Maximum Likelihood Estimation of Probe Vehicle Penetration Rates and Queue Length Distributions From Probe Vehicle Data

Queue length estimation plays an important role in traffic signal control and performance measures of signalized intersections. Traditionally, queue lengths are estimated by applying the shockwave theory to loop detector data. In recent years, the tremendous amount of vehicle trajectory data collected from probe vehicles such as ride-hailing vehicles and connected vehicles provides an alternative approach to queue length estimation. To estimate queue lengths cycle by cycle, many existing methods require the knowledge of the probe vehicle penetration rate and queue length distribution. However, the estimation of the two parameters has not been well studied. This paper proposes a maximum likelihood estimation method that can estimate the parameters from historical probe vehicle data. The maximum likelihood estimation problem is solved by the expectation-maximization (EM) algorithm iteratively. Validation results show that the proposed method could estimate the parameters accurately and thus enable the existing methods to estimate queue lengths cycle by cycle.