# Cyber Physical Systems Dependability Using CPS-IOT Monitoring
## 3 The CPS Dependability Model
### Epidemic Modelling of the CPS-IoT  
As illustrated in Figure 2(a), the states of the nodes of the CPS-IoT can be mapped into epidemic states when considering: (i) The risks and levels of congestion associated with the network collection tree topology and connectivity and (ii) the energy that can be drawn from nodes as a result of such topology and connectivity. As IoT networking uses CTPs, the number of \"children\" carried by a node (node interference), can be translated into an epidemic state expressing the level of contamination of the node. In this paper, two interference thresholds, \(T_{1}\) and \(T_{2}\), have been used to map epidemic states into IoT networking states. Building around the SIR epidemic model, this paper considers the SAR model that uses three epidemic states referred to as Susceptible (safe), Attacked, and Removed statuses. These states are respectively the loose equivalent of the Susceptible, Infected, and Removed states of the SIR model. We define the considered states as follows:  
Figure 3: The epidemic modelling. Susceptible nodes: Are the least or non-interfering nodes in a network. Their total number is denoted by \(S\). Each susceptible node \(n\) is assumed to have weight (level of interference) less than the threshold \(T_{1}\). Attacked nodes: Are highly interfering but still operational nodes. The total number of infected nodes in a network is denoted by \(A\). An infected node is assumed to have weight less than the threshold \(T_{2}\) but at least equal to the threshold \(T_{1}\). Removed nodes: Are nodes that are no longer operational as a result of high levels of interference between themselves. These nodes are also referred to as depleted and their total number is denoted by \(R\). A node is considered to be removed if its interference is at least equal to the threshold \(T_{2}\). Note that the transitions from Susceptible to Attacked (S-to-A) and from Attacked to Removed (A-to-R), may determine the IoT's safety level. From a CPS-IoT safety perspective, high availability translates to a \"healthy\" or \"uninfected\" state, while reliability translates to the ability of a node to accurately and safely carry out its function(s). An analysis of dependability based on the epidemic model proposed in this paper may thus lead to four potential cases depicted in Table 1. Higher migration rates from a state to another are represented by binary values \"1\" while lower migration rates are represented by binary numbers \"0\". * Higher transition rates from a susceptible to an attacked state is an indication of an IoT network with low availability. This is because nodes will move faster from the susceptible (safe) state to the attacked state;
* Lower transition rates from the susceptible to attacked state are an indication of an IoT network with higher availability; that is nodes stay longer in the susceptible state;
* Higher transition rates from attacked to depleted state are an indication of a more reliable IoT network. This is because the infected (attacked) nodes are quickly removed to minimise potential risks to the IoT network;
* Lower transition rates from an attached to removed (depleted) state are an indication of a less reliable IoT network. This is because nodes stay longer in an attacked state, hence increasing the potential risks to the CPS and its IoT network sub-system. Note that as reported in Table 1, the best performance in terms of dependability (safety) is achieved in Case 4. This applies to sensitive applications with hard real-time constraints, which should be deployed with a low migration rate from susceptible to attacked status \(a_{i}\) and a high migration rate from attacked to removed status \(b_{i}\). Such applications will require higher surveillance in terms of anomaly detection and quick response/actuation. For instance, this can be implemented using interference-aware data collection algorithms (such as Least Interference Beaconing Protocol (LIBP) [38]) that can prevent IoT nodes from moving into the attacked state.