## 5 Designing an NMG Testbed and Numerical Results
We monitor the communication network between NMG endpoints to sniff packets and collect control data using the WinDump sniffing tool. Windump is a TCPDump adaptation for the Windows environment [65]. We measure the mean RTT, \(\mu_{ij}\), between NMG  
Figure 8: We integrate a laptop into the existing system to employ as a VS Server. This enables us to increase the variance of background traffic in the communication channel. Figure 7: An overview of the system diagram. Red links represent communication lines, black links represent power lines, and black dashed links represent analog-to-digital signal conversion paths. The \(R\)s denote the 0.242 \(\Omega\) resistors. We connect NMG endpoints, \(i\), \(j\), and \(k\), using Cisco ISRs and establish a communication network for information exchange between the NMG endpoints. endpoints, \(i\) and \(j\), using a sequence of RTT measurements, \(M+1\), which is represented as \(r_{ij}[0]\), \(r_{ij}[1]\), \(\ldots,r_{ij}[M]\). The mean RTT is calculated as  
\[\mu_{ij}=\frac{\sum_{n=0}^{M}r_{ij}[n]}{M+1}. \tag{2}\]  
The standard deviation of RTT between NMG endpoints, \(i\) and \(j\), is represented as \(\sigma_{ij}\) and measured as  
\[\sigma_{ij}=\sqrt{\frac{\sum_{n=0}^{M}(r_{ij}[n]-\mu_{ij})^{2}}{M}}. \tag{3}\]  
We propose a novel formula to quantify the relative congestion level between NMG endpoints in Equation (4). We represent the relative congestion level between NMG endpoints, \(i\) and \(j\), as \(c\). We consider the following parameters: total transmitted data in bits, \(\alpha_{td}\); maximum available bandwidth in Mbps, \(\Lambda\); experiment duration, \(\tau\); and a constant scale-up coefficient, \(\omega\), which is 100. The relative congestion level is determined as  
\[c=\left(\frac{\alpha_{td}}{\Lambda\times t}\right)\times 100\times\omega. \tag{4}\]  
We evaluate the QoD of NMG control data by measuring the mean and standard deviation of the RTTs at different relative congestion levels. These evaluations are compared with industrial communication response time requirements as tabulated in Table 4. These requirements are specified by the European Telecommunications Standards Institute (ETSI) and the International Electrotechnical Commission (IEC). Communication response time requirements vary, with the IEC defining a 4 ms maximum threshold for protection messages, whereas ETSI specifies a 10 ms threshold. Both standards align with the control message requirement of 10 ms. We illustrate the changes in the mean and standard deviation of RTTs across different relative congestion levels in Figures 9 and 10. Notably, the highest mean and standard deviation of RTTs occur when the communication channel is approximately 50% congested. When TCP is used to deliver VS packets, it leads to higher mean and standard deviation of RTTs compared to other protocols, such as UDP, RTSP, and ICMP, as shown in Figures 11 and 12. This suggests that high-variance bit rate in background traffic results in higher mean and standard deviation of RTTs. We analyse the relationship between the mean of RTTs and the standard deviation of RTTs by computing [PERSON]'s correlation coefficient. A scatter plot in Figure 13 presents the relationship between the mean and standard deviation of RTTs, where the correlation coefficient is computed as 0.89. This suggests that there is a strong positive linear relationship. Further analysis in Figure 14 reveals a [PERSON]'s correlation of 0.84 between the mean and standard deviation of RTTs that exceed the ETSI requirement. This strong positive linear relationship persists when the industrial communication response time requirements are considered. As a result, RTTs exceed industrial requirements by more than 25 times for NMG control data. Greater mean and standard deviation of RTTs are measured when high-variance background traffic is present. These findings support our hypothesis that high-variance background traffic negatively affects the QoD of NMG control data.