## 3 Methodology
the same rate of increase) until 180 s. The number of virtual users at a given time, \(\alpha(t)\), can be expressed as follows:  
\[\alpha(t)= \begin{cases}\beta t&\text{se }0<t\leq 60,\\ 60\beta&\text{se }60<t\leq 120,\\ -\beta t+180\beta&\text{se }120<t\leq 180,\\ 0&\text{se }t>180,\end{cases}  \tag{4}\]  
where \(\beta\) is the maximum number of virtual users that the load profile can reach. Tests were carried out with 30 different values for \(\beta\), where each \(k\)-th value can be expressed as \(\beta_{k}\in{1,3,5,\ldots,57,59}\) for \(k=1,2,\ldots,30\). The tests were repeated three times for each \(k\)-th value of \(\beta_{k}\), totaling 90 experiments. The decision to use three repetitions was meticulously based on a comprehensive statistical analysis. This analysis aimed to determine whether the \(x^{\text{cpu}}(n)\), \(x^{\text{TP}}(n)\), and \(m^{\text{P}}(n)\) measurements from each experiment for each \(k\)-th \(\beta_{k}\) value were significantly different. To ensure that the correct hypothesis test was applied, the Kolmogorov-Smirnov test was initially conducted on each dataset to determine whether the distributions were normal. Checking for normality is crucial, as it determines whether the data should be analyzed using a parametric test such as ANOVA or a nonparametric test such as Kruskal-Wallis [38; 39; 40]. Following the Kolmogorov-Smirnov test, it was observed that all \(p\)-values were below 0.05 for every experiment across all \(\beta_{k}\in{1,3,5,\ldots,57,59}\) load values, indicating that the distributions of the variables analyzed (\(x^{\text{cpu}}(n)\), \(x^{\text{TP}}(n)\), and \(m^{\text{P}}(n)\)) did not follow a normal distribution. The average \(p\)-value was around \(1\times 10^{-38}\), reinforcing the conclusion that the normality assumption should be rejected. Based on these results, the nonparametric Kruskal-Wallis test was chosen to assess whether there were significant differences between the repetitions of the experiments [38; 39; 40]. The Kruskal-Wallis test was applied to each replication experiment (\(x^{\text{cpu}}(n)\), \(x^{\text{TP}}(n)\), and \(m^{\text{P}}(n)\)) across all \(\beta_{k}\in{1,3,5,\ldots,57,59}\) load values. The Kruskal-Wallis test determines whether there are statistically significant differences between the medians of two or more independent groups. It starts with the null hypothesis (\(H_{0}\)) that all samples come from the same distribution, meaning that there is no significant difference between the groups. In the event that the \(p\)-value from the test is lower than the significance level (\(p<0.05\)), the null hypothesis is rejected, indicating that at least one of the groups has a different distribution. As the data distributions were abnormal, Kruskal-Wallis represents the appropriate choice for this type of analysis [40]. The results of the Kruskal-Wallis tests showed that the mean \(p\)-value for the \(x^{\text{cpu}}(n)\) variable was 0.5860, with a median of 0.6180 and a standard deviation (std) of 0.2500. For the \(x^{\text{TP}}(n)\) variable, the mean \(p\)-value was 0.4003 with a median of 0.3270 and std of 0.3040. Finally, for the \(m^{\text{P}}(n)\) variable, the mean \(p\)-value was 0.5740 with a median of 0.5860 and std of 0.2550. Table 3 shows all of the \(p\)-value results obtained from the Kruskal-Wallis test for the variables \(x^{\text{cpu}}(n)\), \(x^{\text{TP}}(n)\), and \(m^{\text{P}}(n)\) considering each \(\beta_{k}\) value. These values, as shown in Table 3, indicate that in most cases the \(p\)-values were consistently above the 0.05 threshold, suggesting no statistically significant evidence to reject the null hypothesis. The consistency of these results, as reflected in the mean values and the low variation of the \(p\)-values (std) presented in Table 3, suggests that three repetitions were sufficient to capture the variability of the data without introducing significant differences. Thus, the analysis confirms that three repetitions per experiment were adequate, validating the methodology used in this study.