Integrated optimization of traffic signals and vehicle trajectories for mixed traffic at signalized intersections: A two-level hierarchical control framework

With the rapid advancement of connected and automated vehicle (CAV) technology, the integrated optimization of traffic signals and vehicle trajectories has emerged as a promising approach to enhance intersection performance. However, the complexity of this integrated optimization problem requires substantial computational resources, rendering existing methods impractical for real-time applications. To address this challenge, this paper presents a two-level hierarchical control framework for mixed traffic environments, consisting of both CAVs and human-driven vehicles (HVs), offering a computationally efficient solution without compromising performance. At the upper level, we introduce a platoon-based mixed integer linear programming (PMILP) model to jointly optimize signal timing and desired arrival times, with the main objective of minimizing traffic delay. Building upon the optimized desired arrival times, a Nash-based distributed model predictive control (DMPC) method is developed at the lower level to optimize CAV trajectories, enabling vehicles to pass through intersections at free-flow speeds without stopping and minimizing acceleration fluctuations. Numerical experiments are conducted to assess the performance of the proposed method against three alternatives. Method 1 uses actuated signal control (ASC) for traffic signals, and the Intelligent Driver Model (IDM) for all vehicles. Method 2 combines the controlled optimization of phases (COP) for signal control with DMPC for CAVs and IDM for HVs. Method 3 applies the proposed PMILP method for traffic signals, predictive cruise control (PCC) for CAVs, and IDM for HVs. The results demonstrate that the proposed integrated optimization approach significantly reduces traffic delay, fuel consumption, and idling time, while simultaneously enhancing driving comfort across different CAV penetration rates and degrees of saturation. Notably, the proposed method achieves these improvements with a high level of computational efficiency.