## 3 Methodology  
### Assumptions  
As defined by relevant studies [10; 17; 21], we also made several assumptions to quantify the potential benefits of the CAV environment.  
1. All vehicles are fully automated and connected, and there are no human-driven vehicles, non-motor vehicles, or pedestrians on the road.
2. The influence of communication delay and packet loss can be ignored with the application of 5G networks.
3. There is a control center called the intersection manager that coordinates the sequence and motion of vehicles, and all the vehicles should follow the instructions of intersection manager.
4. The trajectory control error can be ignored; that is, the vehicle can move according to the spatio-temporal trajectory allocated by the intersection manager.
5. The intersection manager can obtain turning decisions of vehicles in advance through V2X technologies. Moreover, all the vehicles have completed lane changing before entering the entrance lane, while the left-turn lane is named lane no. 1, the straight lane is named lane no. 2, and the right-turn lane is named lane no. 3.
6. The length of vehicles is set to 3 or 5 m, representing compact vehicles and mid-sized vehicles, respectively, and the initial speed and arrival time are set as random values.
7. When the vehicle arrives at the entrance lane, the speed will be adjusted from the initial speed to a fixed speed specified by the intersection manager, and the maximum value of acceleration and deceleration are limited in order to ensure ride comfort, which still leaves room for energy-saving improvements.  
Based on these assumptions, a typical two-way six-lane intersection sketch was designed (Figure 1). When the vehicle arrives in the communication area, it will send its passing request, origin and destination, location, and other motion information to the intersection manager. After that, the intersection manager will send back the passing guidance to instruct the vehicle to cross the approach road, intersection, and departure road with an ideal spatio-temporal trajectory, which can ensure both traffic safety and efficiency. The vehicle will follow the guidance to adjust its speed in the approach road, enter the intersection at the speed designated by the intersection manager, and then accelerate to the speed limit provided by law after entering the departure road.  
We use direction and the turning information to number the 12 lanes. For example, E1 illustrates that the lane is coming from the east and can only turn left, and N2 illustrates that the lane is coming from the north and can only go straight. These 12 lanes will form 16 overlapping points (as shown in Figure 2 and Table 1) in the central region that pose a risk of collision accidents, which motivates us to design a conflict resolution mechanism.  
Figure 1: Diagram of the two-way six-lane unsignalized intersection. (**a**) Intersection configuration; (**b**) road segment configuration.  
Figure 2: All possible trajectories and overlapping points.  
As shown in Figure 3, the potential trajectories of vehicles coming from one direction are assumed to be ideal geometrical lines. However, vehicles cannot be regarded as particles because the external sizes of vehicles have an impact on the occupation state of conflict points. As shown in Figure 4, the spatio-temporal trajectory of one vehicle is similar to a prism, and there will be a collision if the trajectories of two vehicles predicted by the intersection manager overlap, which indicates that the two vehicles have occupied the same conflict point at the same time.