## 5 Monte Carlo Simulation  
The proposed algorithm for approaching motion toward uncontrolled blind intersections was evaluated through the Monte Carlo simulation method. The same intersection used in the case study was utilized in this simulation. However, the numbers of target vehicles were increased from one to five to create a more complex driving situation as  
Figure 7: Simulation results for LTAP scenario. (**a**) Longitudinal velocity, (**b**) longitudinal acceleration, (**c**) clearance to conflict point, (**d**) TTC to conflict point.  
shown in Figure 8. The initial position, initial velocity, and maximum velocity of the host and target vehicles were randomly decided using Gaussian distribution as follows:  
\[\begin{array}{l}p_{ini}=N(120\;\text{m},\;20\;\text{m})\\ v_{\text{max}}=N(45\;\text{km}/\text{h},\;5\;\text{km}/\text{h})\\ v_{ini}=N(30\;\text{km}/\text{h},\;10\;\text{km}/\text{h})\end{array} \tag{11}\]  
The Monte Carlo simulation was conducted 100 times for both algorithms. The Monte Carlo simulation results are summarized in Figures 9-12. First, the safety performance of the proposed and base algorithm was analyzed using the _TTC_ and \(C\) for intersection scenarios. Figure 9 shows the safety index distribution of the proposed algorithm in two _TTC_ vs. \(C\) planes, each plane with colored marks in terms of velocity and acceleration. As can be seen in Figure 9, the proposed algorithm managed the risk caused by various driving situations while maintaining _TTC_ and \(C\) above the minimum level, 2 s, and 5 m. In addition, Figure 9a shows that the velocity gradually decreased to zero velocity as the safety index approached the risky region. As shown in Figure 9b, this smooth velocity distribution was derived only using a mild acceleration. In the case of the base algorithm where the proactive motion planner was excluded, Figure 10 shows that a highly dangerous situation occurred even with maximum deceleration. In particular, maximum deceleration was used in most simulation trials because the autonomous vehicle entered the intersection with high velocity. Therefore, the proactive motion planner provided the appropriate approach motion, which improved safety only by using the nominal range of deceleration, as shown in Figure 11, which shows the histogram of the acceleration used.  
The traffic efficiency of both algorithms was compared based on the time required to cross the intersection. The cumulative number of the simulation times to cross the intersection is depicted in Figure 12. Since the intersection approach velocity of the base algorithm was faster than the proposed algorithm, only a short time was used to cross the intersection in several cases. However, safety was not guaranteed in most cases as mentioned earlier in this section. In addition, excessive deceleration was used and a complete stop frequently occurred in order to avoid collision with targets. Therefore, if the autonomous vehicle lost priority for crossing the intersection, there were cases where the autonomous vehicle could not cross the intersection until all targets passed. In this simulation study, 20 cases could not cross the intersection until the simulation was finished. However, all simulation trials of the proposed algorithm  
Figure 8: Multitarget intersection scenario.  
Figure 9: Safety index distribution of the proposed algorithm. (**a**) Distribution with respect to longitudinal velocity, (**b**) distribution with respect to longitudinal acceleration.  
Figure 10: Safety index distribution of the base algorithm. (**a**) Distribution with respect to longitudinal velocity, (**b**) distribution with respect to longitudinal acceleration.