+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/time_scenarios.eps}
+ \caption{The execution times of NAS benchmarks over different scenarios }
+ \label{fig:time_sen}
+\end{figure}
+
+The NAS parallel benchmarks are executed over these two platforms
+ with different number of nodes, as in Table \ref{tab:sc}.
+The overall energy consumption of all the benchmarks solving the class D instance and
+using the proposed frequency selection algorithm is measured
+using the equation of the reduced energy consumption, equation
+(\ref{eq:energy}). This model uses the measured dynamic and static
+power values showed in Table \ref{table:grid5000}. The execution
+time is measured for all the benchmarks over these different scenarios.
+
+The energy consumptions and the execution times for all the benchmarks are
+presented in the plots \ref{fig:eng_sen} and \ref{fig:time_sen} respectively.
+
+For the majority of the benchmarks, the energy consumed while executing the NAS benchmarks over one site scenario
+for 16 and 32 nodes is lower than the energy consumed while using two sites.
+The long distance communications between the two distributed sites increase the idle time which leads to more static energy consumption.
+ The execution times of these benchmarks
+over one site with 16 and 32 nodes are also lower when compared to those of the two sites
+scenario.
+
+However, the execution times and the energy consumptions of EP and MG benchmarks, which have no or small communications, are not significantly affected
+ in both scenarios. Even when the number of nodes is doubled. On the other hand, the communications of the rest of the benchmarks increases when using long distance communications between two sites or increasing the number of computing nodes.
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/eng_s.eps}
+ \caption{The energy saving of NAS benchmarks over different scenarios }
+ \label{fig:eng_s}
+\end{figure}
+
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/per_d.eps}
+ \caption{The performance degradation of NAS benchmarks over different scenarios }
+ \label{fig:per_d}
+\end{figure}
+
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/dist.eps}
+ \caption{The tradeoff distance of NAS benchmarks over different scenarios }
+ \label{fig:dist}
+\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 higher 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 there 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 site 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.
+
+
+ Figure \ref{fig:time_sen} presents the execution times for all the benchmarks over the two scenarios. For most of the benchmarks running over the one site scenario, their execution times are approximately divided by two when the number of computing nodes is doubled from 16 to 32 nodes (linear speed up according to the number of the nodes).
+
+This leads to increased the number of the critical nodes which any one of them may increased the overall the execution time of the benchmarks.
+The EP benchmark gives bigger performance degradation percentage, because there is no
+communications and no slack times in this benchmark which their performance controlled by
+the computing powers of the nodes. \textcolor{red}{les deux phrases précédentes n'ont pas de sens}
+
+
+Figure \ref{fig:dist} presents the distance between the energy consumption reduction and the performance degradation for all benchmarks over both scenarios. This distance can be computed as in the tradeoff function \ref{eq:max}. The one site scenario with 16 and 32 nodes had the best tradeoff distance compared to the two sites scenarios, due to the increase or decreased in the communications as mentioned before. The one site scenario with 16 nodes gives the best energy and performance tradeoff which is on average equal to 26\%. \textcolor{red}{distance is a percentage}
+
+ Therefore, the tradeoff distance is linearly related to the energy saving
+percentage. 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.
+
+\textcolor{red}{compare the two scenarios}
+
+\subsection{The experimental results of multicores 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}. The cores of each node can exchange
+ data via the shared memory \cite{rauber_book}. In
+this section, the proposed scaling algorithm is evaluated over the grid'5000 grid while using multi-core nodes
+selected according to the two platform scenarios described in the section \ref{sec.res}.
+The two platform scenarios, the two sites and one site scenarios, use 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 12,
+in the multi-core scenario the selected nodes is equal to 3 nodes while using
+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 NAS parallel
+benchmarks, class D, over these four different scenarios are presented
+in the figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.
+
+The execution times for most of the NAS benchmarks are higher over the one site multi-cores per node scenario
+ than the execution time of those running over one site 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. On the other hand, the execution times for most of the NAS benchmarks are lower over
+the two site multi-cores scenario than those over the two sites one core scenario.
+
+This goes back when using multicores is decreasing the communications.
+As explained previously, the cores shared same nodes' linkbut the communications between the cores
+are still less than the communication times between the nodes over the long distance
+networks, and thus the over all execution time decreased. \textcolor{red}{this is not true}
+
+The experiments showed that for most of the NAS benchmarks and between the four scenarios, the one site one core scenario gives the best execution times because the communication times are the lowest. Indeed, in this scenario each core has a dedicated network link and all the communications are local.
+Moreover, the energy consumptions of the NAS benchmarks are lower over the
+one site one core scenario than over the one site 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 than the other scenarios \textcolor{red}{ then the new scaled frequencies are decreased the dynamic energy
+consumption which is decreased exponentially
+with the new frequency scaling factors. I do not understand this sentence}
+\textcolor{red}{It is useless to use multi-cores then!}
+
+
+ These experiments also showed that the energy
+consumption and the execution times of the EP and MG benchmarks do not change significantly over these four
+scenarios because there are no or small communications
+which could increase or decrease the static power consumptions. 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 four scenarios are presented in figure \ref{fig:eng-s-mc}. The figure
+shows that the energy saving percentages are higher over the two sites multi-cores scenario
+than over the two sites one core scenario, because the computation
+times are higher in the first scenario than in the latter, thus, more dynamic energy can be saved by applying the frequency scaling algorithm. \textcolor{red}{why the computation times are higher!}
+
+
+In contrast, in the one site one
+core and one site multi-cores scenarios the energy saving percentages
+are approximately equivalent, on average they are up to 25\%. In both scenarios there are a small difference in the
+computations to communications ratios which leads the proposed scaling algorithm
+to select similar frequencies for both scenarios.
+
+The
+performance degradation percentages of the NAS benchmarks are presented in
+figure \ref{fig:per-d-mc}.
+
+It indicates that the performance
+degradation percentages for the NAS benchmarks are higher over the two sites
+multi-cores scenario than over the two sites one core scenario, equal on average to 7\% and 4\% respectively.
+Moreover, using the two sites multi-cores scenario increased
+the computations to communications ratio, which may increase
+the overall execution time when the proposed scaling algorithm is applied and the frequencies scaled down.
+
+
+When the benchmarks are executed over the one
+site one core scenario their performance degradation percentages, on average
+is equal to 10\%, are higher than those executed over one site one core,
+which on average is equal to 7\%. \textcolor{red}{You are comparing the one
+site one core scenario to itself! Please rewrite all the following paragraphs because they are full of mistakes! Look how I modified the previous parts, discover your mistakes and stop making the same mistakes.}
+
+So, in one site
+multicores scenario the computations to communications ratio is decreased
+as mentioned before, thus selecting new frequencies are not increased
+the overall execution time. The tradeoff distances of all NAS
+benchmarks over all scenarios are presented in the figure \ref{fig:dist-mc}.
+These tradeoff distances are used to verified which scenario is the best in term of
+energy and performance ratio. The one sites multicores scenario is the best scenario in term of
+energy and performance tradeoff, on average is equal to 17.6\%, when comparing to the one site one core
+scenario, one average is equal to 15.3\%. The one site multicores scenario
+has the same energy saving percentages of the one site one core scenario but
+with less performance degradation. The two sites multicores scenario is gives better
+energy and performance tradeoff, one average is equal to 14.7\%, than the two sites
+one core, on average is equal to 13.3\%.
+
+Finally, using multi-cores in both scenarios increased the energy and performance tradeoff
+distance. This generally due to using multicores was increased the computations to communications
+ratio in two sites scenario and thus the energy saving percentage increased over the performance degradation percentage, whereas this ratio was decreased
+in one site scenario causing the performance degradation percentage decreased over the energy saving percentage.
+
+
+
+
+
+\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}{*}{Two sites/ one core} & Taurus & 10 & 1 \\ \cline{2-4}
+ & Graphene & 10 & 1 \\ \cline{2-4}
+ & Griffon & 12 & 1 \\ \hline
+\multirow{3}{*}{Two sites/ multicores} & Taurus & 3 & 3 or 4 \\ \cline{2-4}
+ & Graphene & 3 & 3 or 4 \\ \cline{2-4}
+ & Griffon & 3 & 4 \\ \hline
+\multirow{3}{*}{One site/ one core} & Graphite & 4 & 1 \\ \cline{2-4}
+ & Graphene & 12 & 1 \\ \cline{2-4}
+ & Griffon & 12 & 1 \\ \hline
+\multirow{3}{*}{One site/ multicores} & Graphite & 3 & 3 or 4 \\ \cline{2-4}
+ & Graphene & 3 & 3 or 4 \\ \cline{2-4}
+ & Griffon & 3 & 4 \\ \hline
+\end{tabular}
+\label{table:sen-mc}
+\end{table}
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/eng_con.eps}
+ \caption{Comparing the energy consumptions of running NAS benchmarks over one core and multicores scenarios }
+ \label{fig:eng-cons-mc}
+\end{figure}
