+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/per_d_mc.eps}
+ \caption{The performance degradation of running NAS benchmarks over one core and multicores scenarios }
+ \label{fig:per-d-mc}
+\end{figure}
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/dist_mc.eps}
+ \caption{The tradeoff distance of running NAS benchmarks over one core and multicores scenarios }
+ \label{fig:dist-mc}
+\end{figure}
+
+\subsection{Experiments with different static and dynamic powers consumption scenarios}
+\label{sec.pow_sen}
+
+In section \ref{sec.grid5000}, since it was not possible to measure the static power consumed by a CPU, the static power was assumed to be equal to 20\% of the measured dynamic power. This power is consumed during the whole execution time, during computation and communication times. Therefore, when the DVFS operations are applied by the scaling algorithm and the CPUs' frequencies lowered, the execution time might increase and consequently the consumed static energy will be increased too.
+
+The aim of this section is to evaluate the scaling algorithm while assuming different values of static powers.
+In addition to the previously used percentage of static power, two new static power ratios, 10\% and 30\% of the measured dynamic power of the core, are used in this section.
+The experiments have been executed with these two new static power scenarios and over the one site one core per node scenario.
+In these experiments, the class D of the NAS parallel benchmarks are executed over Nancy's site. 16 computing nodes from the three sites, Graphite, Graphene and Griffon, where used in this experiment.
+
+ \begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/eng_pow.eps}
+ \caption{The energy saving percentages for NAS benchmarks of the three power scenario}
+ \label{fig:eng-pow}
+\end{figure}
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/per_pow.eps}
+ \caption{The performance degradation percentages for NAS benchmarks of the three power scenario}
+ \label{fig:per-pow}
+\end{figure}
+
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/dist_pow.eps}
+ \caption{The tradeoff distance for NAS benchmarks of the three power scenario}
+ \label{fig:dist-pow}
+\end{figure}
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.47]{fig/three_scenarios.pdf}
+ \caption{Comparing the selected frequency scaling factors of MG benchmark for three static power scenarios}
+ \label{fig:fre-pow}
+\end{figure}
+
+
+The energy saving percentages of the NAS benchmarks with the three static power scenarios are presented
+in figure \ref{fig:eng_sen}. This figure shows that the 10\% of static power scenario
+gives the biggest energy saving percentage in comparison to the 20\% and 30\% static power
+scenarios. The small value of static power consumption makes the proposed
+scaling algorithm select smaller frequencies for the CPUs.
+These smaller frequencies reduce the dynamic energy consumption more than increasing the consumed static energy which gives less overall energy consumption.
+The energy saving percentages of the 30\% static power scenario is the smallest between the other scenarios, because the scaling algorithm selects bigger frequencies for the CPUs which increases the energy consumption. Figure \ref{fig:fre-pow} demonstrates that the proposed scaling algorithm selects the best frequency scaling factors according to the static power consumption ratio being used.
+
+\textcolor{blue}{
+The performance degradation percentages are presented in the figure \ref{fig:per-pow},
+the 30\% of static power scenario had less performance degradation percentage. This because
+bigger frequencies are selected for the CPUs by the scaling algorithm. While,
+the inverse happens in the 20\% and 30\% scenarios, because the scaling algorithm selects bigger
+frequencies.
+The tradeoff distance percentage for the NAS benchmarks with these three static power scenarios
+are presented in the figure \ref{fig:dist}. It shows that the tradeoff
+distance percentage is the best when the 10\% of static power scenario is used, and this percentage
+is decreased for the other two scenarios because of different frequencies have being selected by the scaling algorithm.
+In EP benchmark, the results of energy saving, performance degradation and tradeoff
+distance are showed small differences when the these static power scenarios are used.
+In this benchmark there are no communications which leads the proposed scaling algorithm to select similar frequencies even if the static power values are different. While, the
+inverse has been shown for the rest of the benchmarks, which have different communication times.
