Traffic Volume Estimation for both Undersaturated and Oversaturated Signalized Intersections with Stopbar Location Estimation Using Trajectory Data

Abstract

We propose an estimator for traffic volumes in signalized intersections using only sparse trajectory data. Each pair of observed trajectories defines a statistical event, from which traffic volume is to be inferred. The interaction between trajectory stop distances, arrival speeds and signal plan define different classes of statistical events, with distinct likelihood expressions. Contrary to recent approaches found in the literature, our method can address oversaturation and residual queues. We also propose a method to estimate stopbar location, crucial to properly estimate stop distances and queue lengths. Arrivals are assumed to be negative exponential, and the method is compatible with any kind of control. The signal plan is assumed to be known, but an estimated signal plan could also be used. The estimation is formulated as a maximum marginal likelihood problem. We show the problem globally concave and thus optimally solvable by standard gradient-based methods. The estimator is first validated by an event-based LWR simulation, suppressing any measurement errors from trajectories and uncertainty from driver behavior. The estimator is found to consistently show a bias below 10% in low-penetration-rate situations, when the $v/c$ ratio is medium to high. Finally, the estimator is tested in a real-world intersection set by the authors in Beijing, China, obtaining a bias of similar of magnitude.

Roger Lloret-Batlle

Assistant Professor of Transportation and Logistics

Market Design, Container Terminal Operations, Urban Logistics, Statistics, Traffic Signal Control