-In the NAS benchmarks there are some programs executed on different number of nodes. The benchmarks CG, MG, LU and FT executed on 2 to a power of (1, 2, 4, 8, ...) of nodes. The other benchmarks such as BT and SP executed on 2 to a power of (1, 2, 4, 9, ...) of nodes. We are take the average of energy saving, performance degradation and distances for all results of NAS benchmarks. The average of these three objectives are plotted to the number of nodes as in plots (\ref{fig:avg_eq} and \ref{fig:avg_neq}). In CG, MG, LU, and FT benchmarks the average of energy saving is decreased when the number of nodes is increased due to the increasing in the communication times as mentioned before. Thus, the average of distances (our objective function) is decreased linearly with energy saving while keeping the average of performance degradation the same. In BT and SP benchmarks, the average of energy saving is not decreased significantly compare to other benchmarks when the number of nodes is increased. Nevertheless, the average of performance degradation approximately still the same ratio. This difference is depends on the characteristics of the benchmarks such as the computation to communication ratio that has.
+
+ Plots (\ref{fig:energy} and \ref{fig:per_deg}) present the energy saving and performance degradation respectively for all the benchmarks according to the number of used
+nodes. As shown in the first plot, the energy saving percentages of the benchmarks MG, LU, BT and FT are decreased linearly when the the number of nodes is increased. While for the EP and SP benchmarks, the energy saving percentage is not affected by the increase of the number of computing nodes, because in these benchmarks there are no communications. Finally, the energy saving of the GC benchmark is significantly decreased when the number of nodes is increased because this benchmark has more communications than the others. The second plot shows that the performance degradation percentages of most of the benchmarks are decreased when they run on a big number of nodes because they spend more time communicating than computing, thus, scaling down the frequencies of some nodes have less effect on the performance.
+
+
+
+
+\subsection{The results for different power consumption scenarios}
+
+The results of the previous section were obtained while using processors that consume during computation an overall power which is 80\% composed of dynamic power and 20\% of static power. In this
+section, these ratios are changed and two new power scenarios are considered in order to evaluate how the proposed algorithm adapts itself according to the static and dynamic power values. The two new power scenarios are the following:
+\begin{itemize}
+\item 70\% dynamic power and 30\% static power
+\item 90\% dynamic power and 10\% static power
+\end{itemize}
+The NAS parallel benchmarks were executed again over processors that follow the the new power scenarios. The class C of each benchmark was run over 8 or 9 nodes and the results are presented in tables (\ref{table:res_s1} and \ref{table:res_s2}). These tables show that the energy saving percentage of the 70\%-30\% scenario is less for all benchmarks compared to the energy saving of the 90\%-10\% scenario. Indeed, in the latter more dynamic power is consumed when nodes are running on their maximum frequencies, thus, scaling down the frequency of the nodes results in higher energy savings than in the 70\%-30\% scenario. On the other hand, the performance degradation percentage is less in the 70\%-30\% scenario compared to the 90\%-10\% scenario. This is due to the higher static power percentage in the first scenario which makes it more relevant in the overall consumed energy. Indeed, the static energy is related to the execution time and if the performance is degraded the total consumed static energy is directly increased. Therefore, the proposed algorithm do not scales down much the frequencies of the nodes in order to limit the increase of the execution time and thus limiting the effect of the consumed static energy .
+
+The two new power scenarios are compared to the old one in figure (\ref{fig:sen_comp}). It shows the average of the performance degradation, the energy saving and the distances for all NAS benchmarks of class C running on 8 or 9 nodes. The comparison shows that the energy saving ratio is proportional to the dynamic power ratio: it is increased when applying the 90\%-10\% scenario because at maximum frequency the dynamic energy is the the most relevant in the overall consumed energy and can be reduced by lowering the frequency of some processors. On the other hand, the energy saving is decreased when the 70\%-30\% scenario is used because the dynamic energy is less relevant in the overall consumed energy and lowering the frequency do not returns big energy savings.
+Moreover, the average of the performance degradation is decreased when using a higher ratio for static power (e.g. 70\%-30\% scenario and 80\%-20\% scenario). Since the proposed algorithm optimizes the energy consumption when using a higher ratio for dynamic power the algorithm selects bigger frequency scaling factors that result in more energy saving but less performance, for example see the figure (\ref{fig:scales_comp}). The opposite happens when using a higher ratio for static power, the algorithm proportionally selects smaller scaling values which results in less energy saving but less performance degradation.
