## 5 Application
Early failure prediction, based on the proposed algorithm, will extend the response time and eliminate the need to maintain full hot stock of spare parts. This will significantly reduce the fixed operating costs of the system. Figure 9: Illustration of the algorithm operation in Figure 8: (**a**) reduction of transmission power; (**b**) reduction of available network nodes. * Some companies base operations on a risk management model. In this case, the model analysis enables precise determination of the value \(p_{t}\), which in turn allows achieving the level of risk acceptable for the entire system (direct connection of the value \(p_{t}\) with the residual risks). In both cases presented in Figure 9, for a considered MESH network, recovery from critical state \(t_{3}\)\(\to t_{2}\) and \(t_{6}\to t_{5}\) could be achieved by placing additional nodes in the communication system. In the first case, this would improve the connection parameters of the system at a lower radius \(r\), and in the second case, this would reduce the power of transmitters and extend their operating time. The optimal location to place the transmitter can be determined on the basis of a simulation based on the \(VN_{1}\) network model. After determining the location, the previously prepared transmitter (provisioning) can be set in a given location by unqualified technical staff. Figure 10 shows the response areas used by the arbiter for the exemplary situations shown in Figure 7. The warning area starts when the radius value falls below \(r\) = 0.51 (and \(p<1\)). If the \(p_{t}\) parameter value falls below 0.5 (\(r<\) 0,3), the network may lose coherence in the case of a small change in several parameters. Below the radius value of 0.28, an adverse change in any parameter will result in the loss of integrity of the entire network. During the simulation, many tests were carried out for various MESH network structures with different numbers of nodes and different radius values. Figures 11 and 12 present select results from these simulations. In these two cases, variants of the MESH network topology with 100, 150, 250, and for a broader analysis, 1000 nodes, were taken into account. The choice of a larger number of nodes resulted from the need to compare potential results with those previously obtained for a smaller number of nodes (Figures 6 and 7). The simulations carried out in these cases included two radius values \(r\) = 0.1 (Figure 11) and \(r\) = 0.4 (Figure 12). As can be seen in particular in Figure 12, an increase in radius value would not be significant at a high saturation of a given area with nodes, since the stable operation phase associated with a 100% probability of ensuring network connectivity remains unchanged in the range from about 0.2 to 1.0. Therefore, the previous statement is confirmed that the number of nodes directly affects the phase transformation process. Therefore, the interfacial area is much narrower (Figures 11 and 12b,d,f,h) and the slope of the graph is much steeper, so the warning and critical areas are much smaller, which forces a quick response from the NMS. Presenting a greater number of cases, e.g., 300, 500, or 750, or over 1000 nodes, will not bring anything new, as the results obtained are similar to those presented in Figures 11 and 12. Analyzing the results obtained in these graphs, it can be observed that the rapid reduction in radius when the system is in the interphase can cause immediate network inconsistency. Therefore, comparing Figures 6, 7, 11 and 12, it can be stated that in the case of a small number of nodes, the stable operation phase is shorter, which is associated with higher energy consumption, while in the case of a large number of nodes, the radius value can  
Figure 10: Areas identified by the arbiter in relation to the cases in Figure 7.  
be significantly reduced, but then infrastructure is much more sensitive to changes in the value of transmitter's power.