Sampled Trajectory Data-Driven Method of Cycle-Based Volume Estimation for Signalized Intersections by Hybridizing Shockwave Theory and Probability Distribution

Abstract

The cycle-based volume is critical for traffic state estimation and signal control optimization at signalized intersections. Traditional volume estimation mainly depends on fixed detectors represented by loop detectors, but limited spatial coverage and detection failure are also prominent. With the development of vehicle positioning, smartphone-based navigation, and connected-vehicle technologies, massive high-resolution trajectory data have recently become available, which can provide rich and timely information on the traffic arrival and departure processes at signalized intersections. Hence, the studies utilizing trajectory data for estimating the queue length and traffic volume at intersections has received increasing attention in the past few years. However, the most existing studies have demanded a comparatively high penetration rate and adopted site-specific assumptions for unsteady arrival patterns. In contrast, this paper solely used trajectory data for cycle-based flow estimation through a generic hybrid method that combined a probabilistic model and shockwave theory to maximize the utilization of limited captured trajectories, especially under a low penetration rate. In this method, within each cycle, the volume of stopped vehicles is estimated based on the shockwave theory, while the volume of non-stopped vehicles is modeled as a parameter estimation problem of a time-dependent constrained Poisson distribution, where the time headway correspondingly obeys an M3 distribution. The cycle-based volume is solved by a maximum likelihood estimation using an expectation-maximization procedure. An empirical case study was conducted with various signal timing schemes and the results showed satisfactory robustness with an accuracy of more than 90% under a penetration rate of 7.6%.