+\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.
+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.
+
+ \textcolor{red}{
+The proposed scaling algorithm selecting smaller frequencies in two sites scenario,
+due to decreasing in the computations to communications ratio when the number of nodes is increased and
+leads to less performance degradation percentage.
+In contrast, 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.
+The inverse is happens in this scenario when the number of computing nodes is increased
+the performance degradation percentage is decreased. So, using double number of computing
+nodes when the communications occur in high speed network not decreased the computations to
+communication ratio. Moreover, as shown in the figure \ref{fig:time_sen}, the execution time of one site scenario with 32 nodes
+are less by approximately double, linear speed-up, for most of the benchmarks comparing to the one site with 16 nodes scenario.
+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 benchmarks is gives the bigger performance degradation ratio, because there is no
+communications and no slack times in this benchmarks which their performance govern
+The tradeoff between these scenarios can be computed as in the tradeoff 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, due to the increase or decreased 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\%. Therefore, the tradeoff distance is related linearly to the energy saving
+percentage. Finally, the best energy and performance tradeoff depends on the all of the following:
+1) the computations to communications ratio when there is a communications and slack times, 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.
+The reason 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. Whereas, 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 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. Generally, executing
+the NAS benchmarks over the one site one core scenario gives smaller execution times
+comparing to other scenarios. This due to 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 communications
+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 which is 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, because the computation
+times in this scenario is higher than the other one, 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\%. In these 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 scenario, on average is equal to 7\%, gives more performance degradation percentage
+than two sites one core scenario, which on average is equal to 4\%.
+Moreover, using the two sites multicores scenario increased
+the computations to communications ratio, which may be increased
+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\%. 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 multicore 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}
+
+
+ \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}
