# Formation Control Algorithm of Multi-UAV-Based Network Infrastructure
## 5 System Evaluation
### \(\mathcal{D}\) Model Verification  
By using the simulation addressed in previous subsections, we verify the network throughput model of multi-UAV-based network infrastructure. At first, we observe the dynamics of \(\mathcal{D}\), which is the basis of the network throughput models addressed in this paper. To estimate \(\alpha\), \(\beta\) of \(\mathcal{D}(n)\), we run the simulation with a single UAV and the varying number of the terrestrial devices \(|M|\), and measure the network throughput. The devices are spread in the 20 m \(\times\) 20 m area on the ground, and the GCS is located at the center of the ground, which is set to the origin. A single UAV is deployed at \((0,5,5)\), and the devices preliminary receive the IP address included at the subset of the UAV. GCS sends data to all of the devices in 1000 Kbps data rate equivalently, and the average network throughput is calculated by the average received data rate among the devices. Each case is simulated by 10 times with 300 s runtime, and \(|M|\) varies to \(1\leq|M|\leq 60\). Figure 6 shows the simulation result and the analytic solution where \(\alpha=9.8170\) and \(\beta=1.2044\). When applying Equation (5), we observed that \(  
throughput model forecasts the network throughput of the multi-UAV-based network infrastructure with acceptable accuracy, by fitting \(\alpha\) and \(\beta\) with respect to the desired network protocol. To verify our formation control algorithm, we expanded the map size to 500 M \(\times\) 500 M, and increase the number of devices to 100. The GCS is located at the center of the map and the UAVs are initially spread around the GCS with the altitude of 60 M. The parameters \(\alpha,\beta\) are applied to the 9.8170 and 1.2044 respectively, and the directions of the UAVs are calculated per 0.5 s. The terrestrial users are deployed with two-dimensional Gaussian distribution, centering a random location \((x,y)\) on the map. We observed the result of the algorithm working on 15 UAVs and graphically represented in Figure 7.  
In Figure 7a,b, grey circles represent the communication range of the AP (\(R_{AP}\)) on the ground, and the number on the icon of the UAVs are the identifiers. Also, both figures show the stabilized (no oscillation by the forces) formation of the UAVs after 30 s. Even though the distribution of the UAVs in Figure 7a are regular, the actual connections to the terrestrial devices are not equalized (see Figure 7c,e) since the distribution of the devices are focused at nearby of UAV 3 and 4. UAV 10, 12 and 13 does not have any connection to the devices, which results in the redundant usage of the UAVs. On the other hand, the formation with \(F_{coneq}\) shown in Figure 7b, the formation of UAVs is reformed toward the cluster of the devices, while each UAV providing the access network to at least 5 devices. Deploying UAV 2, 3, 4, and 6 nearby the cluster of the devices could more reduce the traffic concentration of the infrastructure. Also, \(F_{coneq}\) dynamically adjusts the altitude of the UAVs to efficiently equalize the congestion as shown in Figure 7d. Through the observation, we verified that the algorithm adaptively controls the formation of the UAVs to reduce the network traffic of the multi-UAV based network infrastructure with various deployment cases of the devices. Figure 6: Comparison of the simulation result and the analytic result of the average network throughput where \(\alpha=9.8170\), \(\beta=1.2044\). To observe the dynamics of the formation algorithm, we performed numerical evaluation while varying the number of the terrestrial devices \(|M|\) from 100 to 300, as shown in Figure 8. For each \(|M|\) value, we performed the formation algorithm 50 times for the case with and without \(F_{conq}\) and recorded \(|C_{i}|\) after the formation is stabilized. Successful coverage ratio in Figure 7(a) is calculated by \(\sum|C_{i}|/|M|\), which results in the ratio of the connected mobile devices and the total devices.