Characterizing the dynamics and uncertainty of queues at signalized intersections with left-turn bay

In most signalized intersections, in order to solve the problem of insufficient road space, left-turn bays are commonly set up at intersections with a shared through and left-turn lane. However, this design tends to result in the potential queue overflow and blockage problems, which further make the discharge process of either left-turn vehicles or through vehicles at the intersections to be interrupted unexpectedly during their respective green phase. As a result, the queueing processes of vehicles present high nonlinearity and uncertainty during a signal cycle. In this paper, a stochastic queueing model is proposed to characterize the dynamics and uncertainty of queues at signalized intersections with a left-turn bay. The proposed model takes full account of the random interaction between the through movement and the left-turn movement under the influence of overflow and blockage of queues. We obtain some average performance indicators as well as the signal-state-dependent dynamic performance measure of queues and its variance at any given time point within a signal cycle. The proposed analytical model is validated against the VISSIM simulation model under different scenarios; the results show a good degree of agreement. In addition, in order to systematically determine the queue dynamics and uncertainty, we also conduct a series of numerical simulations to quantitatively capture the queue characteristics of vehicles at signalized intersections with left-turn bay by considering possible factors.