The rapid development of connected vehicle technology and the emergence of ride-hailing services have enabled the collection of a tremendous amount of probe vehicle trajectory data. Due to the large scale, the trajectory data have become a potential substitute for the widely used fixed-location sensors in terms of the performance measures of transportation networks. Specifically, for traffic volume and queue length estimation, most of the trajectory data based methods in the existing literature either require high market penetration of the probe vehicles to identify the shockwave or require the prior information about the queue length distribution and the penetration rate, which may not be feasible in the real world. To overcome the limitations of the existing methods, this paper proposes a series of novel methods based on probability theory. By exploiting the stopping positions of the probe vehicles in the queues, the proposed methods try to establish and solve a single-variable equation for the penetration rate of the probe vehicles. Once the penetration rate is obtained, it can be used to project the total queue length and the total traffic volume. The validation results using both simulation data and real-world data show that the methods would be accurate enough for assistance in performance measures and traffic signal control at intersections, even when the penetration rate of the probe vehicles is very low.
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