-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.
-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.
-
- \textcolor{red}{please correct the following paragraph because I do not understand it at all! Stop using we, this because, effected, while, ...}
-
-
-
- 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 multicores clusters}
-\label{sec.res-mc}
-The grid'5000 clusters have different number of cores embedded in their nodes
-as in the Table \ref{table:grid5000}. Moreover, the cores of each node are
-connected via shared memory model, the data transfer between cores' local
-memories achieved via the global memory \cite{rauber_book}. Therefore, in
-this section the proposed scaling algorithm is implemented over the grid'5000
-clusters which are included multicores in the selected nodes as same as the
-two previous platform scenarios that mentioned in the section \ref{sec.res}.
-The two platform scenarios, the two sites and one site scenarios, with 32
-nodes are reconfigured to used multicores for each node. For example if
-the participating number of nodes from a certain cluster is equal to 12 nodes,
-in the multicores scenario the selected nodes is equal to 3 nodes with using
-4 cores for each of them to produced 12 cores. These scenarios with one
-core and multicores are demonstrated 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 represented
-in the figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.
-The execution times of NAS benchmarks over the one site multicores scenario
-is higher than the execution time of those running over one site multicores scenario.
-This because in the one site multicores scenario the communication is increased significantly,
-and all node's cores share the same node network link which increased
-the communication times. While, the execution times of the NAS benchmarks over
-the two site multicores scenario is less than those executed over the two
-sites one core scenario. This because using multicores decrease the communications,
-while the cores shared same nodes' link but the communications between the cores
-are less than the communication times between the nodes over the long distance
-networks, and thus the over all execution time decreased. Generally, executing
-the NAS benchmarks over the one site one core gives smaller execution times
-comparing to other scenarios. This because each node in this scenario has it's
-dedicated network link that used independently by one core, while in the other
-scenarios the communication times are higher when using long distance communication
-link or using the shared link communications between cores of each node.
-On the other hand, the energy consumptions of the NAS benchmarks over the
-one site one cores is less than the one site multicores scenario because
-this scenario had less execution time as mentioned before. Also, in the
-one site one core scenario the computations to communications ratio is
-higher, then the new scaled frequencies are decreased the dynamic energy
-consumption, because the dynamic power consumption are decreased exponentially
-with the new frequency scaling factors. These experiments also showed, the energy
-consumption and the execution times of EP and MG benchmarks over these four
-scenarios are not change a lot, because there are no or small communications
- which are increase or decrease the static power consumptions.
-The other benchmarks were showed that their energy consumptions and execution times
-are changed according to the decreasing or increasing in the communication
-times that are different from scenario to other or due to the amount of
-communications in each of them.
-
-The energy saving percentages of all NAS benchmarks, as in figure
-\ref{fig:eng-s-mc}, running over these four scenarios are presented. The figure
-showed the energy saving percentages of NAS benchmarks over two sites multicores scenario is higher
-than two sites once core scenario, this because the the computation
-times in the two sites multicores scenario is higher than the computation times
-of the two sites one core scenario, then the more reduction in the
-dynamic energy can be obtained as mentioned previously. In contrast, in the one site one
-core and one site multicores scenarios the energy saving percentages
-are approximately equivalent, on average they are up to 25\%. This
-because in the both scenarios there are a small difference in the
-computations to communications ratio, leading the proposed scaling algorithm
-to selects the frequencies proportionally to these ratios and keeping
-as much as possible the energy saving percentages the same. The
-performance degradation percentages of NAS benchmarks are presented in
-figure \ref{fig:per-d-mc}. This figure indicates that performance
-degradation percentages of running NAS benchmarks over two sites
-multocores, on average is equal to 7\%, gives more performance degradation percentage
-than two sites one core scenario, which on average is equal to 4\%.
-This because when using the two sites multicores scenario increased
-the computations to communications ratio, which may be increased the effect
-on the overall execution time when the proposed scaling algorithm is applied and scaling down the frequencies.
-The inverse was happened when the benchmarks are executed over one
-site one core scenario their performance degradation percentages, on average
-is equal to 10\%, are higher than those executed over one sit one core,
-which on average is equal to 7\%. This because in one site
-multicores scenario the computations to communications ratio is decreased
-as mentioned before, thus selecting new frequencies are less effect
-on 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\%. This because 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 multicore in both scenarios increased the energy and performance tradeoff
-distance. This is because using multicores are increased the computations to communications
-ratio in two sites scenario and thus the energy saving increased over the performance degradation, whereas decreased this ratio
-in one site scenario causing the performance degradation decreased over the energy saving.
-
-
-
-
-
-\begin{table}[]
-\centering
-\caption{The multicores scenarios}
+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.
