+\begin{figure}[!h]
+ \centering
+ \subfloat[Comparing the execution times of running the NAS benchmarks over one core and multi-core scenarios]{%
+ \includegraphics[width=.48\textwidth]{fig/time.eps}\label{fig:time-mc}} \hspace{0.4cm}%
+ \subfloat[Comparing the energy consumptions of running the NAS benchmarks over one core and multi-core scenarios]{%
+ \includegraphics[width=.48\textwidth]{fig/eng_con.eps}\label{fig:eng-cons-mc}}
+ \label{fig:eng-cons}
+ \caption{The energy consumptions and execution times of the NAS benchmarks running over one core and multi-core per node architectures}
+\end{figure}
+
+
+
+The execution times for most of the NAS benchmarks are higher over the multi-core per node scenario
+than over the single core per node scenario. Indeed,
+ the communication times are higher in the one site multi-core 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-core 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-core 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.
+\begin{figure*}[t]
+ \centering
+ \subfloat[The energy saving of running NAS benchmarks over one core and multicore scenarios]{%
+ \includegraphics[width=.48\textwidth]{fig/eng_s_mc.eps}\label{fig:eng-s-mc}} \hspace{0.4cm}%
+ \subfloat[The performance degradation of running NAS benchmarks over one core and multi-core scenarios
+ ]{%
+ \includegraphics[width=.48\textwidth]{fig/per_d_mc.eps}\label{fig:per-d-mc}}\hspace{0.4cm}%
+ \subfloat[The trade-off distance of running NAS benchmarks over one core and multicore scenarios]{%
+ \includegraphics[width=.48\textwidth]{fig/dist_mc.eps}\label{fig:dist-mc}}
+ \label{fig:exp-res2}
+ \caption{The experimental results of one core and multi-core scenarios}
+\end{figure*}
+
+The energy saving percentages of all the NAS benchmarks running over these two scenarios are presented in Figure~\ref{fig:eng-s-mc}.
+The figure shows that the energy saving percentages in the one
+core and the multi-core 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 are higher for the NAS benchmarks executed over the one core per node scenario (on average equal to 10.6\%) than over the multi-core scenario (on average equal to 7.5\%). The performance degradation percentages over the multi-core scenario are lower because the computations to communications ratios are smaller than the ratios of the other scenario.
+
+The trade-off distances percentages of the NAS benchmarks over both scenarios are presented
+in ~Figure~\ref{fig:dist-mc}. These trade-off distances 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 trade-off distance percentages are on average bigger over the multi-core scenario (17.6\%) than over the one core per node scenario (15.3\%).
+
+
+
+
+
+
+
+\subsection{Experiments with different static power 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 were executed over the Nancy site. 16 computing nodes from the three clusters, Graphite, Graphene and Griffon, were used in this experiment.
+
+
+\begin{figure*}[t]
+ \centering
+ \subfloat[The energy saving percentages for the nodes executing the NAS benchmarks over the three power scenarios]{%
+ \includegraphics[width=.48\textwidth]{fig/eng_pow.eps}\label{fig:eng-pow}} \hspace{0.4cm}%
+ \subfloat[The performance degradation percentages for the NAS benchmarks over the three power scenarios]{%
+ \includegraphics[width=.48\textwidth]{fig/per_pow.eps}\label{fig:per-pow}}\hspace{0.4cm}%
+ \subfloat[The trade-off distance between the energy reduction and the performance of the NAS benchmarks over the three power scenarios]{%
+
+ \includegraphics[width=.48\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-pow}. 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 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 trade-off distance percentage for the NAS benchmarks with these three static power scenarios
+are presented in Figure~\ref{fig:dist-pow}.
+It shows that the best trade-off
+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 trade-off
+distance percentages for 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{Comparison of the proposed frequencies selecting algorithm }
