Back-Pressure-based Traffic Signal and Discretized Trajectory Joint Control for Low CAV Penetration Rate Environment

This paper presents an innovative joint traffic signal and trajectory control (JSTC) model for a mixed traffic environment with a low penetration rate of connected autonomous vehicles (CAVs). The JSTC model integrates a back-pressure (BP) signal controller that comprehensively considers the right-of-way with traffic modes and the person-based traffic demand, which aims to enhance intersection throughput and improve the probability of arrival on green (PAOG) of CAVs. Additionally, this paper provides a theoretical stability proof of the control system by deviating the upper bound of the Lyapunov drift penalty function. Furthermore, it simultaneously introduces a discretized CAV trajectory control model by discretizing continuous time variables with vehicle-to-infrastructure (V2I) communication periods for smooth and safe travelling. Simulation results demonstrate that the JSTC model exhibits excellent responsiveness and achieves the lowest convergence value of cycle maximum queue length across various flow-based traffic demand levels. The smoothness of the Lyapunov function values validates the ability to stabilize the control system. Two months of connected transit buses (CTB) operation data shows that substantial progress has achieved. These include the elimination of unnecessary stops, an over 20km/h increase in daily average speed, a 17% reduction in weekly average delay, and at least 10% reduction in weekday travel time.