## 4 Results and Discussion  
### Initial Tests and Result Collection  
For each test outlined in Section 3, statistical analyses of the gathered results were performed, including the mean, median, standard deviation, and 95% confidence interval for each measured latency. Each measurement shown in Figure 2 was collected for each of the targeted network scenarios. The results for the wired LAN scenario are shown in Figure 7, which presents data from 8730 samples taken during this experiment. From these results, we can see that the robot's IK solver contributed the highest latency for the total request duration, while the [PERSON] robot accepted movement commands with negligible latency. Table 1 presents the mean, median, standard deviation, and confidence interval of the round-trip time. The confidence interval for this analysis was set at 95 percent. The observed mean latency was 6.616 ms, which indicates that in this scenario, we could achieve a very low latency that also remained low and consistent throughout the entire test. None of the measured samples exceeded 18 ms, and these samples were influenced by the IK solver time. The 95% confidence interval (CI) is 0.3966, giving us a range of 6.220 ms to 7.013 ms. These results show a high level of reliability within the LAN test and, similarly, high reliability of the robot in responding to movement commands. Finally, this test confirmed that the robot reliably handled the bounding box controls for its operating area, with no failures observed by the IK solver. Figure 7: Box plot of latency over University network. Figure 8 presents the collected data for the Lab Wi-Fi-to-University network connection scenario, including the use of the VPN. A total of 1019 samples were recorded during this experiment. The round-trip time and total request duration noticeably increase in value compared to the wired LAN scenario. Most importantly, we observe that the impact of the network scenario change and corresponding latency increase do not appreciably influence the total duration of the static control loop elements between the host and the robot when compared to the previous test. However, this test shows the impact that a network topology utilizing access control, specifically a VPN, can have on an application's end-to-end latency. While the test was conducted at the same physical location, the latency is over 8 times larger than what we observed during the initial wired LAN test. This is, however, a necessary component for telerobotics, as access control mechanisms help ensure the safety and security of the robot against malicious actors. Table 2 presents the corresponding mean, median, standard deviation, and confidence interval of the round-trip time. The mean latency measured is 58.459 ms, which is still below the previously recommended 100 ms for critical applications such as telesurgery [16]. The median is 57.455 ms, a difference of 1 ms from the mean, which shows that the data are consistent throughout the samples. The standard deviation is 3.628, from which we can conclude that there is slightly more variance in the samples we collected than in the previous test. The 95% confidence interval is 0.222, which gives a range of 58.237 ms to 58.681 ms. These results show that implementing a VPN, while resulting in increased latency, does not introduce enough latency to make telerobotics infeasible. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Round-Trip Time (ms)**} \\ \hline Mean & 6.617 \\ Median & 5.667 \\ Standard Dev. & 1.357 \\ Confidence Int. & 0.397 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Round-trip time in the wired non-VPN University network connection scenario. Figure 8: Box plot of latency for Lab Wi-Fi-to-University network connection scenario including VPN. With the testing of the VPN-controlled network access over Wi-Fi completed, the same test was performed with a cellular hotspot for the client connection, as opposed to the University Wi-Fi network.