# Model for Quantifying the Quality of Secure Service
## 5 Case Studies of Multi-Channel QoS
### Eight-Channel Network  
The third example presents a communication network with eight discrete, heterogeneous channels. In this example, \(n=8\), \(\sigma=3\) listeners, and \(\rho=3\) disruptors. The original message is fragmented into eight equal portions, \(\{f_{1},f_{2},...,f_{8}\}\), of which \(\{f_{1},f_{2}\}\) are transmitted on Channel 1, \(\{f_{2},f_{3}\}\) on Channel 2, \(\{f_{3},f_{4}\}\) on Channel 3, and so on. Here, \(AL=0.25\), and \(DF=2\) because each fragment is sent twice. Table 5 shows the theorized input for the eight-channel network.  
Of particular note, Table 5 has the same input as Table 4 for Channels 1-3, and other values for Channels 4-8, although with different results [13]. The only difference from the three-channel case is that, with eight channels, the message is fragmented across more channels, causing the confidentiality and integrity to increase. The average values for \(P(int)\), \(P(dcr)\), and \(P(dco)\) are the same for the single-channel, three-channel, and eight-channel networks, although the average \(P(I)\) and \(P(C)\) are notably different.  
As expected, the single-channel network has the lowest theorized QoSS values. With a slightly higher percentage of listeners, the eight-channel network has a slightly higher \(P(I)\) and correspondingly lower \(P(C)\) than the three-channel network [14]. Similarly, the average values for \(P(n)\), \(P(s)\), and \(P(inj)\) are the same for the single-channel, three-channel, and eight-channel networks, yet the \(P(c)\) and \(P(I)\) are significantly different.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \(Channel\) (\(n\)) & \(P_{n}(int)\) & \(P_{n}(dcr)\) & \(P_{n}(dco)\) & \(P_{n}(l)\) & \(P_{n}(C)\) & \(P_{n}(n)\) & \(P_{n}(s)\) & \(P_{n}(inj)\) & \(P_{n}(c)\) & \(P_{n}(l)\) \\ \hline
1 & 0.5 & 1 & 1 & 0.1667 & 0.8333 & 0.25 & 1 & 0.33 & 0.2219 & 0.7781 \\
2 & 0.75 & 1 & 1 & 0.2500 & 0.7500 & 0.25 & 1 & 0.4 & 0.2248 & 0.7752 \\
3 & 0.25 & 1 & 1 & 0.0833 & 0.9167 & 0.25 & 1 & 0.26 & 0.2191 & 0.7809 \\ \hline Avg & 0.5 & 1 & 1 & 0.1667 & 0.8333 & 0.25 & 1 & 0.33 & 0.2219 & 0.7781 \\ \hline \end{tabular}
\end{table}
Table 4: Input and output values for a three-channel network.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \(Channel\) (\(n\)) & \(P_{n}(int)\) & \(P_{n}(dcr)\) & \(P_{n}(dco)\) & \(P_{n}(l)\) & \(P_{n}(C)\) & \(P_{n}(n)\) & \(P_{n}(s)\) & \(P_{n}(inj)\) & \(P_{n}(c)\) & \(P_{n}(l)\) \\ \hline
1 & 0.5 & 1 & 1 & 0.1875 & 0.8125 & 0.25 & 1 & 0.33 & 0.2402 & 0.7598 \\
2 & 0.75 & 1 & 1 & 0.2813 & 0.7188 & 0.25 & 1 & 0.4 & 0.2414 & 0.7586 \\
3 & 0.25 & 1 & 1 & 0.0938 & 0.9063 & 0.25 & 1 & 0.26 & 0.2389 & 0.7611 \\
4 & 0.2 & 1 & 1 & 0.0750 & 0.9250 & 0.25 & 1 & 0.05 & 0.2353 & 0.7647 \\
5 & 0.35 & 1 & 1 & 0.1313 & 0.8688 & 0.25 & 1 & 0.1 & 0.2361 & 0.7639 \\
6 & 0.4 & 1 & 1 & 0.1500 & 0.8500 & 0.25 & 1 & 0.2 & 0.2379 & 0.7621 \\
7 & 0.7 & 1 & 1 & 0.2625 & 0.7375 & 0.25 & 1 & 0.6 & 0.2449 & 0.7551 \\
8 & 0.85 & 1 & 1 & 0.3188 & 0.6813 & 0.25 & 1 & 0.7 & 0.2467 & 0.7533 \\ \hline Avg & 0.5 & 1 & 1 & 0.1875 & 0.8125 & 0.25 & 1 & 0.33 & 0.2402 & 0.7598 \\ \hline \end{tabular}
\end{table}
Table 5: Input and output values for an eight-channel network.