\maketitle
-\begin{abstract}
-
-
-\end{abstract}
-
\section{Introduction}
\label{sec.intro}
+\textcolor{blue}{
+The need for more computing power is continually increasing. To partially
+satisfy this need, most supercomputers constructors just put more computing
+nodes in their platform. The resulting platforms may achieve higher floating
+point operations per second (FLOPS), but the energy consumption and the heat
+dissipation are also increased. As an example, the Chinese supercomputer
+Tianhe-2 had the highest FLOPS in June 2015 according to the Top500 list
+\cite{TOP500_Supercomputers_Sites}. However, it was also the most power hungry
+platform with its over 3 million cores consuming around 17.8 megawatts.
+Moreover, according to the U.S. annual energy outlook 2015
+\cite{U.S_Annual.Energy.Outlook.2014}, the price of energy for 1 megawatt-hour
+was approximately equal to \$70. Therefore, the price of the energy consumed by
+the Tianhe-2 platform is approximately more than \$10 million each year. The
+computing platforms must be more energy efficient and offer the highest number
+of FLOPS per watt possible, such as the Shoubu-ExaScaler from RIKEN
+which became the top of the Green500 list in June 2015 \cite{Green500_List}.
+This heterogeneous platform executes more than 7 GFLOPS per watt while consuming
+50.32 kilowatts.
+}
+Besides platform improvements, there are many software and hardware techniques
+to lower the energy consumption of these platforms, such as scheduling, DVFS,
+\dots{} DVFS is a widely used process to reduce the energy consumption of a
+processor by lowering its frequency
+\cite{Rizvandi_Some.Observations.on.Optimal.Frequency}. However, it also reduces
+the number of FLOPS executed by the processor which may increase the execution
+time of the application running over that processor. Therefore, researchers use
+different optimization strategies to select the frequency that gives the best
+trade-off between the energy reduction and performance degradation ratio. In
+\cite{Our_first_paper} and \cite{pdsec2015} , a frequencies selecting algorithm was proposed to reduce
+the energy consumption of message passing iterative applications running over
+homogeneous and heterogeneous clusters respectively.
+The results of the experiments show significant energy
+consumption reductions. In this paper, a new frequency selecting algorithm
+adapted for heterogeneous platform is presented. It selects the vector of
+frequencies, for a heterogeneous grid platform running a message passing iterative
+application, that simultaneously tries to offer the maximum energy reduction and
+minimum performance degradation ratio. The algorithm has a very small overhead,
+works online and does not need any training or profiling.
+\textcolor{blue}{
+This paper is organized as follows: Section~\ref{sec.relwork} presents some
+related works from other authors. Section~\ref{sec.exe} describes how the
+execution time of message passing programs can be predicted. It also presents
+an energy model that predicts the energy consumption of an application running
+over a heterogeneous grid. Section~\ref{sec.compet} presents the
+energy-performance objective function that maximizes the reduction of energy
+consumption while minimizing the degradation of the program's performance.
+Section~\ref{sec.optim} details the proposed frequencies selecting algorithm.
+Section~\ref{sec.expe} presents the results of applying the algorithm on the
+NAS parallel benchmarks and executing them on a grid'5000 testbed.
+It shows the results of running different scenarios using multi-cores and one core per node
+and comparing them. It also shows the results of running
+three different power scenarios and comparing them. Moreover, it shows the
+comparison results between the proposed method and an existing method. Finally,
+in Section~\ref{sec.concl} the paper ends with a summary and some future works.}
\section{Related works}
\label{sec.relwork}
+DVFS is a technique used in modern processors to scale down both the voltage and
+the frequency of the CPU while computing, in order to reduce the energy
+consumption of the processor. DVFS is also allowed in GPUs to achieve the same
+goal. Reducing the frequency of a processor lowers its number of FLOPS and may
+degrade the performance of the application running on that processor, especially
+if it is compute bound. Therefore selecting the appropriate frequency for a
+processor to satisfy some objectives, while taking into account all the
+constraints, is not a trivial operation. Many researchers used different
+strategies to tackle this problem. Some of them developed online methods that
+compute the new frequency while executing the application, such
+as~\cite{Hao_Learning.based.DVFS,Spiliopoulos_Green.governors.Adaptive.DVFS}.
