Queue profile estimation at a signalized intersection by exploiting the spatiotemporal propagation of shockwaves

Queues at signalized intersections bring interruptions to the smooth movement of vehicles and slow down the traffic in urban road networks. Although queue length estimation has attracted much attention in the literature, recent studies indicate increasing interest in queue profile estimation, which is crucial to many extensive analysis. In this research, we propose an innovative approach to estimating the queue profile at a signalized intersection by exploiting the spatiotemporal propagation of shockwaves. The input to our model includes locations and speeds of probe vehicles on a signalized link and the starting time of red in signal cycles. The model then outputs the corresponding queue profile. We first classify data points of probe vehicles into moving and stopped states. We then develop an integer programming model with a set of novel constraints to estimate the queue profile, which conforms to the spatiotemporal propagation of shockwaves. Unlike existing studies that use triangles or polygons to approximate queue profiles, our model allows us to detect queue profiles of any shape. Our model can also categorize cycles into different types and utilize data in cycles of the same type, which helps to construct the queue profile. We validate our model using both simulated and real data. Results show that our model is capable of producing satisfactory results even when the penetration rate is as low as 10–20% and the sampling interval is as high as 20–30 seconds.