## 5 Application
Apart from \(VN_{1}\), the input data are: \(p_{t}\)--the borderline value of probability of providing connections \(p\) acceptable to the business owner of the network; \(t\)--time (time step) defining how often the network status control procedure is run. In order to save energy consumption of individual nodes, the three types of messages described above can be sent as one collective message. At this stage, the key is the proper selection of the \(t\) parameter, which is responsible for the frequency of sending these messages. This translates into energy consumption by the node. Therefore, the value of this parameter may depend on the assumed level of network reliability, service level agreement, and the current node's battery level. In the next step, the PTC chart is determined for a given topology. On this basis, the current point at which the network is located in terms of phase transition and acceptable risk is determined. Figure 9 illustrates this process. Figure 8: Architecture of the early warning system against loss of consistency. At the moment \(t_{1}\) (Figure 9a), the operating parameters of the system (available number of nodes, their location, and range of transmission) ensure the possibility of maintaining full coherence in the network; i.e., making connections with probability of \(p=1\). Let us assume that the power of transmitters is reduced as a result of system operation due to the depleted node batteries. As a result, the probability is \(p=0.8\) at \(t_{2}\). In this case, the system generates a warning message to the network management system (NMS) system, informing it about deteriorating network reliability. If the power of the transmitters decreases further at the time of \(t_{3}\), the system sends a message about the critical state of the network and the need to take immediate action (e.g., the need to replace the battery). It should be noted that the arbiter is connected both to the MESH network structure using a wireless network and uses a reliable connection (GSM, cable connection, etc.) to the network management system (NMS). The question of how to replace the battery can be implemented in many ways, e.g., by technical staff. A separate issue, discussed later in this article, is how to set the parameter value \(p_{t}\). The second case is considered here (Figure 9b). Compared to the first case, the number of available network nodes dropped as a result of failure directly affecting the shape of the PTC curve. The way the curve shape changes for the interfacial area depending on the number of nodes is presented for sample networks in Figure 6. To maintain consistency, nodes must increase the transmission range. As a result of these events, the network becomes very sensitive to power drops (a very small \"green\" area on the PTC chart) of transmitters and requires relatively much energy for proper operation. In such a situation, the arbiter quickly reports warning (\(t_{4}\)) messages and corrective action will be required. The probability limit \(p_{t}\) can be determined experimentally during system operation. Correct timing is crucial because of the system operation costs. During the interviews with a group of entrepreneurs, the following aspects were identified related to the correct selection of time:  
* Huge and constantly growing costs of maintaining own IT department responsible for maintaining the company's IT systems, including the considered network system [46]. In order to reduce operation costs, companies use outsourcing of ICT services. Generally, the costs of such a service include: cost of maintaining engineers' readiness (fixed monthly fee), cost of response time (fixed monthly fee), cost of work performed on site (variable man-hour charge), maintenance of spare parts warehouse (fixed fee monthly). If the company operates a critical communication system, it strives to ensure that the response time is as short as possible (maximum 4 h), and that the outsourcing company maintains all types of spare parts. In this case, the value \(p_{t}\) should be close to 1 (e.g., 0.9).