Estimating queues at signalized intersections: Value of location and time data from instrumented vehicles

Vehicles instrumented with location tracking and wireless communication technologies (i.e., the so called probe vehicles) can serve as sensors for monitoring traffic conditions on transportation links. This paper is focused on estimating queue lengths in real-time at a signalized intersection approach based on the location and time data from probe vehicles that may constitute a given percentage of the total traffic. The paper also addresses the evaluation of the accuracy of such estimates. Using a virtual queuing model and conditional probability distributions, new expressions are derived for the variance of the estimates to understand how accuracy is affected by the percentage of probes in the traffic stream and by the type of information collected, which include (i) location of probes in the queue and (ii) both the location of probes and the times/instances at which they join the back-of-the queue. Numerical examples are presented to compare and contrast the accuracies of these two cases. The findings and the formulation presented in this paper could be used in evaluating and designing a traffic monitoring system that relies on probe vehicle data for queue length estimation at signalized intersections.