile sensor. Three cases are based on the space relationships between the rear of a queue, the point sensor location, and the vehicle stop or start-up point. When the data of point sensors and mobile sensors are fused, critical break points can be identified to indicate several key states of the queue formation and dissipation. Estimation models of the maximum queue length, based on the Lighthill-Whitham-Richards theory, are proposed for the three cases. The presented algorithm does not impose any restrictions on the traffic condition (i.e., oversaturated and undersaturated conditions). The methodology is applied to ground truth data observed from the field in Shanghai, China. The mean average percentage errors of the first two cases are 11.60% and 9.98%, which means the models for the cases have reasonable estimating accuracy. The mean average percentage error of the model for the third case is 26.40%, indicating that the performance degrades but still has acceptable accuracy. Limitations on application of the proposed models and directions for future research are discussed.