## 2 Methodology
### Potential Conflict Risk Index  
The design of an SSM should consider the temporal-spatial proximity of conflicts and the severity of potential collisions. In this paper, PCRI quantifies the proximity of conflicts and the severity of potential collisions from three aspects: time to region, exposure distance in region, and time related to speed and direction. By incorporating these variates, PCRI offers a comprehensive framework for evaluating vehicle conflict risk under different conflict types. Before constructing different variates, it is essential to initially define the conflict risk region. In this study, a circular risk region centered around the lead vehicle is conceptualized. At any time, the potential scenarios concerning the positional relationship  
Figure 2: The definitions of variables related to TTC. between the subject vehicle's trajectory relative to the lead vehicle and the risk region can be described in Figure 3. As Figure 3 shows, both the lead vehicle and the subject vehicle are simplified to a point by considering the geometric center of the vehicle. The ray with an arrow signifies the subject vehicle's trajectory relative to the lead vehicle. The direction of this ray corresponds to the speed vector of the subject vehicle relative to the lead vehicle. And \(R\) is the radius of the risk region, \(d_{\text{min}}\) represents the minimum distance between the subject vehicle's trajectory relative to the lead vehicle and the position of the lead vehicle. In Figure 3a, if the subject vehicle continues at its current speed and direction, it will enter the risk region after a period of time and subsequently exit it, indicating a great conflict risk between the two vehicles in this condition. Figure 3b shows that the subject vehicle will reach the boundary of the risk region and then immediately move away from it, indicating there is no conflict risk between the two vehicles. Figure 3c illustrates that the subject vehicle will neither enter the risk region nor reach its boundary, indicating no conflict risk. In events where the subject vehicle's trajectory relative to the lead vehicle intersects the risk region at multiple points, it indicates that the subject vehicle is projected to intrude into the defined risk region. This situation suggests a potential risk for conflicts under the condition that \(d_{\text{min}}<R\). Conversely, if the trajectory intersects with the risk region at only one point or does not intersect at all, the lead vehicle will not invade the risk region, corresponding to the condition \(d_{\text{min}}\geq R\). TTR considers the elapsed time before a conflict occurred, which can reflect the initial conditions of an event by the temporal proximity. This enables the interpretation of the temporal proximity of conflicts to indicate the probability of a potential conflict, even in the absence of an actual collision [21]. The calculation of TTR is governed by Equation (5). \[TTR= \begin{cases}\frac{dTR}{|\mathbf{v_{i}}-\mathbf{v_{j}}|},d_{\text{min}}<R \\ M,d_{\text{min}}\geq R\end{cases}  \tag{5}\]  
where \(\mathbf{v_{i}}\) and \(\mathbf{v_{j}}\) represent the speed vectors of the lead and subject vehicles, respectively. \(M\) is a sufficiently large positive value and \(dTR\) is the distance to the boundary of the risk region. If \(d_{\text{min}}<R\), there are still three possible positional relationships between the subject vehicle and the risk region, and these relationships will affect the value of \(dTR\). Figure 4 shows these three possible positional relationships between the subject vehicle and the risk region. The longer a vehicle remains in the risk region, the more time it has to make a reasonable evasive maneuver, thereby reducing the risk of conflicts. For the definition of TTR in Equation (5), a larger value of TTR indicates a lower conflict risk. Thus, the magnitude of TTR can reflect the conflict risk conditions of a specific scenario. Figure 3: The relationship between risk region and the subject vehicle’s trajectory.