A Bayesian approach for estimating vehicle queue lengths at signalized intersections using probe vehicle data

•A novel Bayesian approach is proposed for estimating queue lengths at signalized intersections.•High-frequency probe vehicle trajectory data are used.•Both the queue length and the discharging shockwave speed are modelled stochastically.•An efficient expectation maximum algorithm is developed.•Estimates are accurate and robust even under low penetration of probe vehicles.