An analytical model for a tandem of two traffic-light intersections under semi-actuated and fixed control

With increasing congestion in urban areas, it is important to characterise existing traffic control policies in terms of their performance and their optimal settings. In this paper, we propose a queueing model for traffic-light networks under fixed and semi-actuated control. In our model, we explicitly consider slow-departing vehicles in the beginning of a green period and the offsets between intersections. Our approach proves to be both accurate and fast compared to traffic microsimulation, allowing us to optimise the traffic-light settings and offsets.
By analysing our model for two intersections in tandem, we show the important differences between semi-actuated and fixed controls. We observe that semi-actuated control is better for the average delay in comparison to fixed control when the main road has the same or a higher load than the crossing roads. If the loads are similar, the results of both types of control are close, and it may be advisable to use fixed control to avoid additional costs. The optimal traffic-light settings are shown to heavily depend on the type of control. For example, the effect of offsets in case of semi-actuated control is minor when the loads are relatively low, while the performance of fixed control may significantly vary depending on the offset between the intersections for any load.