-this cluster is replaced with Taurus cluster that be more powerful in computing power.
-Therefore, the energy saving of EP benchmarks are bigger in the two site scenario due
-to increase in the differences between the computing powers of the nodes. This means, the higher
-differences between the nodes' computing powers make the proposed frequencies selecting
-algorithm to selects smaller frequencies in the nodes of the higher computing power,
-producing less energy consumption and thus more energy saving.
-The best energy saving percentage was for one site scenario with 16 nodes, on average it
-saves the energy consumption up to 30\%.
-
-Figure \ref{fig:per_d}, presents the performance degradation percentages for all benchmarks.
-It shows that the performance degradation percentages of the one site scenario with
-32 nodes, on average equal to 10\%, is higher than the performance degradation of one 16 nodes,
-which on average equal to 3\%. This because selecting smaller frequencies in the one site scenarios,
-when the computations grater than the communications , increase the number of the critical nodes
-when the number of nodes increased. The inverse happens in the tow sites scenario,
-this due to the lower computations to communications ratio that decreased with highest
-communications. Therefore, the number of the critical nodes are decreased. The average performance
-degradation for the two sites scenario with 16 nodes is equal to 8\% and for 32 nodes is equal to 4\%.
-The EP benchmarks is gives the bigger performance degradation ratio, because there is no
-communications and no slack times in this benchmarks that is always their performance effected
-by selecting big or small frequencies.
-The tradeoff between these scenarios can be computed as in the trade-off function \ref{eq:max}.
-Figure \ref{fig:dist}, presents the tradeoff distance for all benchmarks over all
-platform scenarios. The one site scenario with 16 and 32 nodes had the best tradeoff distance
-compared to the two sites scenarios, because the increase in the communications as mentioned before.
-The one site scenario with 16 nodes is the best scenario in term of energy and performance tradeoff,
-which on average is up 26\%. Then, the tradeoff distance is related linearly to the energy saving
-percentage. Finally, the best energy and performance tradeoff depends on the increase in all of:
-1) the computations to communications ratio, 2) the differences in computing powers
-between the computing nodes and 3) the differences in static and the dynamic powers of the nodes.
-
-\subsection{The experimental results of multi-cores clusters}
-\label{sec.res}
+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 of 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 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 and. Moreover, the cores of a node share the memory bus which can be also saturated and become a bottleneck.
+%
+%
+%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 memory bus 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 when compared to the ratios of the other scenarios.
+%More energy reduction was achieved when this ratio is increased because the proposed scaling algorithm selects smaller frequencies that decrease the dynamic power consumption.
+%
+% \textcolor{blue}{ Whereas, the energy consumption in the two sites one core scenario is higher than the energy consumption of the two sites multi-core scenario. This is according to the increase in the execution time of the two sites one core scenario. }
+%
+%
+%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 the figure \ref{fig:eng-s-mc}. It shows that the energy saving percentages over the two sites multi-cores scenario
+%and over the two sites one core scenario are on average equal to 22\% and 18\%
+%respectively. The energy saving percentages are higher in the former scenario because its computations to communications ratio is higher than the ratio of the latter scenario as mentioned previously.
+%
+%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 shows 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 are equal on average
+%to 10\% and are higher than those executed over the one site multi-cores scenario,
+%which on average is equal to 7\%.
+%
+%\textcolor{blue}{
+%The performance degradation percentages over one site multi-cores is lower because the computations to communications ratio is decreased. Therefore, selecting bigger
+%frequencies by the scaling algorithm are proportional to this ratio, and thus the execution time do not increase significantly.}
+%
+%
+%The tradeoff distance percentages of the NAS
+%benchmarks over all scenarios are presented in the figure \ref{fig:dist-mc}.
+%These tradeoff distance percentages are used to verify which scenario is the best in terms of energy reduction and performance. The figure shows that using muti-cores in both of the one site and two sites scenarios gives bigger tradeoff distance percentages, on overage equal to 17.6\% and 15.3\% respectively, than using one core per node in both of one site and two sites scenarios, on average equal to 14.7\% and 13.3\% 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}{*}{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}
+%
+%
+% \begin{figure}
+% \centering
+% \includegraphics[scale=0.5]{fig/time.eps}
+% \caption{Comparing the execution times of running NAS benchmarks over one core and multicores scenarios }
+% \label{fig:time-mc}
+%\end{figure}
+%
+% \begin{figure}
+% \centering
+% \includegraphics[scale=0.5]{fig/eng_s_mc.eps}
+% \caption{The energy saving of running NAS benchmarks over one core and multicores scenarios }
+% \label{fig:eng-s-mc}
+%\end{figure}
+%
+%\begin{figure}
+% \centering
+% \includegraphics[scale=0.5]{fig/per_d_mc.eps}
+% \caption{The performance degradation of running NAS benchmarks over one core and multicores scenarios }
+% \label{fig:per-d-mc}
+%\end{figure}
+%
+%\begin{figure}
+% \centering
+% \includegraphics[scale=0.5]{fig/dist_mc.eps}
+% \caption{The tradeoff distance of running NAS benchmarks over one core and multicores scenarios }
+% \label{fig:dist-mc}
+%\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
+ \includegraphics[scale=0.5]{fig/eng_pow.eps}
+ \caption{The energy saving percentages for the nodes executing the NAS benchmarks over the three power scenarios}
+ \label{fig:eng-pow}
+\end{figure}
