# An Energy-Saving Forwarding Mechanism Based on Clustering for Opportunistic Networks
## 6 Performance Evaluation
### Tukey Test--Infocom Scenario  
Equation (8) previously described in the subsection performance evaluation was applied to use the Tukey test in the Infocom scenario. By applying the equation to the values found in the ANOVA calculation and the other variables, we have the following result HSD = 0.058. The HSD (minimum significant difference) is used to identify, through statistical tests, which algorithms are the same or different in the delivery performances according to the tested energy ranges. When the absolute difference of the averages (average module) calculated is greater than the value of the HSD, we say that the averages of the delivery rates of the algorithms are statistically different. We can conclude from the results that there are relevant differences in the average performance of the delivery rates between all routing algorithms for the case where the battery range is \(E\) = [25, 100]. \(\epsilon\)GPDMI maintained the highest results with an approximately 80% delivery rate, compared with PRoPHET and GPDMI. We found no significant difference in average performance between the PRoPHET and GPDMI routing algorithms for the remaining battery ranges. In \(E\) = [50, 100] and \(E\) = [75, 100] energy ranges, there are significant differences between the performance of the \(\epsilon\)GPDMI and the GPDMI and PRoPHET algorithms, with rates of approximately 80% and 85% delivery for the proposed algorithm, while GPDMI and PRoPHET were in the 25% range for energy cooperation in the \(E\) = [75, 100] range and 40% in delivery performance when \(E\) = [50, 100]. Finally, the Tukey test also showed differences in the performance of delivery rates between all the algorithms in the \(E\) = [0, 100] range. PRoPHET and GPDMI delivered approximately 85% of the messages on the network, and \(\epsilon\)GPDMI did not exceed 70%. The exact values for the Tukey test are described in Table 9. These results support the previous ones in the message delivery probability, where our proposal (\(\epsilon\)GPDMI) achieved statistically different performance for all the battery load limits. Statistically, it is possible to compare the differences between the means. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Variation** & \(\boldsymbol{SQ}\) & \(\boldsymbol{gl}\) & \(\boldsymbol{MS}\) & \(\boldsymbol{F}\) & \(\boldsymbol{p}\)**-Value** & \(\boldsymbol{F}\)**-Critical** \\ \hline Battery Range & 2.62350745 & 3 & 0.874502483 & 295.1720982 & 7.154413 \(\times\) 10\({}^{-52}\) & 2.688691468 \\ Routing Algorithm & 2.426933741 & 2 & 1.213466871 & 409.583242 & 3.787614 \(\times\) 10\({}^{-51}\) & 3.080386863 \\ Battery \(\times\) Routing Algorithm & 2.733700332 & 6 & 0.455616722 & 153.7849764 & 1.544337 \(\times\) 10\({}^{-50}\) & 2.183656883 \\ Inside & 0.319970176 & 108 & 0.002962687 & & & \\ Total & 8.104111699 & 119 & 0.874502483 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Analysis of variance vs. delivery rate in scenario Infocom. Comparing the data in Figure 6, we see that \(e\)GPDMI had a performance of approximately 142.85% better in the delivery probability regarding GPDMI and PRoPHET. Moreover, we remarked that \(e\)GPDMI had a worse performance of average delivery delay, around 13% difference (Figure 7). However, analyzing the results of the average delivery delay between \(e\)GPDMI and GPDMI, the standard deviation was 18.53 and 21.82, respectively. These values indicated that there was not a significant difference between the results. Thus, an unpaired \(t\)-test was applied to find the value of \(p\) = 0.3533, keeping the null hypothesis H\({}_{0}\) prevailed, mean of \(e\)GPDMI = mean of GPDMI. It is essential to highlight that the same test was applied to \(e\)GPDMI and PRoPHETto obtain a \(p\)-value > 0.05. It is important to emphasize that the performance of average delivery delay is statistically similar for GPDMI and PRoPHET. Furthermore, the average delivery delay was close between \(e\)GPDMI and the other routing algorithms in all battery ranges cases.