+This makes the scaling algorithm proportionally selects big or small frequencies for each benchmark,
+because the communication times proportionally increase or decrease the static energy consumption. }
+
+
+\subsection{The comparison of the proposed frequencies selecting algorithm }
+\label{sec.compare_EDP}
+\textcolor{blue}{
+The tradeoff between the energy consumption and the performance of the parallel
+applications had significant importance in the domain of the research.
+Many researchers, \cite{EDP_for_multi_processors,Energy_aware_application_scheduling,Exploring_Energy_Performance_TradeOffs},
+have optimized the tradeoff between the energy and the performance using the well known energy and delay product, $EDP=energy \times delay$.
+This model is also used by Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS},
+the objective is to select the frequencies that minimized EDP product for the multi-cores
+architecture when DVFS is used. Moreover, their algorithm is applied online, which synchronously optimized the energy consumption
+and the execution time. Both energy consumption and execution time of a processor are predicted by the their algorithm.
+In this section the proposed frequencies selection algorithm, called Maxdist is compared with Spiliopoulos et al. algorithm, called EDP.
+To make both of the algorithms follow the same direction and fairly comparing them, the same energy model, equation \ref{eq:energy} and
+the execution time model, equation \ref{eq:perf}, are used in the prediction process to select the best vector of the frequencies.
+In contrast, the proposed algorithm starts the search space from the lower bound computed as in equation the \ref{eq:Fint}. Also, the algorithm
+stops the search process when it is reached to the lower bound as mentioned before. In the same way, the EDP algorithm is developed to start from the
+same upper bound used in Maxdist algorithm, and it stops the search process when a minimum available frequencies is reached.
+Finally, the resulting EDP algorithm is an exhaustive search algorithm that test all possible frequencies, starting from the initial frequencies,
+and selecting those minimized the EDP product.
+Both algorithms were applied to NAS benchmarks, class D, over 16 nodes selected from grid'5000 clusters.
+The participating computing nodes are distributed between two sites and one site to have two different scenarios that used in the section \ref{sec.res}.
+The experimental results: the energy saving, performance degradation and tradeoff distance percentages are
+presented in the figures \ref{fig:edp-eng}, \ref{fig:edp-perf} and \ref{fig:edp-dist} respectively.
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/edp_eng}
+ \caption{Comparing of the energy saving for the proposed method with EDP method}
+ \label{fig:edp-eng}
+\end{figure}
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/edp_per}
+ \caption{Comparing of the performance degradation for the proposed method with EDP method}
+ \label{fig:edp-perf}
+\end{figure}
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/edp_dist}
+ \caption{Comparing of the tradeoff distance for the proposed method with EDP method}
+ \label{fig:edp-dist}
+\end{figure}
+As shown form these figures, the proposed frequencies selection algorithm, Maxdist, outperform the EDP algorithm in term of energy and performance for all of the benchmarks executed over the two scenarios.
+Generally, the proposed algorithm gives better results for all benchmarks because it is
+optimized the distance between the energy saving and the performance degradation in the same time.
+Moreover, the proposed scaling algorithm gives the same weight for these two metrics.
+Whereas, the EDP algorithm gives some times negative tradeoff values for some benchmarks in the two sites scenarios.
+These negative tradeoff values mean that the performance degradation percentage is higher than energy saving percentage.
+The higher positive value of the tradeoff distance percentage mean that the energy saving percentage is much higher than the performance degradation percentage.
+The time complexity of both Maxdist and EDP algorithms are $O(N \cdot M \cdot F)$ and
+$O(N \cdot M \cdot F^2)$ respectively. Where $N$ is the number of the clusters, $M$ is the number of nodes and $F$ is the
+maximum number of available frequencies. The proposed algorithm, Maxdist, has selected the best frequencies in a small execution time,
+on average is equal to 0.01 $ms$, when it is executed over 32 nodes distributed between Nancy and Lyon sites.
+While the EDP algorithm was slower than Maxdist algorithm by ten times over the same number of nodes and same distribution, its execution time on average
+is equal to 0.1 $ms$.
+}
