Cycle-by-Cycle Estimation of Queue Length at Signalized Intersections Using Spatially Sparse Connected Vehicle Trajectories

Queue length is one of the most commonly used indicators to evaluate traffic operation at signalized intersections. Many studies aim to estimate queue length using trajectory data, but this remains a challenge with spatially sparse trajectories. This paper introduces a probabilistic-based method for cycle-by-cycle estimation of queue length distribution and the point estimate in closed form using connected vehicle (CV) trajectories. The method is applicable to isolated signalized intersections with under-saturated traffic. It works well in a low CV penetration rate environment by exploiting the trajectories of both queued and non-queued CVs. Vehicle arrival rates and CV penetration rates are first estimated to capture the vehicle arrival pattern within a time of day (TOD) using the maximum likelihood estimation approach. The closed forms of the probability distribution of queue length are derived for each cycle, which are attractive for applications such as adaptive signal timing considering traffic uncertainty. The queue length with the highest probability is taken as the point estimate. Numerical and empirical studies demonstrate that the proposed method outperforms the benchmark method in estimating CV penetration rates, particularly at low penetration rates. In term of queue length estimation, the proposed method is also superior to existing methods in most scenarios and is especially effective for cycles with observed trajectories. Sensitivity analysis reveals that the method is robust to different demand levels, signal timings, and variability in arrival patterns with under-saturated traffic. Additionally, the suggested requirements for the number of collected trajectories are investigated to provide practical guidance.