\maketitle
+
+\begin{abstract}
+\textcolor{blue}{
+ In recent years, green computing topic has being became an important topic in
+ the domain of the research. The increase in computing power of the computing
+ platforms is increased the energy consumption and the carbon dioxide emissions.
+ Many techniques have being used to minimize the cost of the energy consumption
+ and reduce environmental pollution. Dynamic voltage and frequency scaling (DVFS)
+ is one of these techniques. It used to reduce the power consumption of the CPU
+ while computing by lowering its frequency. Moreover, lowering the frequency of
+ a CPU may increase the execution time of an application running on that
+ processor. Therefore, the frequency that gives the best trade-off between
+ the energy consumption and the performance of an application must be selected.
+ In this paper, a new online frequency selecting algorithm for heterogeneous
+ grid (heterogeneous CPUs) is presented. It selects the frequencies and tries to give the best
+ trade-off between energy saving and performance degradation, for each node
+ computing the message passing iterative application. The algorithm has a small
+ overhead and works without training or profiling. It uses a new energy model
+ for message passing iterative applications running on a heterogeneous
+ grid. The proposed algorithm is evaluated on real testbed, grid'5000 platform, while
+ running the NAS parallel benchmarks. The experiments show that it reduces the
+ energy consumption on average up to \np[\%]{30} while declines the performance
+ on average by \np[\%]{3}. Finally, the algorithm is
+ compared to an existing method, the comparison results show that it outperforms the
+ latter in term of energy and performance trade-off.}
+\end{abstract}
+
+
\section{Introduction}
\label{sec.intro}
\textcolor{blue}{
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 small
+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 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
\label{fig:fre-pow}
\end{figure}
-
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 }
\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
-presented in the figures \ref{fig:edp-eng}, \ref{fig:edp-perf} and \ref{fig:edp-dist} respectively.
+
+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
\includegraphics[scale=0.5]{fig/edp_eng}
\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.
-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.
+
+
+
+As shown in these figures, the proposed frequencies selection algorithm, Maxdist, outperforms the EDP algorithm in terms of energy consumption reduction and performance for all of the benchmarks executed over the two scenarios.
+The proposed algorithm gives better results than EDP because it
+maximizes the energy saving and the performance at the same time.
Moreover, the proposed scaling algorithm gives the same weight for these two metrics.
-Whereas, the EDP algorithm gives some times negative tradeoff values for some benchmarks in the two sites scenarios.
+Whereas, the EDP algorithm gives sometimes negative tradeoff values for some benchmarks in the two sites scenarios.
These negative tradeoff values mean that the performance degradation percentage is higher than energy saving percentage.
-The higher positive value of the tradeoff distance percentage mean that the energy saving percentage is much higher than the performance degradation percentage.
+The high positive values of the tradeoff distance percentage mean that the energy saving percentage is much higher than the performance degradation percentage.
The time complexity of both Maxdist and EDP algorithms are $O(N \cdot M \cdot F)$ and
-$O(N \cdot M \cdot F^2)$ respectively. Where $N$ is the number of the clusters, $M$ is the number of nodes and $F$ is the
-maximum number of available frequencies. The proposed algorithm, Maxdist, has selected the best frequencies in a small execution time,
-on average is equal to 0.01 $ms$, when it is executed over 32 nodes distributed between Nancy and Lyon sites.
-While the EDP algorithm was slower than Maxdist algorithm by ten times over the same number of nodes and same distribution, its execution time on average
-is equal to 0.1 $ms$.
-}
+$O(N \cdot M \cdot F^2)$ respectively, where $N$ is the number of the clusters, $M$ is the number of nodes and $F$ is the
+maximum number of available frequencies. When Maxdist is applied to a benchmark that is being executed over 32 nodes distributed between Nancy and Lyon sites, it takes on average $0.01 ms$ to compute the best frequencies while EDP is on average ten times slower over the same architecture.
+
\section{Conclusion}
