## 1 Introduction  
As vehicular network technology matures, connected and automated vehicles (CAVs) (CAVs are equipped with advanced onboard sensors, controllers, actuators, and other devices. They integrate modern communication and network technologies, enabling intelligent information exchange and sharing between vehicles, humans, infrastructure, and backend systems) are poised to integrate into the broader traffic environment. The networked and autonomous nature of CAV resolves the coupling issues between control methods and human drivers, providing new solutions to existing traffic problems. Before the complete implementation of fully CAVs, the phenomenon of mixed traffic flow with CAVs and traditional manually driven vehicles (HDVs) will become the norm. Due to the differences in driving subjects, CAVs and HDVs exhibit different characteristics, and the mixed traffic flow composed of both increases the complexity of the traffic environment. Therefore, it is necessary to conduct forward-looking research to reasonably analyze new problems that may exist in mixed traffic flow and to anticipate and predict them. This will provide a theoretical foundation for the future planning, design, and traffic management of corresponding road networks. Therefore, analyzing the car-following characteristics of mixed traffic flow and leveraging the advantages of CAVs in mixed traffic scenarios to enhance traffic control efficiency and safety is a current research focus. Many scholars have explored this area, improving existing models like the IDM [1; 2; 3], CACC [4; 5], and Gipps models [6; 7] to suit various mixed traffic scenarios. For instance, [PERSON] [8] et al. enhanced car-following models using driver memory, while [PERSON] [9] et al. considered multiple leading vehicles in a full-velocity difference model. In speed guidance, scholars have incorporated signal timing to plan CAV trajectories for eco-friendly intersection crossing. For example, [PERSON] et al. [10] proposed an eco-driving vehicle control system for intersection vehicle collaboration. [PERSON] [11] aimed to minimize delay time, fuel consumption, and safety risk, finding the optimal speed trajectory scheme for intersection vehicles under fixed signal timing conditions. [PERSON] et al. [12] aiming to minimize vehicle travel time, proposed a speed control strategy to reduce fuel consumption during trips. The results demonstrated that this speed control strategy could achieve a 23.7% reduction in fuel consumption. [PERSON]. [13] focused on minimizing idling time and the number of stops at signalized intersections by introducing a cooperative speed optimization framework based on game theory. [PERSON] [14] utilized the entropy weight method to determine the weights for a comprehensive optimization objective, including vehicle delay, CO\({}_{2}\) emissions, and fuel consumption, and employed a particle swarm optimization algorithm to solve for the optimal speed. Some scholars have also focused on the efficiency of intersection traffic flow. [PERSON] [15] considered the impact of weather factors in the optimal speed planning of vehicles and established a minimum transportation energy optimization model with travel time constraints and a minimum travel time optimization model with transportation energy constraints. [PERSON] [16] et al. proposed two speed guidance algorithms based on single-vehicle and multi-vehicle travel time optimization. [PERSON] [17] et al. proposed corresponding speed guidance strategy models based on the different situations of guided vehicles arriving at intersections. [PERSON] [18] et al. proposed a hierarchical multi-objective optimization framework based on sampling vehicle trajectories at isolated signalized intersections to increase vehicle throughput, reduce queue lengths, and traffic delays. [PERSON] and [PERSON] [19] established an optimal speed recommendation curve based on the predictive behavior of leading vehicles in the foresight vision and traffic signal timing. Some scholars have focused on unsignalized intersections.