## 5 Results and Discussion
### Distributions Performance  
Evidence of work has yet to determine the performance of the distribution functions used in random deployment for underground mining. The selection of probabilistic distributions for random implementations depends on the application and the system's objectives to be deployed. Coverage, connectivity, energy consumption, and cost are some objectives that can be chosen to consider a probability function. It is also possible to use combinations of distributions or customize distributions according to the application's needs. The performance of three distribution functions in terms of number of nodes was evaluated. The proposed methodology was applied in two mines generated from coordinates obtained of the total station. The distribution functions considered were exponential, normal, and uniform. Figure 7a,b show each event's relative frequency of occurrence, with its corresponding fitting curve, providing a comprehensive visualization of the patterns observed in the data for exponential, normal, and uniform distributions. Figure 6: Deployment proposed by [PERSON] and [PERSON]. Image from [43]. As can be seen, the nodes added in the second step, random deployment, using the distribution functions, follow the expected pattern. According to the distribution function used in the random deployment, it is possible to calculate the number of nodes necessary to cover a RoI in underground mines. The number of nodes allows for determining the type of node sensor and the cost deployment, which is information suitable for planning the safety and health system and operational and financial planning. Figure 8a,b show the number of nodes by exponential, normal, and uniform distributions, where the number of each bar represents the relative frequency of the number of sensors added. For example, in Figure 8a, for the exponential distribution, 24 times 30 sensors were assigned. Figure 7: Data distribution and fitting curve. (**a**) Graph of data distribution and fitting curve for small-sized mine. (**b**) Graph of data distribution and fitting curve for medium-sized mine. Table 3 summarizes the ranges of sensors added and the variability associated with each probability function in small and medium-sized mines. An increase in the minimum and maximum number of deployed sensors is observed when moving from small to medium-sized mines, which is consistent with the expectation that larger mines would require more sensors to achieve adequate coverage. Figure 8: Number of nodes by distribution function. (**a**) Number of nodes chosen by distribution function (exponential, normal, uniform) for small-sized mine. (**b**) Number of nodes chosen by distribution function (exponential, normal, uniform) for medium-sized mine. In small mines, the exponential function showed the most significant variability in the number of sensors added, with a difference of 25 sensors between the minimum and maximum and a standard deviation of 4.47, which could reflect an adaptability in the density of the deployment in response to topological variations within the mine. The normal and uniform distribution presented less variability, indicating a more controlled and predictable deployment. When increasing the mine size to medium, all probability functions showed an increase in the number of sensors deployed, particularly notable in the exponential function, where the minimum number of sensors increased by 11 and the maximum by 16, with a slight rise in the standard deviation. This change may imply that the exponential function is more sensitive to mine size, adjusting the number of sensors more steeply to maintain deployment effectiveness. The uniform distribution function in medium-sized mines also presented an increase in variability (standard deviation of 1.43), suggesting that, although the deployment attempts to be homogeneous, there are factors within medium-sized mines that introduce a more excellent dispersion in the number of sensors.