## 5 Simulation Results
### Reliability Maximization with Latency Constraints  
In the following, some comparison results of the joint placement problem between OEAJ, SACA, JPKM, and SAPKM are shown. The joint gateway and controller problem aims to maximize the network reliability with network latency constraints. Since satellite gateways and SDN controllers are deployed on certain switches separately, the latency plays a significant role in system performance. On the other hand, the controller-switch latency also affects the efficiency and effectiveness of the system performance, especially for supporting consistency. Thus, both controller-switch links and controller-gateway links determine the network reliability. As mentioned above, the gateway-switch latency is defined as the network latency, which mainly depends on the placement of satellite gateways. Then, we investigated the joint placement problem using different algorithms, i.e., SACA, JPKM, and SAPKM, and made comparisons on the average network reliability, running time, and average/maximum controller-switch propagation latency. It is noted that JPKM is defined as the initial status of SAPKM, which means that JPKM only implements the first four steps in Algorithm 2. Figures 8 and 9 analyze the effect of the number of controllers on network latency and controller-switch latency, respectively. Simulation results in the topology Chinnet are shown with three gateways deployed. Figures 10 and 11 depict comparisons of both the overall running time and the overall average network reliability on the above topologies. Figure 8: Comparisons of the overall network latency in Chinnet. Figure 8 depicts the comparison of both maximum and average network latency in Chinnet, where the dotted lines represent the maximum network latency and the solid lines represent the average network latency. Since the purpose of solving the joint placement problem is to improve network reliability with network latency constraints, as long as the constraints are met, the proposed algorithm with better reliability performance is more advantageous than others. Apparently, JPKM had the best-settled latency performance among the joint placement algorithms when the number of controllers varied. Although JPKM outperformed SAPKM and SACA in Figure 8, one can observe that  
Figure 11: Comparisons of the overall average network reliability. Figure 10: Comparisons of the overall running time. Figure 9: Comparisons of the overall controller-switch latency in Chinnet. SAPKM had better performance than SACA on both maximum and average network latency. Since maximizing the network reliability adjusts the placement of both gateways and controllers, the latency performance of SACA and SAPKM fluctuated as the number of controller increased. Figure 9 also shows a monotone decreasing trend of controller-switch propagation latency with an increasing number of controllers, where the dotted lines and the solid lines represent the maximum and the average controller-switch latency, respectively. Therein, SAPKM surpassed on average controller-switch latency when \(m\) was greater than four, while JPKM surpassed when \(m\) was larger than six. Besides, SACA always had the largest maximum controller-switch latency, which demonstrates the uneven distribution of controllers. Both JPKM and SAPKM ultimately obtained better average controller-switch propagation latency than that of SACA. Another virtue of both JPKM and SAPKM was the much lower maximum controller-switch propagation latency than that of SACA. The distribution of controller-switch latency demonstrated that the joint placement solutions derived from SAPKM were more reasonable than those of SACA. Figure 10 demonstrates the comparison results of the overall running time in different topologies when the number of gateways was two and the number of controllers four. It is evident that SAPKM cost much less running time than SACA, with less than 1 ms to converge, while SACA cost hundreds of ms to converge, not to mention OEAJ.