+
+\subsection{The experimental results over multi-cores clusters}
+\label{sec.res-mc}
+
+The clusters of grid'5000 have different number of cores embedded in their nodes
+as shown in Table \ref{table:grid5000}. In
+this section, the proposed scaling algorithm is evaluated over the grid'5000 platform while using multi-cores nodes selected according to the one site scenario described in the section \ref{sec.res}.
+The one site scenario uses 32 cores from multi-cores nodes instead of 32 distinct nodes. For example if
+the participating number of cores from a certain cluster is equal to 14,
+in the multi-core scenario the selected nodes is equal to 4 nodes while using
+3 or 4 cores from each node. The platforms with one
+core per node and multi-cores nodes are shown in Table \ref{table:sen-mc}.
+The energy consumptions and execution times of running the class D of the NAS parallel
+benchmarks over these four different scenarios are presented
+in the figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.
+
+\begin{table}[]
+\centering
+\caption{The multicores scenarios}
+\begin{tabular}{|*{4}{c|}}
+\hline
+Scenario name & Cluster name & \begin{tabular}[c]{@{}c@{}}No. of nodes\\ in each cluster\end{tabular} &
+ \begin{tabular}[c]{@{}c@{}}No. of cores\\ for each node\end{tabular} \\ \hline
+\multirow{3}{*}{One core per node} & Graphite & 4 & 1 \\ \cline{2-4}
+ & Graphene & 14 & 1 \\ \cline{2-4}
+ & Griffon & 14 & 1 \\ \hline
+\multirow{3}{*}{Multi-cores per node} & Graphite & 1 & 4 \\ \cline{2-4}
+ & Graphene & 4 & 3 or 4 \\ \cline{2-4}
+ & Griffon & 4 & 3 or 4 \\ \hline
+\end{tabular}
+\label{table:sen-mc}
+\end{table}
+
+
+\begin{figure}
+ \centering
+ \subfloat[Comparing the execution times of running NAS benchmarks over one core and multicores scenarios]{%
+ \includegraphics[width=.4\textwidth]{fig/time.eps}\label{fig:time-mc}} \hspace{1cm}%
+ \subfloat[Comparing the energy consumptions of running NAS benchmarks over one core and multi-cores scenarios]{%
+ \includegraphics[width=.4\textwidth]{fig/eng_con.eps}\label{fig:eng-cons-mc}}
+ \label{fig:eng-cons}
+ \caption{The energy consumptions and execution times of NAS benchmarks over one core and multi-cores per node architectures}
+\end{figure}
+
+
+
+The execution times for most of the NAS benchmarks are higher over the multi-cores per node scenario
+than over single core per node scenario. Indeed,
+ the communication times are higher in the one site multi-cores scenario than in the latter scenario because all the cores of a node share the same node network link which can be saturated when running communication bound applications. Moreover, the cores of a node share the memory bus which can be also saturated and become a bottleneck.
+Moreover, the energy consumptions of the NAS benchmarks are lower over the
+ one core scenario than over the multi-cores scenario because
+the first scenario had less execution time than the latter which results in less static energy being consumed.
+The computations to communications ratios of the NAS benchmarks are higher over
+the one site one core scenario when compared to the ratio of the multi-cores scenario.
+More energy reduction can be gained when this ratio is big because it pushes the proposed scaling algorithm to select smaller frequencies that decrease the dynamic power consumption. These experiments also showed that the energy
+consumption and the execution times of the EP and MG benchmarks do not change significantly over these two
+scenarios because there are no or small communications. Contrary to EP and MG, the energy consumptions and the execution times of the rest of the benchmarks vary according to the communication times that are different from one scenario to the other.
+
+
+The energy saving percentages of all NAS benchmarks running over these two scenarios are presented in the figure \ref{fig:eng-s-mc}.
+The figure shows that the energy saving percentages in the one
+core and the multi-cores scenarios
+are approximately equivalent, on average they are equal to 25.9\% and 25.1\% respectively.
