## 4 Performance Analysis
### Simulations Results Corresponding to BS Motion
#### 4.3.4 Analysis of \(\Delta D_{BA12}\)  
The variability in \(\Delta D_{BA12}\) is determined by conditions such as the direction of AUV movement, the direction of BS motion, and the magnitude of BS motion. Through the analysis of \(D_{BA}\), described in Section 4.3.1, it was observed that the \(D_{BA}\) value varies over time relative to the direction of BS motion compared to the stationary BS, based on the point where the \(D_{BA}\) value reaches its minimum. Building on this result, the analysis of \(D_{BA12}\) in Section 4.3.3 indicates that, depending on the motion directions of BS1 and BS2, the \(D_{BA12}\) value can increase in the overlapping region or reach its maximum at the network edge. To statistically examine the variability introduced by BS motion to \(D_{BA12}\), we analyzed the mean and standard deviation of \(\Delta D_{BA12}\) according to the direction and magnitude of BS motion, as presented in Table 5.  
Similar to \(\Delta D_{BA1}\) and \(\Delta D_{BA2}\), the mean of \(\Delta D_{BA12}\) also varies between positive and negative values depending on the direction of BS motion, yet the absolute values remain comparably similar. Furthermore, the absolute value of the mean increases as the sea state code rises. The standard deviation of \(\Delta D_{BA12}\) also maintains nearly identical values regardless of the direction of BS motion, with an increase in standard deviation as the sea state code increases. Based on these results, the mean and standard deviation of \(\Delta D_{BA12}\) are more influenced by the magnitude of BS motion rather than its direction, consistent with the results in Section 4.3.2. In the two cases where the direction of motion for BS1 and BS2 is the same, the values of \(\Delta D_{BA12}\) are equal but have opposite signs. Similarly, in the other two cases, where the direction of motion for BS1 and BS2 differs, the pattern remains the same. Considering this symmetry of \(\Delta D_{BA12}\) with respect to the direction of BS motion, we can consider \(|\Delta D_{BA12}|\) as an indicator of variability due to the effect of BS motion instead of \(\Delta D_{BA12}\); that is, \(|\Delta D_{BA12}|\) can be used to infer when the variability in the AUV-BS distance might become significantly severe. As depicted in Figure 6a, in cases where the direction of motion for BS1 and BS2 is the same, the value of \(|\Delta D_{BA12}|\) is larger during the period passing through the overlapping region than at the points crossing the edges, and this difference increases as the sea state code rises. In cases where the direction of motion for BS1 and BS2 is opposite, the pattern of \(|\Delta D_{BA12}|\) is found to be the exact opposite, as shown in Figure 6b. However, as depicted in Figure 5b, when \(D_{BA12}\) exceeds 150 m at the network edge, a variability of less than 50 m in \(|\Delta D_{BA12}|\) does not affect the handover decision. Conversely, as illustrated in Figure 5a,d, when \(D_{BA12}\) is less than 50 m, variations in \(|\Delta D_{BA12}|\) below 50 m can lead to erroneous handover decisions. These analytical findings suggest that considering only cases where variability increases in the overlapping region is sufficient. In addition, the analysis of \(|\Delta D_{BA12}|\) allows us to identify the timepoints where the impact of BS motion is most significant, and to infer the extent of variability caused by the direction and magnitude of BS motion. This suggests that \(|\Delta D_{BA12}|\) can serve as a measure to evaluate the degree of variability introduced to the AUV-BS distance due to BS motion.