Mixed integer programming of joint optimization of signal timing and phasing and vehicle trajectories under mixed traffic environment

Intelligent intersection management has been a research hotspot in recent years within the domain of intelligent transportation systems (ITS). Existing studies exhibit a deficiency in explicitly addressing the trajectories of human driven vehicles (HDVs) under mixed traffic environment, and they fall short of harnessing the full potential of connected and automated vehicles (CAVs) and Vehicle-to-Infrastructure (V2I) technologies for the joint optimization of signal timing and phasing and vehicle trajectories. In this study, we propose a cooperative intersection management method designed for mixed traffic environment. Our approach jointly optimizes the green time durations, phase order of traffic signals, and vehicle trajectories. To account for the impact of traffic signals on HDVs, we incorporate it as a virtual leading vehicle within the optimal velocity model (OVM). The comprehensive model is formulated as a nonlinear programming problem and then converted into a mixed integer programming problem using the big-M method. We conduct simulations of the proposed method in various scenarios at different MPRs. The results reveal a significant reduction in average travel time compared to the actuated signal control, highlighting the enhanced efficiency of the intersection achieved through our proposed method.