+Others used offline methods that may need to run the application and profile
+it before selecting the new frequency, such
+as~\cite{Rountree_Bounding.energy.consumption.in.MPI,Cochran_Pack_and_Cap_Adaptive_DVFS}.
+The methods could be heuristics, exact or brute force methods that satisfy
+varied objectives such as energy reduction or performance. They also could be
+adapted to the execution's environment and the type of the application such as
+sequential, parallel or distributed architecture, homogeneous or heterogeneous
+platform, synchronous or asynchronous application, \dots{}
+
+In this paper, we are interested in reducing energy for message passing
+iterative synchronous applications running over heterogeneous grid platforms. Some
+works have already been done for such platforms and they can be classified into
+two types of heterogeneous platforms:
+\begin{itemize}
+\item the platform is composed of homogeneous GPUs and homogeneous CPUs.
+\item the platform is only composed of heterogeneous CPUs.
+\end{itemize}
-\section{The performance and energy consumption measurements on heterogeneous architecture}
+For the first type of platform, the computing intensive parallel tasks are
+executed on the GPUs and the rest are executed on the CPUs. Luley et
+al.~\cite{Luley_Energy.efficiency.evaluation.and.benchmarking}, proposed a
+heterogeneous cluster composed of Intel Xeon CPUs and NVIDIA GPUs. Their main
+goal was to maximize the energy efficiency of the platform during computation by
+maximizing the number of FLOPS per watt generated.
+In~\cite{KaiMa_Holistic.Approach.to.Energy.Efficiency.in.GPU-CPU}, Kai Ma et
+al. developed a scheduling algorithm that distributes workloads proportional to
+the computing power of the nodes which could be a GPU or a CPU. All the tasks
+must be completed at the same time. In~\cite{Rong_Effects.of.DVFS.on.K20.GPU},
+Rong et al. showed that a heterogeneous (GPUs and CPUs) cluster that enables
+DVFS gave better energy and performance efficiency than other clusters only
+composed of CPUs.
+
+The work presented in this paper concerns the second type of platform, with
+heterogeneous CPUs. Many methods were conceived to reduce the energy
+consumption of this type of platform. Naveen et
+al.~\cite{Naveen_Power.Efficient.Resource.Scaling} developed a method that
+minimizes the value of $\mathit{energy}\times \mathit{delay}^2$ (the delay is
+the sum of slack times that happen during synchronous communications) by
+dynamically assigning new frequencies to the CPUs of the heterogeneous cluster.
+Lizhe et al.~\cite{Lizhe_Energy.aware.parallel.task.scheduling} proposed an
+algorithm that divides the executed tasks into two types: the critical and non
+critical tasks. The algorithm scales down the frequency of non critical tasks
+proportionally to their slack and communication times while limiting the
+performance degradation percentage to less than \np[\%]{10}.
+In~\cite{Joshi_Blackbox.prediction.of.impact.of.DVFS}, they developed a
+heterogeneous cluster composed of two types of Intel and AMD processors. They
+use a gradient method to predict the impact of DVFS operations on performance.
+In~\cite{Shelepov_Scheduling.on.Heterogeneous.Multicore} and
+\cite{Li_Minimizing.Energy.Consumption.for.Frame.Based.Tasks}, the best
+frequencies for a specified heterogeneous cluster are selected offline using
+some heuristic. Chen et
+al.~\cite{Chen_DVFS.under.quality.of.service.requirements} used a greedy dynamic
+programming approach to minimize the power consumption of heterogeneous servers
+while respecting given time constraints. This approach had considerable
+overhead. In contrast to the above described papers, this paper presents the
+following contributions :
+\begin{enumerate}
+\item two new energy and performance models for message passing iterative
+ synchronous applications running over a heterogeneous grid platform. Both models
+ take into account communication and slack times. The models can predict the
+ required energy and the execution time of the application.
+
+\item a new online frequency selecting algorithm for heterogeneous grid
+ platforms. The algorithm has a very small overhead and does not need any
+ training or profiling. It uses a new optimization function which
+ simultaneously maximizes the performance and minimizes the energy consumption
+ of a message passing iterative synchronous application.
