Cycle-Based End of Queue Estimation at Signalized Intersections Using Low-Penetration-Rate Vehicle Trajectories

Queue length is a crucial measure of intersection performance. Probe vehicles (PVs) with advanced sensors are capable of recording vehicle trajectories that can be used to estimate queue length, a technique of which has received considerable attention in the past decade. Noticeably, this technique usually requires high PV penetration rates (e.g., above 25%) in order to ensure estimation accuracy. Though the PVs are expected to increase, their penetration rate will still remain relatively low in the near future. Meanwhile, the initial queue length is another important factor that directly relates to queue dynamics at each cycle. However, most of the studies failed to adequately account for the effect of the initial queue on cyclic queue length estimation. To address the above challenges, this paper proposes a cycle-based end of queue estimation method using sampled vehicle trajectory data under relatively low penetration rates. Two major steps are involved: first, vehicle arrival process is modeled as a certain distribution in line with traffic conditions and an expectation maximum (EM) procedure is employed to estimate the arrival rate of each cycle; then, both ends of the queue and initial queue are estimated at each cycle based on shockwave theory. Microscopic traffic simulator VISSIM is utilized to examine the performance of the method. The experimental results reveal that the cycle-based end of the queue can be estimated with desirable accuracy in different scenarios, e.g., undersaturated, oversaturated, and queue spillback conditions. The comparison with the state-of-the-art methods further helps to verify the advantage of the method, especially under low-penetration-rate conditions.