A Matrix Completion Method for Cycle-based Traffic Volume Estimation Using Sampled Trajectory Data

Abstract

Cycle-based volume can describe the fluctuation of traffic demand in a more sophisticated manner, which is helpful for performance evaluation and optimization of signalized intersections. Solely using sampled vehicle trajectory data for traffic volume estimation has received increasing attention recently. However, most existing methods commonly rely on historical data or site-specific vehicle arrival distributions. This study proposes a data-driven method for cycle-based volume estimation at signalized intersections. Using the sampled trajectory data, the cyclic vehicle arrival is represented as an arrival flow rate vector to discretize the continuous arrival flow. So for a TOD (time-of-day) period, an incomplete arrival rate matrix can be constructed with a rasterization standardization step to ensure equal sizes of the arrival rate vector for each cycle. The cycle-based volume estimation problem is then transformed into a matrix completion problem, and solved through the Singular Value Thresholding (SVT) algorithm. The proposed method is evaluated through an empirical case and two simulation cases. Empirical case results show that given a penetration rate of 8.4%, the proposed method can reach 5.7% for hourly volume estimation and 17.6% for cycle-based volume estimation. Even under a penetration rate of 3.4%, it shows better robustness than three existing methods, A simulation case is done to explore the sensitivity of the proposed method to the degree of saturation, the number of lanes and the penetration rate, while another simulation case demonstrates the applicability of the proposed method in large-scale network, which is also one advantage of the proposed data-driven approach.