## 3 Urban Road Intersection Traffic Spatiotemporal Collaborative Optimization Methods  
Urban road intersections are critical nodes within urban road networks, with their operational efficiency directly affecting the performance of the entire urban transportation system. As traffic demands continue to grow and vehicle technologies rapidly develop, traditional single-dimension control methods can no longer meet the complex requirements of modern urban traffic. Spatiotemporal collaborative optimization, as an intersection optimization approach that comprehensively considers temporal resources (signal timing) and spatial resources (lane allocation, vehicle trajectories), is gradually becoming an important pathway for addressing this issue. Traditional fixed-time signal timing optimization methods primarily rely on traffic volume data collected by infrastructure detectors (such as inductive loops), which typically involve high maintenance costs and low coverage. With the development of probe vehicle technology, vehicle trajectory data provides richer traffic state information, opening new possibilities for signal optimization. Research by [PERSON] et al. [11] and [PERSON] et al. [12] demonstrate that optimization methods based on vehicle trajectories can achieve effects even under low penetration rate conditions. The hierarchical multi-objective optimization framework developed by [PERSON] et al. [11] compensates for the limitations of low penetration rate probe vehicles through the \"Same-ratio Principles\", while [PERSON] et al. [12] proposed a probabilistic time-space diagram method, establishing connections between stochastic point-queue models and vehicle trajectories. These methods have performed excellently in practical applications, with implementation results in Birmingham, Michigan showing reductions in intersection delay and stop frequency by up to 20% and 30%, respectively. Building upon these trajectory-based optimization successes, the rapid development of connected and automated driving technology has provided an even broader scope for intersection spatiotemporal collaborative optimization. Compared to traditional methods, collaborative control based on vehicle-to-everything (V2X) environments can simultaneously optimize signal timing and vehicle trajectories, achieving more efficient traffic management. [PERSON] et al. [13] modeled intersection control as a two-stage optimization problem: the first stage optimizes signal timing through dynamic programming to minimize vehicle delays, while the second stage applies optimal control theory to optimize vehicle trajectories to reduce fuel consumption and emissions. Simulation results indicate that this collaborative optimization method can reduce vehicle delays and CO2 emissions by up to 24.0% and 13.8%, respectively. [PERSON] et al. [14] went further by proposing a single-layer joint optimization method that simultaneously optimizes signal phase durations and vehicle platoon accelerations without requiring pre-specified terminal conditions, outperformingtraditional methods in average travel delay, capacity, fuel consumption, and emissions. These studies demonstrate the enormous potential of spatiotemporal collaborative optimization in improving intersection efficiency and environmental sustainability. In real traffic environments, connected and automated vehicles (CAVs) and human-driven vehicles (HVs) will coexist for an extended period, forming heterogeneous traffic flows. This mixed environment imposes higher requirements on traffic control, necessitating simultaneous consideration of the different characteristics of both vehicle types. To address this challenge, researchers have proposed various innovative methods. [PERSON] et al. [15] introduced a traffic control model based on shared-phase-dedicated-lanes (SPDLs), allowing left-turns and CAVs to share dedicated lanes and pass through intersections together with HVs during shared phases.