+
+\begin{figure}
+ \centering
+ \subfloat[The energy reduction while executing the NAS benchmarks over different scenarios ]{%
+ \includegraphics[width=.33\textwidth]{fig/eng_s.eps}\label{fig:eng_s}} \hspace{0.08cm}%
+ \subfloat[The performance degradation of the NAS benchmarks over different scenarios]{%
+ \includegraphics[width=.33\textwidth]{fig/per_d.eps}\label{fig:per_d}}\hspace{0.08cm}%
+ \subfloat[The tradeoff distance between the energy reduction and the performance of the NAS benchmarks
+ over different scenarios]{%
+ \includegraphics[width=.33\textwidth]{fig/dist.eps}\label{fig:dist}}
+ \label{fig:exp-res}
+ \caption{The experimental results of different scenarios}
+\end{figure}
+
+The energy saving percentage is computed as the ratio between the reduced
+energy consumption, equation (\ref{eq:energy}), and the original energy consumption,
+equation (\ref{eq:eorginal}), for all benchmarks as in figure \ref{fig:eng_s}.
+This figure shows that the energy saving percentages of one site scenario for
+16 and 32 nodes are bigger than those of the two sites scenario which is due
+to the higher computations to communications ratio in the first scenario
+than in the second one. Moreover, the frequency selecting algorithm selects smaller frequencies when the computations times are bigger than the communication times which
+results in a lower energy consumption. Indeed, the dynamic consumed power
+is exponentially related to the CPU's frequency value. On the other side, the increase in the number of computing nodes can
+increase the communication times and thus produces less energy saving depending on the
+benchmarks being executed. The results of the benchmarks CG, MG, BT and FT show more
+energy saving percentage in one site scenario when executed over 16 nodes comparing to 32 nodes. While, LU and SP consume more energy with 16 nodes than 32 in one site because their computations to communications ratio is not affected by the increase of the number of local communications.
+
+
+The energy saving percentage is reduced for all the benchmarks because of the long distance communications in the two sites
+scenario, except for the EP benchmark which has no communications. Therefore, the energy saving percentage of this benchmark is
+dependent on the maximum difference between the computing powers of the heterogeneous computing nodes, for example
+in the one site scenario, the graphite cluster is selected but in the two sits scenario
+this cluster is replaced with Taurus cluster which is more powerful.
+Therefore, the energy saving of EP benchmarks are bigger in the two sites scenario due
+to the higher maximum difference between the computing powers of the nodes.
+
+In fact, high differences between the nodes' computing powers make the proposed frequencies selecting
+algorithm select smaller frequencies for the powerful nodes which
+produces less energy consumption and thus more energy saving.
+The best energy saving percentage was obtained in the one site scenario with 16 nodes, the energy consumption was on average reduced up to 30\%.
+
+
+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\% or 4\% 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 higher 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\% or 10\% respectively. In opposition 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 tradeoff distance percentage can be
+computed as in equation \ref{eq:max}. The one site scenario with 16 nodes gives the best energy and performance
+tradeoff, on average it is equal to 26\%. The one site scenario using both 16 and 32 nodes had better energy and performance
+tradeoff 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 tradeoff 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-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}
