# Multi-Controller Deployment in SDN-Enabled 6G Space-Air-Ground Integrated Network
## 3 Results
### Result Analysis  
2.1 In the Case of Different Number of Controllers, the Load of Each Controller and the Maximum Propagation Delay from the Switch Node to the Controller Are Calculated  
As shown in Figure 6 (to visualize how the controller handles packet-in, where the load indicates the packet-in packet received by the controller), each subgraph represents the current number of controllers, changes in load and maximum propagation delay for each controller. With the increase in the number of controllers, the maximum propagation delay from the switch to the controller decreases, and the load difference between the controllers decreases, in order to better analyze the relationship between the load and the propagation delay and the number of controllers, the graph of the relationship between the number of controllers and the variance and average delay of the controller load is given in Figure 7.  
Through the analysis of the graph above, the average delay of the whole network shows a downward trend with the increase in the number of controllers, which is in line with our theoretical formula, but combined with the analysis of the load value, the load of the six controllers is the best at the time of load; however, the propagation delay is not optimal at this time. When the transmission delay changes from seven controllers to eight controllers, the load decreases, but the delay increases. This is also in line with our theoretical derivation, and the number of controllers can be determined according to the minimum required delay and the optimal load. If the minimum propagation delay is less than 20 (ms), the number of controllers can be determined according to the minimum required delay and load; if the controller load variance is less than 6000, you can choose seven controllers.  
Figure 6: Diagram of delay and load variation for each controller.  
3.2.2. The Controller Load Varies with the Packet-In Request Packet of the Switch  
To better analyze the switching process, the packet-IN request packets of the switch node are linearly increased by 100 packets per time slice in a simulation. On the basis of the first experiment, after reaching the optimal number and position of controller deployment, Algorithm 2 should be run once per time slice. The simulation results show that the controller load changes linearly with packet-IN request packets (time slice). The results of the simulation are shown in Figure 8.  
Figure 8: Diagram of controller load versus time slice.  
Figure 7: Diagram of the number of controllers and the variation of load variance and delay.  
Due to the linear growth of switch traffic with time slice, the controller load also shows a linear growth trend. The position of the curvilinear punctuation marks the time slice in which the switch node migration occurs, where the time slice [5; 6; 7; 8; 9; 10; 11; 12] is due to the variance of all controller loads greater than 6000 (packet-IN), leading to the switch node migration, and the time slice [17; 19; 20] is migrated by 85% of the switch nodes with C2 and C7 loads greater than the maximum load. The specific information is shown in Table 2.  
Figure 9 shows the change in controller load variance before and after switch migration. In order to show the simulation effect better, the results show the change of the first 14 time slices. As can be seen from the diagram, the variance of the controller load increases with the time slice from 1 to 4. 5 to 12 time slices, controller load variance over 6000, triggered switch migration, and with controller load variance that decreased significantly. After the 13 th time slice, the controller load variance decreases gradually, and no switch migration occurs.