Queue length estimation from probe vehicle location and the impacts of sample size

Probe vehicles are increasingly receiving more attention as an alternative means of collecting real-time traffic data needed for system optimization. This paper focuses on real-time estimation of queue lengths from the location information of probe vehicles in a queue at an isolated and undersaturated intersection. The paper also addresses the evaluation of the accuracy of such estimates as a function of the market penetration of probe vehicles. An analytical formulation based on conditional probability distributions is developed for estimating the expected queue length and its variance. It is found that, for the given settings, only the location information of the last probe vehicle in the queue is sufficient for the estimation. Exact expressions for the conditional mean and variance of queue length are derived. Various numerical results are documented to show how estimation errors behave by the volume to capacity ratio and by market penetration.