# Cyber Physical Systems Dependability Using CPS-IOT Monitoring
## 5 Performance Evaluation
### Inbound Surveillance  
We conducted a number of simulations to determine a performance pattern of the diffusion sets under varied conditions. To study the effect of inbound surveillance, we considered four experimental scenarios corresponding to four diffusion sets. In the first \(I_{1}\) we set \(\{S=95,A=5,R=0\}\), this depicts an ideal initial condition where most of the nodes are in the safe state and batteries are mostly fully charged. For \(I_{2}\), \(I_{3}\), and \(I_{4}\), we set \(\{S=70,A=30,R=0\}\), \(\{S=60,A=40,R=0\}\), and \(\{S=50,A=50,R=0\}\) respectively representing a system with 70%, 60%, and 50% of their nodes in safe states. The settings of \(I_{2}\) and \(I_{3}\) were similar, hence only that of \(I_{2}\) is reported for the purpose of brevity. Figure 7 depicting three of these four scenarios reveal how inbound surveillance can be achieved by tracking the evolution in time of the epidemic curves. Scenario \(I_{1}\) is depicted by Figure 7a while Figure 7b illustrates scenario \(I_{2}\). Scenario \(I_{4}\) is depicted by Figure 7c. Different other scenarios depicted by different epidemic curves can emerge from the inbound surveillance to reveal different network conditions when monitoring the CPS-IoT. Susceptible states: In all three diffusion sets, a 'birth-decrease' pattern was observed where the number of susceptible nodes gradually reduces as nodes transit from the suscep \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline N & Total number of nodes & 100 \\ \hline m & Number of diffusion sets & 4 \\ \hline \(S_{i}^{0}\) & Initial number of susceptible nodes in set \(i\) & \(S_{1}^{0}=95\), \(S_{2}^{0}=70\), \(S_{3}^{0}=60\), \(S_{4}^{0}=50\) \\ \hline \(A_{i}^{0}\) & Initial number of attacked nodes in set \(i\) & \(A_{1}^{0}=5\), \(A_{2}^{0}=30\), \(A_{3}^{0}=40\), \(A_{4}^{0}=50\) \\ \hline \(R_{i}^{0}\) & Initial number of removed nodes in set \(i\) & \(R_{1}^{0}=0\), \(R_{2}^{0}=0\), \(R_{3}^{0}=0\), \(R_{4}^{0}=0\) \\ \hline \(\lambda_{ij}\) & Transmission rate from \(S_{i}\) to \(A_{j}\) & \(\lambda_{12}=0.04\), \(\lambda_{21}=0.03\), \(\lambda_{ij}=0\), \\  & with \(i>2\) or \(j>2\) \\ \hline \(\rho_{ij}\) & Transmission rate from \(A_{i}\) to \(R_{j}\) & \(\rho_{12}=0.01=\rho_{21}\), \(\rho_{ij}=0\), with \(i>2\) or \\  & & \(j>2\) \\ \hline \(b_{i}\) & Migration rate from \(S_{i}\) to \(A_{i}\) & gamma random distribution \\ \hline \(c_{i}\) & Migration rate from \(A_{i}\) to \(i\) & \(c_{1},c_{2},c_{3},c_{4}=0.02\) \\ \hline \(\beta_{i}\) & Susceptibility of a node in diffusion set \(i\) & \(\beta_{1}\), \(\beta_{2}\), \(\beta_{3}\), \(\beta_{4}=0.11\) \\ \hline \(\gamma_{i}\) & Infectiousness of a node in diffusion set \(i\) & \(\gamma_{1}\), \(\gamma_{2}\), \(\gamma_{3}\), \(\gamma_{4}=4.0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Diffusion model’s parameters. tible to infected (attacked or removed). In Figure 7a, it took about 60 s for all susceptible nodes to be transited to other states, while it took about 35 s in scenario 2 and only 20 s in the third scenario. Attacked states: Across all scenarios, a 'birth-growth-decrease' was observed at the attacked state. As the interference level on susceptible nodes increased (as a result of accepting more child nodes), their numbers reduced until they reached the threshold (\(T_{1}\)), above which they migrated to the attacked state. In scenario 1, the number of susceptible and attacked nodes were equal (50 each) after about 20 s, with the attack nodes peaking at 50 s. It is important to note that at its peak, there were only about 70 nodes in the attacked state. This is because some nodes had migrated directly to the removed state. Removed states: A 'birth-growth-plateau' pattern was observed in all scenarios. Here the number of removed (battery depleted) nodes initially rose quickly until it equaled the number of attacked, after which the growth rate reduced slightly.