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 and 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 sites, Graphite, Graphene and Griffon, where used in this experiment.
+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
The energy saving percentages of the NAS benchmarks with the three static power scenarios are presented
in figure \ref{fig:eng_sen}. This figure shows that the 10\% of static power scenario
-gives the biggest energy saving percentage in comparison to the 20\% and 30\% static power
-scenarios. The small value of static power consumption makes the proposed
+gives the biggest energy saving percentages in comparison to the 20\% and 30\% static power
+scenarios. The small value of the static power consumption makes the proposed
scaling algorithm select smaller frequencies for the CPUs.
These smaller frequencies reduce the dynamic energy consumption more than increasing the consumed static energy which gives less overall energy consumption.
The energy saving percentages of the 30\% static power scenario is the smallest between the other scenarios, because the scaling algorithm selects bigger frequencies for the CPUs which increases the energy consumption. Figure \ref{fig:fre-pow} demonstrates that the proposed scaling algorithm selects the best frequency scaling factors according to the static power consumption ratio being used.
-\textcolor{blue}{
-The performance degradation percentages are presented in the figure \ref{fig:per-pow},
-the 30\% of static power scenario had less performance degradation percentage. This because
-bigger frequencies are selected for the CPUs by the scaling algorithm. While,
-the inverse happens in the 20\% and 30\% scenarios, because the scaling algorithm selects bigger
-frequencies.
-The tradeoff distance percentage for the NAS benchmarks with these three static power scenarios
-are presented in the figure \ref{fig:dist}. It shows that the tradeoff
-distance percentage is the best when the 10\% of static power scenario is used, and this percentage
-is decreased for the other two scenarios because of different frequencies have being selected by the scaling algorithm.
-In EP benchmark, the results of energy saving, performance degradation and tradeoff
-distance are showed small differences when the these static power scenarios are used.
-In this benchmark there are no communications which leads the proposed scaling algorithm to select similar frequencies even if the static power values are different. While, the
-inverse has been shown for the rest of the benchmarks, which have different communication times.
-This makes the scaling algorithm proportionally selects big or small frequencies for each benchmark,
-because the communication times proportionally increase or decrease the static energy consumption. }
+The performance degradation percentages are presented in the figure \ref{fig:per-pow}.
+The 30\% static power scenario had less performance degradation percentage because the scaling algorithm
+had selected big frequencies for the CPUs. While,
+the inverse happens in the 10\% and 20\% scenarios because the scaling algorithm had selected CPUs' frequencies smaller than those of the 30\% scenario. The tradeoff distance percentage for the NAS benchmarks with these three static power scenarios
+are presented in the figure \ref{fig:dist}.
+It shows that the best tradeoff
+distance percentage is obtained with the 10\% static power scenario and this percentage
+is decreased for the other two scenarios because the scaling algorithm had selected different frequencies according to the static power values.
+
+In the EP benchmark, the energy saving, performance degradation and tradeoff
+distance percentages for the these static power scenarios are not significantly different because there is no communication in this benchmark. Therefore, the static power is only consumed during computation and the proposed scaling algorithm selects similar frequencies for the three scenarios. On the other hand, for the rest of the benchmarks, the scaling algorithm selects the values of the frequencies according to the communication times of each benchmark because the static energy consumption increases proportionally to the communication times.
+
-\subsection{The comparison of the proposed frequencies selecting algorithm }
+\subsection{The comparison between the proposed frequencies selecting algorithm and the energy and delay product algorithm}
\label{sec.compare_EDP}
-\textcolor{blue}{
-The tradeoff between the energy consumption and the performance of the parallel
-applications had significant importance in the domain of the research.
-Many researchers, \cite{EDP_for_multi_processors,Energy_aware_application_scheduling,Exploring_Energy_Performance_TradeOffs},
-have optimized the tradeoff between the energy and the performance using the well known energy and delay product, $EDP=energy \times delay$.
-This model is also used by Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS},
-the objective is to select the frequencies that minimized EDP product for the multi-cores
-architecture when DVFS is used. Moreover, their algorithm is applied online, which synchronously optimized the energy consumption
-and the execution time. Both energy consumption and execution time of a processor are predicted by the their algorithm.
-In this section the proposed frequencies selection algorithm, called Maxdist is compared with Spiliopoulos et al. algorithm, called EDP.
-To make both of the algorithms follow the same direction and fairly comparing them, the same energy model, equation \ref{eq:energy} and
-the execution time model, equation \ref{eq:perf}, are used in the prediction process to select the best vector of the frequencies.
-In contrast, the proposed algorithm starts the search space from the lower bound computed as in equation the \ref{eq:Fint}. Also, the algorithm
-stops the search process when it is reached to the lower bound as mentioned before. In the same way, the EDP algorithm is developed to start from the
-same upper bound used in Maxdist algorithm, and it stops the search process when a minimum available frequencies is reached.
-Finally, the resulting EDP algorithm is an exhaustive search algorithm that test all possible frequencies, starting from the initial frequencies,
-and selecting those minimized the EDP product.
-Both algorithms were applied to NAS benchmarks, class D, over 16 nodes selected from grid'5000 clusters.
-The participating computing nodes are distributed between two sites and one site to have two different scenarios that used in the section \ref{sec.res}.
-The experimental results: the energy saving, performance degradation and tradeoff distance percentages are
+
+Finding the frequencies that gives the best tradeoff between the energy consumption and the performance for a parallel
+application is not a trivial task. Many algorithms have been proposed to tackle this problem.
+In this section, the proposed frequencies selecting algorithm is compared to well known energy and delay product method, $EDP=energy \times delay$, that have been used by many researchers \cite{EDP_for_multi_processors,Energy_aware_application_scheduling,Exploring_Energy_Performance_TradeOffs}.
+This method was also used by Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS} where they select the frequencies that minimize the EDP product and apply them with DVFS operations to the multi-cores
+architecture. Their online algorithm predicts the energy consumption and execution time of a processor before using the EDP method.
+
+To fairly compare the proposed frequencies scaling algorithm to Spiliopoulos et al. algorithm, called Maxdist and EDP respectively, both algorithms use the same energy model, equation \ref{eq:energy} and
+execution time model, equation \ref{eq:perf}, to predict the energy consumption and the execution time for each computing node.
+Moreover, both algorithms start the search space from the upper bound computed as in equation \ref{eq:Fint}.
+Finally, the resulting EDP algorithm is an exhaustive search algorithm that tests all the possible frequencies, starting from the initial frequencies (upper bound),
+and selects the vector of frequencies that minimize the EDP product.
+
+Both algorithms were applied to the class D of the NAS benchmarks over 16 nodes.
+The participating computing nodes are distributed according to the two scenarios described in section \ref{sec.res}.
+The experimental results, the energy saving, performance degradation and tradeoff distance percentages, are
presented in the figures \ref{fig:edp-eng}, \ref{fig:edp-perf} and \ref{fig:edp-dist} respectively.
\begin{figure}
\centering
\caption{Comparing of the tradeoff distance for the proposed method with EDP method}
\label{fig:edp-dist}
\end{figure}
-As shown form these figures, the proposed frequencies selection algorithm, Maxdist, outperform the EDP algorithm in term of energy and performance for all of the benchmarks executed over the two scenarios.
+\textcolor{blue}{As shown form these figures, the proposed frequencies selection algorithm, Maxdist, outperform the EDP algorithm in term of energy and performance for all of the benchmarks executed over the two scenarios.
Generally, the proposed algorithm gives better results for all benchmarks because it is
optimized the distance between the energy saving and the performance degradation in the same time.
Moreover, the proposed scaling algorithm gives the same weight for these two metrics.
