# Multi-Controller Deployment in SDN-Enabled 6G Space-Air-Ground Integrated Network
## 4 Conclusions  
Aiming to solve the problems of a large number of nodes and dynamic changes in the network topology of the SDN-based hierarchical space-air-ground integrated network scenario, this paper first constructs a delay model, a load model, and a loss function model. The loss function model is defined by two factors, namely the propagation delay from the controller to the switch node and the load of the controller. Then, a multi-control deployment strategy based on simulated annealing is proposed, and a strategy for dynamic switch migration with the change in time slice is proposed. In the multi-control deployment strategy, the loss function is used as a measure of algorithm convergence. In the switch  
Figure 11: The running times of different algorithms vary with the number of switch nodes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Constellation Name** & **Altitude (km)** & **Orbital Planes** & **Satellites per Plane** & **Total Number of Satellites** \\ \hline Walker 1 & 580 & 4 & 43 & **172** \\ Walker 2 & 550 & 11 & 22 & **242** \\ Walker 3 & 580 & 4 & 43 & 172 & **414** \\ Walker 3 & 550 & 11 & 22 & 242 & \\ Hybrid orbit constellation & 570 & 36 & 20 & 720 & **786** \\ Walker 4 & 780 & 6 & 11 & 66 & **1584** \\ Walker 4 & 550 & 72 & 22 & **1584** & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Detailed parameters for different constellations. migration strategy, the introduction of the controller load variance is used as a condition for judging whether the controller load satisfies the balance. Finally, the experimental part of this paper compares and analyzes the changes in controller load and average delay under different numbers of controllers, and a specific deployment plan is given under the condition of specifying the maximum delay and maximum controller load. In addition, to verify the reliability of the switch migration strategy, a comparison experiment before and after the switch migration load was also conducted. To verify the superiority of the algorithm, a comparison experiment was carried out with the two algorithms of n-k-means and OCLDS in terms of the load performance and running time of the controller, and the experimental data were all derived from reliable data simulated by STK. The results show that the algorithm in this paper improves the load performance of the controller by about 7.71% compared with the other two algorithms. Our future work will introduce the vehicle and UAV into our SAGIN infrastructure [35], and discuss the mobile controller equipped on the vehicle and/or UAV to fulfill the service requirements from ground and space area. Conceptualization, C.C., Q.P. and Z.L. ; methodology, C.C. and Z.L. ; software, Z.L. ; validation, C.H. ; formal analysis, C.C. ; investigation, J.J.; resources, C.C., C.H. and Z.L. ; data curation, Y.J. ; writing original draft preparation, Z.L. ; supervision, C.C. ; project administration, Q.P. ; funding acquisition, C.H. and Q.P. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Key Research and Development Program of China (2020 YFB1807500), the National Natural Science Foundation of China (62072360, 62001357, 61672131, 61901367), the key research and development plan of Shaanxi province (2021 ZDLGY02-09, 2020)Q-844), the key laboratory of embedded system and service computing (Tongji University) (ESSCKF2019-05), Ministry of Education, Xi'an Science and Technology Plan (20 RGZN0005) and the Xi'an Key Laboratory of Mobile Edge Computing and Security (201805052-ZD3 CG36). Not applicable. The data presented in this study are available on request from the corresponding author. These authors would like to thank the China Electronics Technology Group to provide some orbital statistics. The authors declare no conflict of interest. The following abbreviations are used in this manuscript: