+Figure \ref{fig:per_d} presents the performance degradation percentages for all benchmarks over the two scenarios.
+The performance degradation percentage for the benchmarks running on two sites with
+16 or 32 nodes is on average equal to 8.3\% or 4.7\% respectively.
+For this scenario, the proposed scaling algorithm selects smaller frequencies for the executions with 32 nodes without significantly degrading their performance because the communication times are high with 32 nodes which results in smaller computations to communications ratio. On the other hand, the performance degradation percentage for the benchmarks running on one site with
+16 or 32 nodes is on average equal to 3.2\% and 10.6\% respectively. In contrary to the two sites scenario, when the number of computing nodes is increased in the one site scenario, the performance degradation percentage is increased. Therefore, doubling the number of computing
+nodes when the communications occur in high speed network does not decrease the computations to
+communication ratio.
+
+The performance degradation percentage of the EP benchmark after applying the scaling factors selection algorithm is the highest in comparison to
+the other benchmarks. Indeed, in the EP benchmark, there are no communication and slack times and its
+performance degradation percentage only depends on the frequencies values selected by the algorithm for the computing nodes.
+The rest of the benchmarks showed different performance degradation percentages which decrease
+when the communication times increase and vice versa.
+
+Figure \ref{fig:dist} presents the distance percentage between the energy saving and the performance degradation for each benchmark over both scenarios. The trade-off distance percentage can be
+computed as in Equation~\ref{eq:max}. The one site scenario with 16 nodes gives the best energy and performance
+trade-off, on average it is equal to 26.8\%. The one site scenario using both 16 and 32 nodes had better energy and performance
+trade-off comparing to the two sites scenario because the former has high speed local communications
+which increase the computations to communications ratio and the latter uses long distance communications which decrease this ratio.
+
+ Finally, the best energy and performance trade-off depends on all of the following:
+1) the computations to communications ratio when there are communications and slack times, 2) the heterogeneity of the computing powers of the nodes and 3) the heterogeneity of the consumed static and dynamic powers of the nodes.
+
+
+
+
+\subsection{The experimental results over multi-core 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 Section~\ref{sec.res}.
+The one site scenario uses 32 cores from multi-core 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 4 nodes are selected and
+3 or 4 cores from each node are used. The platforms with one
+core per node and multi-core 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 two different platforms are presented
+in Figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.
+
+
+\begin{table}[!h]
+\centering
+\caption{The multi-core scenarios}
+\begin{tabular}{|*{4}{c|}}
+\hline
+Scenario name & Cluster name & Nodes per cluster &
+ Cores per node \\ \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-core 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}[!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\%).
+
