-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.
-
-\subsection{The results for different powers scenarios}
-
-The results of the previous section are obtained using a percentage of 80\% for
-dynamic power and 20\% for static power of total power consumption. In this
-section we are change these ratio by using two others scenarios. Because is
-interested to measure the ability of the proposed algorithm to changes it
-behavior when these power ratios are changed. In fact, we are use two different
-scenarios for dynamic and static power ratios in addition to the previous
-scenario in section (\ref{sec.res}). Therefore, we have three different
-scenarios for three different dynamic and static power ratios refer to as:
-70\%-20\%, 80\%-20\% and 90\%-10\% scenario. The results of these scenarios
-running NAS benchmarks class C on 8 or 9 nodes are place in the tables
-(\ref{table:res_s1} and \ref{table:res_s2}).
-
- \begin{table}[htb]
- \caption{The results of 70\%-30\% powers scenario}
+Figures \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 decrease linearly when the number of nodes
+increase. 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 little or no communications. Finally, the energy saving of
+the GC benchmark significantly decrease when the number of nodes increase
+because this benchmark has more communications than the others. The second plot
+shows that the performance degradation percentages of most of the benchmarks
+decrease 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
+has less effect on the performance.
+
+
+
+
+\subsection{The results for different power consumption scenarios}
+\label{sec.compare}
+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 of 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\% of dynamic power and 30\% of static power
+\item 90\% of dynamic power and 10\% of static power
+\end{itemize}
+
+The NAS parallel benchmarks were executed again over processors that follow 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 smaller 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 smaller
+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 amount of consumed
+static energy directly increases. Therefore, the proposed algorithm does not
+really significantly scale 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.
+
+Both 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 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 decreases when the 70\%-30\%
+scenario is used because the dynamic energy is less relevant in the overall
+consumed energy and lowering the frequency does not return 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 Figure (\ref{fig:scales_comp}). The opposite happens when using a
+higher ratio for static power, the algorithm proportionally selects smaller
+scaling values which result in less energy saving but also less performance
+degradation.
+
+
+ \begin{table}[!t]
+ \caption{The results of the 70\%-30\% power scenario}
