## 4 Results of the Statistical Analysis of DARP
### Statistical Analysis of the Number of Control Message  
An ANOVA study was performed simultaneously analyzing the six main factors and allowing the interaction between them. As indicated in the previous section, for each of the factor configurations, multiple simulations were performed (a total of 20,413 simulations were carried out). Table 3 shows the results for the dependent variable Number of control messages sent during the set-up time. Table 3 shows, for each of the factors and for the significant interactions, the sum of squares (a measure that represents the variation or deviation with respect to the mean, and calculated as a sum of the squares of the differences with respect to the mean), degrees of freedom (difference between number of observations and parameters to be estimated), mean square (that represents an estimate of the variance of the population) and the F-Ratio (significance of the factor under study) and \(p\)-value(which corresponds to the lowest possible level of significance that can be chosen, for which the alternative hypothesis would still be accepted with the current observations). From the data and information presented in the Table 3, the statistical test F-Ratio and the associated \(p\)-value are the most relevant ones. Generally, when the \(p\)-value associated with the F-Ratio value is smaller than 0.05, then the null hypothesis must be rejected and should be accepted that there are differences between the means of the different factor levels (or in our case of interactions) selected. Analyzing the \(p\)-value of Table 3, it can be concluded that there are three factors, whose choice among the three different values of their levels, significantly affect the variable Number of Control Message. These factors, ordered by their relevance, are: Reconnection Timer (T_REC), ACK timer and Link Timer. Regarding the relevant interaction, it is important to comment the interaction between the Reconnection Timer (T_REC) and ACK timer, and the interaction between Reconnection Timer and Link Timer (for reasons of space and compression, only the most significant interactions are shown). The main objective studying the behavior of the different factors by ANOVA, was to know if these levels differ significantly from each other and therefore have an impact on the dependent variable. Once detected the most relevant factors and the existence of differences between the effects of the factor, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **Df** & **Mean Square** & **F-Ratio** & \(p\)**-Value** \\ \hline \hline MAIN EFFECTS & & & & & \\ \hline A: Baselevel Threshold (TH_B) & 81.7 & 2 & 40.85 & 2.91 & 0.0545 \\ B: Role Threshold (TH_R) & 31.6 & 2 & 15.80 & 1.13 & 0.3244 \\ C: ACK Timer (T\_ACK) * & \(1.63\times 10^{4}\) & 2 & \(8.1\times 10^{3}\) & 580 & 0.0000 \\ D: Reconnection Timer (T\_REC) * & \(3.36\times 10^{5}\) & 2 & \(1.68\times 10^{5}\) & \(1.20\times 10^{4}\) & 0.0000 \\ E: Down Timer (T\_DOWN) & 3.99 & 2 & 1.99 & 0.14 & 0.8675 \\ F: Link Timer (T\_LINK) * & 4834 & 2 & \(2.41\times 10^{3}\) & 172 & 0.0000 \\ \hline INTERACTIONS & & & & & \\ \hline CD * & 7093 & 4 & \(1.77\times 10^{3}\) & 126 & 0.0000 \\ CF * & 4660 & 4 & \(1.16\times 10^{3}\) & 82 & 0.0000 \\ DF * & 6751 & 4 & \(1.69\times 10^{3}\) & 120 & 0.0000 \\ \hline RESIDUAL & \(2.85\times 10^{5}\) & 20,314 & 9.77 \(\times\) 10\({}^{4}\) & & \\ TOTAL (CORRECTED) & \(7.31\times 10^{5}\) & 20,412 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the ANOVA table, which decomposes the variability of Number of control messages sent during the set-up time into contributions due to several factors. The main factors marked with * are statistically significant. Because the interactions between factors have been allowed in the ANOVA, the statistically relevant interactions are also marked with *. it is important to know which specific levels produces the greatest effect or which are different/equal levels of each factor.