A hidden Markov model for the estimation of correlated queues in probe vehicle environments

Abstract

Queue length estimation is critical for traffic signal control and performance measures. With the development of connected vehicle technologies and the popularization of ride-hailing services, probe vehicle data are now being collected on a large scale. Some studies have shown that queue lengths can be estimated using only probe vehicle data. The relevant literature usually assumes the queue lengths in different traffic signal cycles are independent and identically distributed or treats the queues independently. However, in the real world, the queue lengths in different cycles might be correlated. For instance, when there exists an overflow queue, the queue length in the following cycle is correlated with the queue length in the previous cycle. In fact, the correlation of different cycles can provide additional information and thus improve the queue length estimation accuracy. In this paper, we model such queueing processes in probe vehicle environments using a hidden Markov model (HMM), where the queue length in each cycle is a hidden state, and the observed pattern of probe vehicles is an observation. Based on the HMM, we propose two novel cycle-by-cycle queue length estimation methods. In the case where the parameters of the HMM are unknown, we also provide an algorithm that can estimate the parameters from historical probe vehicle data. Validation results show that the proposed cycle-by-cycle queue length estimation methods outperform the existing methods, and the parameter learning algorithm can estimate the parameters adequately.