# Multi-Controller Deployment in SDN-Enabled 6G Space-Air-Ground Integrated Network
## 3 Results
### Result Analysis
#### 3.2.3 Compare the Load Variances of Different Algorithms with Time  
In this contrast experiment, OCLDS [26] and n-k-means [31] were selected as the contrast experiments; the former divides the load into four states, with a switch migration  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time Slice** & **Switch No.** & **Src Controller No.** & **Des Controller No.** \\ \hline
5 & S1 & C2 & C7 \\
5 & S5 & C3 & C1 \\
6 & S8 & C2 & C6 \\
7 & S14 & C2 & C7 \\
8 & S15 & C2 & C1 \\
9 & S16 & C2 & C6 \\
10 & S19 & C2 & C1 \\
11 & S7 & C2 & C1 \\
12 & S11 & C2 & C5 \\
17 & S4 & C2 & C6 \\
19 & S1 & C7 & C1 \\
20 & S26 & C2 & C5 \\  & S12 & C7 & C6 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Switch migration information.  
Figure 9: Variation of controller load variance before and after switch migration.  
strategy, and the latter has no migration strategy. Each time slice requires an algorithm to be run to redistribute the relationship between the switch and the controller.  
As shown in Figure 10, this strategy is compared with the other two algorithms in terms of controller load variance. First, the size of the comparison is obviously the best result obtained by the n-k-means strategy, and the load variance of the first 14 time-slice controllers does not change much. The main reason for this is that each time slice needs to re-execute the algorithm and re-distribute the relationship between the switch and the controller. Although this result is the best, it takes so long that there is not enough time to complete the switch migration before the next time slice starts. Secondly, as the analysis above, the switch migration occurs from the fifth time slice, and the controller load variance is equal to n-k-means, which is better than the OCLDS algorithm, and the controller load variance obtained by this strategy and OCLDS is increased first and then decreased, but the latter is delayed by several time slices. The reason for this is that the switch migration is restricted by the controller load variance and 85% of the maximum controller load, while OCLDS only controls the switch migration by the controller load segmentation; therefore, the performance of this strategy is improved by about 7.71% compared to OCLDS (calculated here by averaging the difference between the two time slices). Finally, because this strategy and OCLDS have developed a strategy to trigger the switch migration, it takes less time to complete the migration before the next time slice than the redistribution of n-k-means.  
2.4 Compared with Different Algorithms, the Running Time of the Migration Algorithm Changes with the Increase in Switch Nodes  
In addition to the 66 polar-orbiting satellites in the iridium constellation, the switch node uses the satellite data from the Starlink program and in turn uses STK to simulate the four Walker constellations (inclined orbits), a hybrid orbital constellation model (inclined and polar orbits) with the parameters in Table 3.  
Figure 10: Variation of controller load variance with time slice for different algorithms.  
As shown in Figure 11, the scattered points represent the number of nodes corresponding to the algorithm running time and running time of the calculation: the information of a cycle of each time slice of the running time is given as the average value. The curve represents the polynomial fitting of scattered points, and the running time of the three algorithms increases with the number of nodes. According to the time complexity analysis, the migration strategy of this paper and OCLDS is O(m), so the fitting curve shows a linear increasing trend. The time complexity of n-k-means is approximately O(n * m), where m is the number of controllers and n is the node of switches. In addition, when the number of nodes exceeds 1000, n-k-means uses more than half of a time slice to figure out the migration strategy, and it is highly likely that the controller fails to complete the migration within a time slice. The other two strategies are significantly faster than n-k-means.