## 5 Results and Discussion
### Number of Nodes  
The number of nodes deployed is a crucial factor in planning WSNs because it affects the cost of implementation. Coverage density in a WSN is a crucial metric that measures the number of sensors deployed per unit area. This metric, which represents the number of sensors per square meter, is handy for comparing the efficiency of different methodologies in terms of resources used, regardless of the total size of the deployment areas, and provides direct information on the efficiency of the network in terms of the resources used for coverage. Lower coverage density indicates that fewer sensors are needed to monitor a unit area, which indicates greater efficiency and potentially lower deployment and maintenance costs. Coverage density is calculated by dividing the total number of sensors deployed by \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Mine Size** & **Distribution Function** & **Sensors Minimum** & **Sensors Maximum** & **Standard Deviation** \\ \hline Small & Exponential & 30 & 55 & 4.47 \\ Small & Normal & 20 & 24 & 0.88 \\ Small & Uniform & 19 & 26 & 1.08 \\ Medium & Exponential & 41 & 71 & 4.69 \\ Medium & Normal & 26 & 32 & 1.02 \\ Medium & Uniform & 25 & 33 & 1.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Sensors added for distribution function and mine size. the total area that the network must cover. This formula provides a normalized comparison independent of the network's absolute size or deployment area, allowing networks of different scales to be compared. It is impossible to directly compare the results of the strategy proposed in this work because the tool recreates the accurate and complete structure of the mine. However, comparing the number of nodes deployed in a specific tunnel is possible. Over a tunnel of 180 m without inclinations, [PERSON] and [PERSON] [43] deployed 28 nodes, [PERSON] et al. [51] deployed 29 nodes, while our proposal deployed 29 nodes, in the worst case, using the exponential distribution function, in the main tunnel of 345 m in length with inclinations, guaranteeing the coverage and connectivity requirements. Our results show that the proposed methodology achieves a coverage density of approximately 0.0274 sensors per square meter, while the methods of [PERSON] and [PERSON] and [PERSON] et al. present densities of 0.0346 and 0.0358 sensors per square meter, respectively (see Figure 9). This indicates that our methodology requires fewer sensors to cover the same area, guaranteeing coverage and connectivity, which suggests greater efficiency in network deployment. A slightly larger number of sensors deployed over a greater distance of the tunnel indicates that, despite not prioritizing optimization, our methodology can maintain a comparable sensor density under more complex and realistic conditions. This suggests that our methodology could offer similar or even superior results regarding coverage and efficiency in natural mining environments. Notably, the smaller number of sensors required means a lower cost deployment and reduces the initial hardware investment and network complexity. This reduction can lead to easier maintenance and greater system longevity. This efficient approach is especially advantageous in challenging environments such as underground mines, where installing and maintaining nodes can be costly and logistically complicated. Additionally, by decreasing the number of sensors required to achieve complete coverage, our methodology can decrease the interference between sensors and improve battery life across the network as fewer devices compete for the same power and communication resources. It is essential to emphasize that our methodology is based on real sensing and communication range values. This means that each sensor is configured and located, taking into account the actual limitations and needs of the mine, which can result in a more effective sensor network suitable for the specific conditions of each mine.