+
+\end{enumerate}
+
+
+
+\section{The performance and energy consumption measurements on heterogeneous grid architecture}
\label{sec.exe}
\subsection{The execution time of message passing distributed iterative
\end{algorithm}
-
In this section, the scaling factors selection algorithm for grids, algorithm~\ref{HSA}, is presented. It selects the vector of the frequency
scaling factors that gives the best trade-off between minimizing the
energy consumption and maximizing the performance of a message passing
selected clusters and are presented in table \ref{table:grid5000}.
-
-
\begin{figure}[!t]
\centering
\includegraphics[scale=1]{fig/grid5000}
\label{fig:grid5000}
\end{figure}
-
The energy model and the scaling factors selection algorithm were applied to the NAS parallel benchmarks v3.3 \cite{NAS.Parallel.Benchmarks} and evaluated over grid'5000.
The benchmark suite contains seven applications: CG, MG, EP, LU, BT, SP and FT. These applications have different computations and communications ratios and strategies which make them good testbed applications to evaluate the proposed algorithm and energy model.
The benchmarks have seven different classes, S, W, A, B, C, D and E, that represent the size of the problem that the method solves. In this work, the class D was used for all benchmarks in all the experiments presented in the next sections.
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.
+scenario. Moreover, most of the benchmarks running over the one site scenario their execution times are approximately divided by two when the number of computing nodes is doubled from 16 to 32 nodes (linear speed up according to the number of the nodes).
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.
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:time_sen} presents the execution times for all the benchmarks over the two scenarios. For most of the benchmarks running over the one site scenario, their execution times are approximately divided by two when the number of computing nodes is doubled from 16 to 32 nodes (linear speed up according to the number of the nodes).
-
-
-\textcolor{blue}{
-The performance degradation percentage of EP benchmark is the higher when it is compared with
-the other benchmarks. There are no communication and slack times in this benchmark and its
-performance degradation percentage depends on the frequency value selected in the computing node.
-The rest of the benchmarks showed different performance degradation percentages, which are decreased
-when the communication times are increased and vice versa.}
-
-\textcolor{blue}{Figure \ref{fig:dist} presents the tradeoff distance percentage between the energy saving and the performance degradation for all benchmarks over both scenarios. The tradeoff distance percentage can be
-computed as in the tradeoff function \ref{eq:max}. The one site scenario with 16 nodes gives the best energy and performance
-tradeoff, on average is equal to 26\%. As a result, one site scenario using both 16 and 32 nodes had better energy and performance
-tradeoff comparing to the two sites scenario. This because the former used high speed local communications
-which increased the computations to communications ratio and the latter used long distance communications which decreased this ratio. } \textcolor{red}{The last paragraph has compared the two scenarios}
+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:
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. On the other hand, the execution times for most of the NAS benchmarks are lower over
-the two sites multi-cores scenario than those over the two sites one core scenario.
-
-\textcolor{blue}{Furthermore, in two sites multi-cores per node scenario part of the communications happened via shared memory
-and the rest via long distance network. According to the high latency in the long distance network, the
-communication times are smaller compared to the communication times of the shared memory.
-Therefore, using the shared memory communications mixed with the long distance communications
-has decreased the communication times, and thus the overall execution time is decreased.}
+ 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.
+
+ \textcolor{blue}{On the other hand, the execution times for most of the NAS benchmarks are lower over
+the two sites multi-cores scenario than those over the two sites one core scenario. ???????
+}
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.
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.
-\textcolor{blue}{
-Therefore, the computations to communications ratios of the NAS benchmarks are higher over
-the one site one core scenario compared to the other scenarios.
-More energy reduction has achieved when this ratio increased, because the proposed scaling algorithm selecting smaller frequencies that decreased the dynamic power consumption. Whereas, the energy consumption in the two sites multi-cores scenario is higher than the energy consumption
-of the two sites one core scenario. Actually, using multi-cores in this scenario decreased the communication times that decreased the static energy consumption.}
+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
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.
-\textcolor{blue}{
-The energy saving percentages of all NAS benchmarks running over these four scenarios are presented in the figure \ref{fig:eng-s-mc}. This figure
-shows that the energy saving percentages are higher over the two sites multi-cores scenario
-than over the two sites one core scenario, on average they are equal to 22\% and 18\%
-respectively. This is according to the increase or decrease in the computations to communications ratio as mentioned previously.}
+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
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 indicates that the performance degradation percentages for the NAS benchmarks are higher over the two sites
+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.
