## 3 Urban Road Intersection Traffic Spatiotemporal Collaborative Optimization Methods
This approach achieved significant improvements in intersection efficiency through a three-level optimization model (signal optimization, phase configuration, and CAV trajectory planning). Fully leveraging CAV advantages to guide heterogeneous traffic flow represents another research focus. [PERSON] et al. [16] innovatively proposed viewing CAVs as \"catalysts\" for vehicle platoons, promoting controllable platoon formation through various \"catalytic\" modes such as cooperative, accelerated, or direct lane-changing. Their two-stage optimization model optimizes vehicle delays and emissions, respectively, with numerical experiments indicating good results even at 20% CAV market penetration rates, reducing average vehicle delays and emissions by 54.32% and 19.1%, respectively. Similarly, research by [PERSON] et al. [17] combined lane assignment with signal-vehicle coupled control, achieving the most significant benefits at moderate traffic demand levels with low sensitivity to CAV market adoption rates, indicating its applicability throughout the CAV adoption process. Notably, compared to direct CAV control, routing control represents another method for improving heterogeneous traffic efficiency. The multi-objective routing control method developed by [PERSON] et al. [18] based on deep Q-networks distributes traffic flow by controlling driving directions at intersections, proving particularly effective in dynamic traffic environments by enabling smooth traffic flow along optimal routes and reducing automated vehicles' travel distances, times, and waiting times. [PERSON] et al. [19] approached from a behavior prediction perspective, proposing a hierarchical prediction framework considering traffic signals and interactive agents, combining discrete intention prediction and continuous trajectory prediction to support automated driving decision-making in complex urban scenarios. Beyond signal timing and vehicle trajectory optimization, lane allocation represents an important means for improving intersection throughput efficiency. Traditional design methods treat lane marking patterns as fixed inputs, limiting signal timing optimization space. [PERSON] and [PERSON] [20] broke this limitation by incorporating lane markings as binary control variables into optimization models, achieving synchronized optimization of lane marking patterns and signal timing. [PERSON] et al. [21] and [PERSON] et al. [22] further investigated phase swap sorting strategies, allowing different types of vehicle movements to be reorganized through pre-signals, enabling all lanes to discharge vehicles during green phases, significantly enhancing intersection capacity. These studies demonstrate that flexible allocation of lane functions and collaborative optimization with signal timing can more fully utilize limited road space resources. Research on urban road intersection spatiotemporal collaborative optimization has achieved significant progress, conducting systematic exploration across multiple dimensions from vehicle trajectory data application, intelligent connected environment collaborative control, and heterogeneous traffic environment adaptation to flexible lane allocation. Research indicates that even under low penetration rate conditions, trajectory-based optimization methods can achieve significant effects; spatiotemporal collaborative control in intelligent connected environments simultaneously optimizes signal timing and vehicle trajectories, achieving dual reductions in delays and emissions; innovative strategies in heterogeneous traffic environments can fully leverage limited CAV resources to influence overall traffic flow; while flexible lane configurations and coordinated optimization with signal timing further improve the utilization efficiency of limited spatial resources. With the continuous development of vehicle networking and autonomous driving technologies, future research will increasingly emphasize collaborative control strategies and multi-objective balancing under heterogeneous traffic flow conditions.