# Deployment Optimization of Defense Stations in an Attack-Defense Aerial War Game
## 3 Simulation Results and Statistical Analysis
The CDF on \(\zeta_{4}\) shows score 0 in 39 games, score 1 in 46 games, and the highest score is 3. Since more defense stations are placed around the major post on \(\zeta_{3}\) as compared with \(\zeta_{1}\), \(\zeta_{2}\) and \(\zeta_{4}\), most games on \(\zeta_{3}\) result in lower score than on the other \(\zeta\)'s. Figure 10: CDF of (**a**) impact score on major post; (**b**) impact score on south post; (**c**) impact score on north post; (**d**) number of lost defense stations; (**e**) number of launched interceptors; (**f**) number of lost attackers, against slant attack formation, black: \(\zeta_{1}\), orange: \(\zeta_{2}\), green: \(\zeta_{3}\), purple: \(\zeta_{4}\). Figure 10b shows the CDF curves of impact score on the south post. In general, the scores on \(\zeta_{2}\) and \(\zeta_{3}\) are higher than those on \(\zeta_{1}\), which in turn are higher than those on \(\zeta_{4}\). The highest scores on \(\zeta_{1}\), \(\zeta_{2}\), \(\zeta_{3}\), and \(\zeta_{4}\) are 1, 2, 3, and 0, respectively. Score 0 is received in 79, 56, 34, and 100 games on \(\zeta_{1}\), \(\zeta_{2}\), \(\zeta_{3}\), and \(\zeta_{4}\), respectively. Figure 10c shows the CDF curves of impact score on the north post. In general, the score is the highest on \(\zeta_{3}\), second on \(\zeta_{2}\), third on \(\zeta_{4}\) and the lowest on \(\zeta_{1}\). Based on \(\zeta_{1}\), \(\zeta_{2}\), \(\zeta_{3}\), and \(\zeta_{4}\), the lowest scores are 0, 1, 2, and 1, respectively, the highest scores are 2, 4, 4, and 3, respectively, and score 1 is received in 51, 41, 0, and 86 games, respectively. The highest score on the north post takes place on \(\zeta_{3}\) since no defense stations are placed around it. The scores on the north post on \(\zeta_{1}\) and \(\zeta_{4}\) are lower than that on \(\zeta_{2}\), since no defense stations are placed within 40 km of the north post on \(\zeta_{2}\). Figure 10d shows that the least number of defense stations are lost on \(\zeta_{2}\) in most games, with 1 or 2 defense stations lost in 29 games. Based on \(\zeta_{1}\), \(\zeta_{2}\), \(\zeta_{3}\), and \(\zeta_{4}\), the lowest numbers of lost defense stations are 3, 1, 2, and 3, respectively, and the highest numbers of lost defense stations are 6, 6, 7, and 6, respectively. Figure 10e shows that similar numbers of interceptors are fired on \(\zeta_{1}\), \(\zeta_{2}\) and \(\zeta_{3}\). The number ranges from 62 to 69 on \(\zeta_{1}\), from 65 to 66 on \(\zeta_{2}\), from 62 to 71 on \(\zeta_{3}\), and from 66 to 72 on \(\zeta_{4}\). Figure 10f shows similar numbers of lost attackers on \(\zeta_{1}\) and \(\zeta_{2}\). Slightly more attackers are lost on \(\zeta_{4}\) in most games because all the posts are well protected, especially the south post. Fewer attackers are lost on \(\zeta_{3}\) in most games, which is related to the high score on the north post. Figure 11a shows that the impact score on the major post is the highest on \(\zeta_{1}\), and similar on the other three \(\zeta\)'s. The higher score on \(\zeta_{1}\) in most games is related to the deployment of fewer defense stations within 40 km of the major post. Based on \(\zeta_{1}\), \(\zeta_{2}\), \(\zeta_{3}\), and \(\zeta_{4}\), the highest scores are 7, 4, 5, and 5, respectively, the score is 0 in 15, 38, 33, and 50 games, respectively, and the score is 1 in 33, 42, 41, and 24 games, respectively. Figure 11b shows that the impact scores on the south post based on \(\zeta_{3}\) and \(\zeta_{4}\) are lower than the other two \(\zeta\)'s. The lower score on \(\zeta_{4}\) is attributed to the nearest defense station that not only intercepts some attackers but also attracts some attacker upon itself. The score on \(\zeta_{2}\) is the highest in most games because the nearest defense station is far away from the south post, and there is only one defense station between the south attack stations and the south post.