-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 controlled by
-the computing powers of the nodes.
-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.
+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 8.3\% or 4.7\% 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 3.2\% or 10.6\% 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 26.8\%. 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.
