## 4 Results and Discussion
### Initial Tests and Result Collection
This test introduced a cellular network component to these experiments that requires additional cellular session establishment, with more restricted network resources available for uplink communications, especially in terms of throughput, and adds additional network segments and route hops through the cellular provider's backhaul network before once again reaching our University's network edge and its access control mechanisms. For this test, 410 samples were taken during our experiments. From the results presented in Figure 9, we can see that the latency nearly doubled compared to the previous test, averaging 115 ms for the total request duration. We also observe an increase in outliers that reach as high as a 300 ms delay, which is approaching concerning levels of delay for smooth telerobotic operation. This illustrates the need for telerobotics research to consider remedies to make telerobotics tolerant to spurious large latency spikes. Table 3 presents the mean, median, standard deviation, and confidence interval of the round-trip time. The mean of the samples collected is 115.381 ms, which shows the latency reaching levels that would be noticeable to the operator. Given that the median is 107.515 ms, a nearly 8 ms difference, the test data contain more outliers with higher values than previous tests and contain a larger latency spread. Due to this, the standard deviation \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Round-Trip Time (ms)**} \\ \hline Mean & 58.459 \\ Median & 57.455 \\ Standard Dev. & 3.629 \\ Confidence Int. & 0.223 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Round-trip time of Lab Wi-Fi-to-University network connection scenario including VPN. Figure 9: Box plot of latency from Mobile Hotspot-to-University network connection scenario including VPN. is 30.577 ms, and the 95% confidence interval is 2.960 ms, giving us a range of 112.421 ms to 118.340 ms. The final test conducted for the experiments on the operator's control latency was a connection from VTT in Finland to the University of Nebraska in the United States, with both locations shown in the map in Figure 10.  
This test provided a substantial challenge to the reliability of the control scripts and video stream reliability, as additional network routes are added through a transatlantic Internet connection. However, both VTT and the University of Nebraska each have reliable, high-speed network infrastructures, and consequently, our tests showed high reliability of the overall control elements, as shown in Figure 11. These results present the latency of 53 movement request measurements taken during this experiment. The average total request time increases significantly. However, there is increased reliability compared to the previous cellular test. This test also shows the negligible effect of the robot's processing time on the system's overall request time. With the increased client-to-host round-trip time, our control scheme only sends four commands per second to ensure valid execution of the previous command. This slow request interval limit may not be sufficient in some use cases, illustrating the need for complex \"request debouncing\" techniques to be implemented to ensure stable and reliable telerobotics controls. Similar to our previous tests, Table 4 presents the statistical analysis of the tests conducted for this network. The mean value is 240.769 ms, and the median is 240.316 ms, which shows a highly reliable network without much variation. Given the additional network complexities that were added with this test, successful telerobotics operations would require high-reliability network connections on both the operator and robot sides. We also see a much lower standard deviation than the previous test of only 1.714 ms, which does indicate some variance within the measured latency. The calculated 95% confidence interval is 0.857, giving a range of 239.912 ms to 240.855 ms.  
Figure 10: A map showing the endpoint locations of our overseas tests between UNL and VTT.