+The energy consumption is reduced at the same rate in the two scenarios when compared to the energy consumption of the executions without DVFS.
+
+
+The performance degradation percentages of the NAS benchmarks are presented in
+figure \ref{fig:per-d-mc}. It shows that the performance degradation percentages is higher for the NAS benchmarks over the one core per node scenario (on average equal to 10.6\%) than over the multi-cores scenario (on average equal to 7.5\%). The performance degradation percentages over the multi-cores scenario is lower because the computations to communications ratio is smaller than the ratio of the other scenario.
+
+The tradeoff distance percentages of the NAS benchmarks over the two scenarios are presented
+in the figure \ref{fig:dist-mc}. These tradeoff distance between energy consumption reduction and performance are used to verify which scenario is the best in both terms at the same time. The figure shows that the tradeoff distance percentages are on average bigger over the multi-cores scenario (17.6\%) than over the one core per node scenario (15.3\%).
+
+
+
+\begin{figure}
+ \centering
+ \subfloat[The energy saving of running NAS benchmarks over one core and multicores scenarios]{%
+ \includegraphics[width=.4\textwidth]{fig/eng_s_mc.eps}\label{fig:eng-s-mc}} \hspace{2cm}%
+ \subfloat[The performance degradation of running NAS benchmarks over one core and multicores scenarios
+ ]{%
+ \includegraphics[width=.4\textwidth]{fig/per_d_mc.eps}\label{fig:per-d-mc}}\hspace{2cm}%
+ \subfloat[The tradeoff distance of running NAS benchmarks over one core and multicores scenarios]{%
+ \includegraphics[width=.4\textwidth]{fig/dist_mc.eps}\label{fig:dist-mc}}
+ \label{fig:exp-res}
+ \caption{The experimental results of one core and multi-cores scenarios}
+\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 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 clusters, Graphite, Graphene and Griffon, where used in this experiment.
+
+
+\begin{figure}
+ \centering
+ \subfloat[The energy saving percentages for the nodes executing the NAS benchmarks over the three power scenarios]{%
+ \includegraphics[width=.4\textwidth]{fig/eng_pow.eps}\label{fig:eng-pow}} \hspace{2cm}%
+ \subfloat[The performance degradation percentages for the NAS benchmarks over the three power scenarios]{%
+ \includegraphics[width=.4\textwidth]{fig/per_pow.eps}\label{fig:per-pow}}\hspace{2cm}%
+ \subfloat[The tradeoff distance between the energy reduction and the performance of the NAS benchmarks over the three power scenarios]{%
+
+ \includegraphics[width=.4\textwidth]{fig/dist_pow.eps}\label{fig:dist-pow}}
+ \label{fig:exp-pow}
+ \caption{The experimental results of different static power scenarios}
+\end{figure}
+
+
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/three_scenarios.pdf}
+ \caption{Comparing the selected frequency scaling factors for the MG benchmark over the 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 percentages in comparison to the 20\% and 30\% static power
+scenarios. The small value of the 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.
+
+The performance degradation percentages are presented in the figure \ref{fig:per-pow}.
+The 30\% static power scenario had less performance degradation percentage because the scaling algorithm
+had selected big frequencies for the CPUs. While,
+the inverse happens in the 10\% and 20\% scenarios because the scaling algorithm had selected CPUs' frequencies smaller than those of the 30\% scenario. 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 best tradeoff
+distance percentage is obtained with the 10\% static power scenario and this percentage
+is decreased for the other two scenarios because the scaling algorithm had selected different frequencies according to the static power values.
+
+In the EP benchmark, the energy saving, performance degradation and tradeoff
+distance percentages for the these static power scenarios are not significantly different because there is no communication in this benchmark. Therefore, the static power is only consumed during computation and the proposed scaling algorithm selects similar frequencies for the three scenarios. On the other hand, for the rest of the benchmarks, the scaling algorithm selects the values of the frequencies according to the communication times of each benchmark because the static energy consumption increases proportionally to the communication times.
+
+
+
+\subsection{The comparison of the proposed frequencies selecting algorithm }
