Analytical Evaluation of the Error in Queue Length Estimation at Traffic Signals From Probe Vehicle Data

Probe vehicle data are increasingly becoming more attractive for real-time system state estimation in transportation networks. This paper presents analytical models for the real-time estimation of queue lengths at traffic signals using the fundamental information (i.e., location and time) that probe vehicles provide. For a single queue with Poisson arrivals, analytical models are developed to evaluate how error changes in queue length estimation as the percentage of probe vehicles in the traffic stream varies. When the overflow queue is ignored, a closed-form solution is obtained for the variance of the estimation error. For the more general case with the overflow queue, a formulation for the error variance is presented, which requires the marginal probability distribution of the overflow queue as the input. In addition, an approximate model is presented for the latter case, which yields results that are comparable with the exact solution. Overall, the formulations presented here can be used to assess the error in queue length estimation from probe data without conducting simulation runs for various scenarios of probe vehicle market-penetration rates and congestion levels.