# Automated Methodology for Dependability Evaluation of Wireless Visual Sensor Networks
## 5 Results and Discussion
### Example 1  
In order to highlight the proposed approach, first we evaluate the dependability of a small network, composed by a sink node (\(Snk\)), a scalar node (\(S1\)) and a visual node (\(V2\)), as shown in Figure 10(a). The visual node is represented by a circle attached to a triangle, which is the camera's FoV. The system uses FLOODING strategy and considers the occurrence of 1 hardware failure per year and one link failure per every two days, which implies hardware and link failure rates as \(\lambda_{hw}=1.1416\times 10^{-4}/\)h and \(\lambda_{lk}=0.02083/\)h, respectively. In addition, it is considered that it takes 72 h to repair the hardware and 15 min to a link to be reestablished, which implies the hardware and link repair rates as \(\mu_{hw}=0.013894/\)h and \(\mu_{lk}=4/\)h, respectively. It is important to notice that the assignment of values to link failure and repair rates depends on several aspects, e.g., network physical layer, communication environment, network deployment, etc. However, since the goal of the paper is to present a methodology to evaluate and compare different network implementations, the method to define these rates is assumed as secondary in this paper. Since we have only one visual node, Algorithm 1 identifies node \(V2\) as the unique one responsible for the monitoring. Therefore, the network failure condition must be \(NFC=V2\), i.e., if the node \(V2\) fails, the visual application fails. Then, the network topology is known by the Algorithm 4, and it is represented by the following adjacency matrix:  
\[mAdj=\left[ \begin{array}{ccc}1&1&0\\ 1&1&1\\ 0&1&1\end{array} \right]. \tag{8}\]  
This means that the sink (index 1 of the matrix) is connected only to the scalar node (index 2 of the matrix), whereas the scalar node is also connected to the visual node (index 3 of the matrix). This information is used by Algorithm 5 to find all paths from the NFC devices (\(V2\), in this case) to the sink, by a depth-first search (Algorithm 6). There is only one path with this feature, which is \(V2\to L2\to S1\to L1\to Snk\), where \(L1\) is the link connecting \(Snk\) and \(S1\), and \(L2\) is the link connecting \(S1\) and \(V2\). Thus, Algorithm 7 will generate a Fault Tree that represents this behavior, as shown in Figure 10(b). Notice that the logic expression indicates that if any link (\(lk_{1}\), \(lk_{2}\)) or device (\(fc\_Dev_{0}\), \(fc\_Dev_{1}\), \(fc\_Dev_{2}\)) fails, the path will be interrupted and the application fails. Additionally, as this system has only one device associated with the NFC and one path from this device to the sink, then the AND-gate related to the failure condition of combinations (Figure 8(b)) has only one input, and the same happens to the OR-gate related to the failure condition of paths (Figure 8(c)). These gates were replaced by a bypass connection in the Fault Tree structure. The generated Fault Tree (SHARPE) model can be seen in Listing 1. Notice that each event (Lines 2-9) is represented by an availability function. For instance, in Line 9, there is a reference to the availability of the Markov Chain model (\(BT\_model\_Dev0\)) of the sink's battery (\(Dev0\)). This model is described in Listing 2. Finally, Listing 3 shows how to invoke the availability evaluation of the system. The evaluation period is \(T=150\) h, with a time step of \(t_{s}=15\) min (0.25 h) (Line 2). All of these models have been generated by Algorithm 7. Figure 12 shows the graphical output, indicating that, after 50 h of execution, the availability of the system is slightly higher than 86%. Figure 11: (**a**) system topology and (**b**) its Fault Tree (FT).