# Deployment Optimization of Defense Stations in an Attack-Defense Aerial War Game
## 3 Simulation Results and Statistical Analysis
There are two defense stations between the major post and the north post to cover both, and two defense stations between the major post and the south post to cover both. Figure 9d shows the optimal deployment plan of defense stations based on defense cost \(\zeta_{4}\). There are six defense stations near the major post, four of them are within 40 km, with three to the east and one to the south. There is only one defense station to the west of the south post, within 40 km of the latter. However, it is surprising that no defense station is placed near the north post. Since the major post has the highest weighting and is targeted by many more attackers, more defense stations are placed around it. There is one defense station between the major post and the north post to guard both. Table 4 lists the statistics of loss against slant attack formation, including average hits on the major post, north post and south post, respectively, the percentage of defense stations lost, interceptors launched, and attackers lost, respectively. The average defense cost, median of defense cost, 80%, and 95% confidence intervals (CIs) are also listed. With the optimal deployment plan based on \(\zeta_{1}\), the average hits on the three posts are low since each post is guarded by at least one defense station within 40 km, and some defense stations are placed between two adjacent posts. The hits on the major post are  
Figure 9: Optimal deployment of defense stations against pincer formation, based on (**a**) \(\zeta_{1}\); (**b**) \(\zeta_{2}\); (**c**) \(\zeta_{3}\); (**d**) \(\zeta_{4}\) square with cross: major post, square with slash: minor post, blue square: defense station. higher than those on the two minor posts because many more attackers target at the former. The hits on the south post (0.21) are lower than that on the north post (0.61). Both minor posts have a number of defense stations within 40 km, but there are more defense stations placed in the southern area (between south post and major post) than in the northern area (between north post and major post). One of the defense stations is hit by an attacker in the middle of the game, and an interceptor chasing this attacker is released to intercept another attacker aiming for the south post. In addition, another defense station attracts an assault to itself, relieving a possible hit on the south post. More interesting and enlightening details will be demonstrated in the next section. With the optimal deployment plan based on \(\zeta_{2}\), the average hit on the south post (0.66) is low, but that on the north post (1.87) is higher since no defense station is placed within 40 km of the latter. The hit on the major post (1.35) is the highest among all four cases. The loss rate of defense stations (30.2%) is lower than the other three cases because two out of four defense stations near the major post have some cohort defense stations within 40 km to cover them, One of these four stations is able to fire an additional interceptor upon an attacker within 50 km of of the former. It turns out that three of these stations are hard to kill, but the 4 th one is hit for sure. With the optimal deployment plan based on \(\zeta_{3}\), the average hit on the major post (0.13) is very low since many more defense stations are placed around it. On the other hand, the hit on the north post (2.25) is relatively high because no defense stations are placed nearby. The hit on the south post (0.72) is much lower than that on the north post because the former is guarded by two defense stations to the west and one defense station within 40 km of it. The attacker loss rate (77.125%) is the lowest among the four cases, which is related to the poor protection on the north post. With the optimal deployment plan based on \(\zeta_{4}\), the average hit on the south post is 0, since each post is more evenly covered by defense stations, with at least one defense station within 40 km of it.