# Extending the Quality of Secure Service Model to Multi-Hop Networks
## 4 Case Studies of Multi-Channel and Multi-Hop QoS
### 3-Channel, 3-Hop Network  
This final example incorporates the previous two examples to create a realistic network, to highlight the order needed to reduce the complexity, and to demonstrate the QoS analysis process. The final example features three channels, two of which have two intermediate nodes and the third with only one intermediate node, thus creating a three-channel, multi-hop network, as shown in Figure 8. In the same manner in which the network shown in Figure 4 may utilize three different interconnecting channels for each of the intermediate links and the network shown in Figure 6 may utilize three different interconnecting paths or media for each channel, so too may Figure 8 utilize different interconnecting channels, which may feature different distances, architectures, or technologies, for each of the eight different, independent links. Most important is the fact that the end-user must remain agnostic of the underlying architecture.  
In this example, and providing continuity with the example network shown in Figure 4, there is \(\rho=1\) listener and \(\sigma=1\) disruptor with access to the network, and they may have access to any of the channels. The data are fragmented across the three channels such that the \(AL\), the average percentage of the message on any of the channels, is 0.66 and the \(DF\), the average number of times a given fragment is transmitted, is 2. The QoS is again similar to all of the previous examples with some minor variations in the characteristics to highlight the possibility that each of the eight different, independent links feature different distances, architectures, or technologies.  
The first step, as detailed in Section 3.4, calculates the QoS for each independent link. The next step eliminates the intermediary nodes from each of the three channels. The final step consolidates the multi-channel architecture into one point-to-point connection. With the single point-to-point connection, it becomes trivial to compare the QoS characteristics of Figure 8 to the more simple system architectures presented in Figures 3, 4, and 6 and their respective single-channel, point-to-point equivalents.  
Based on the comparison of the equivalent QoS characteristics of Figure 8 to the QoS characteristics of Figures 3, 4, and 6, there are several details that must be highlighted. The example that has, after reduction, the highest probability of confidentiality and probability of integrity is Figure 6 primarily because it employs three channels that feature message fragmentation and duplication across the three available channels. It is observed that simply splitting the data across the available channels, with some duplication, provides a significant increase to the available security of the system, despite the number of potential listeners and disruptors. Conversely, the example that has, after reduction, the lowest  
Figure 8: A Three-Channel, Three-Hop Network with QoS Characteristics and Equivalent Network Characteristics.  
probability of confidentiality and probability of integrity is Figure 4 because it employs a single channel with two intermediate nodes. The intermediate nodes provide opportunities for adversarial intervention in the transmission. Furthermore, since there is only one channel, there is no benefit of message fragmentation and duplication, and any listener or disruptor has just the one channel to target. As an adequate median example, Figure 8 demonstrates the improved QoS characteristics of utilizing multiple channels and message fragmentation and duplication across the three available channels while also demonstrating some of the potentially degraded QoS because of the multiple intermediary nodes.