Queue-length estimation using real-time traffic data

We consider the problem of estimating queue-lengths at an intersection from a pair of advance and stop bar detectors that count vehicles, when these measurements are noisy and biased. The key assumption is that we know weather the queue is empty or not. We propose a real-time queue estimation algorithm based on stochastic gradient descent. The algorithm provably learns the detector bias, and efficiently estimates the queue-length with theoretical guarantee. The algorithm is tested in a simulation and in a case study using traffic data from an intersection in Beaufort, North Carolina.