  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.