-\textcolor{blue}{
+
When the benchmarks are executed over the one
-site one core scenario their performance degradation percentages, on average
-is equal to 10\%, are higher than those executed over one site multi-cores,
-which on average is equal to 7\%. This because using multi-cores in one site scenario
-decreased the computations to communications ratio. Therefore, selecting small
-frequencies by the scaling algorithm do not increase the execution time significantly.}
+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 small
+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 verified which scenario is the best in term of the energy and performance ratio. The figure indicates that using muti-cores in both of the one site and two sites scenarios gives bigger tradeoff distance percentages, on overage they are equal to 17.6\% and 15.3\% respectively. On the contrary, using one core per node in both of one site and two sites scenarios gives lower tradeoff distance percentages, on average they are equal to 14.7\% and 13.3\% respectively. }
+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
\label{fig:dist-mc}
\end{figure}
-\subsection{The results of using different static power consumption scenarios}
+\subsection{Experiments with different static and dynamic powers consumption scenarios}
\label{sec.pow_sen}
-\textcolor{blue}{
-The static power consumption for one core is the leakage power
-consumption when it is idle. The measured static power of the node,
-as in section \ref{sec.grid5000}, had a collection of power values such as
-all cores static powers and the power consumptions of the other devices. Furthermore, the static power for one core is hard to measured precisely. On the other hand, the core has consumed the static power during
-the communication and computation times. However, the static power consumption becomes more important when the execution time is
-increased using DVFS. Therefore, the objective of this section is to verify the ability of the proposed
-scaling algorithm to select the best frequencies when the static power consumption is changing.
-All the results obtained in the previous sections depend on the measured dynamic power
-consumptions as in table \ref{table:grid5000}. Moreover, the static power consumption for one core is represented by 20\% of the measured dynamic power consumption.
-This assumption is extended in this section to taking into account other ratios for the static power consumption.
-In addition to the previous ratio of the static power consumption, two other static power ratios are used, which are 10\% and 30\% of the measured dynamic power of the core.
-As a result, all of these static power scenarios is denoted as follow:
-\begin{itemize}
-\item 10\% of static power scenario
-\item 20\% of static power scenario
-\item 30\% of static power scenario
-\end{itemize}
-The NAS parallel benchmarks, class D, are executed over Nancy site.
-The number of computing nodes used is 16 nodes distributed between three cluster, which are Graphite, Graphene and Griffon. The NAS benchmarks rerun
-with these two new static power scenarios over one site scenario
-using one core per node. }
+
+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.
\begin{figure}
\centering
\label{fig:fre-pow}
\end{figure}
-\textcolor{blue}{
-The energy saving percentages of NAS benchmarks with these three static power scenarios are presented
-in figure \ref{fig:eng_sen}. This figure shows that 10\% of static power scenario
-gives the biggest energy saving percentage comparing to 20\% and 30\% static power
-scenarios. The smaller ratio of the static power consumption makes the proposed
-scaling algorithm to select smaller frequencies, bigger scaling factors.
-These smaller frequencies has reduced the dynamic energy consumption and thus the
-overall energy consumption is decreased.
-The energy saving percentages of 30\% static power scenario is the smallest between the other scenarios, because of the scaling algorithm selects bigger frequencies, smaller scaling factors, that increased the energy consumption. For example, figure \ref{fig:fre-pow}, illustrates that the proposed scaling algorithm is proportionally selected the best frequency scaling factors according to the static power consumption ratio being used.
-Furthermore, the proposed scaling algorithm tries to limit selecting smaller frequencies, which increased the execution time. Hence, the increase in the execution time is relatively increased the static energy consumption.
-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 was selected due to the big ratio in the static power consumption.
-The inverse happens in the 20\% and 30\% scenarios, the scaling algorithm is selecting
-smaller frequencies, bigger scaling factors, according to the ratio of the static power.
-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 propositionally to their static power ratios.
-In EP benchmark, the results of energy saving, performance degradation and tradeoff
-distance are showed small differences when the these static power scenarios were used.
-The absent of the communications in this benchmark made the proposed scaling algorithm to select equivalent 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
-that increased the static energy consumption proportionally. Therefore, the scaling algorithm relatively selects
-different frequencies for each benchmark when these static power scenarios are used. }
+
+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 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.
+
+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.
\section{Conclusion}
\label{sec.concl}
-
+\textcolor{blue}{
+This paper has been presented a new online frequencies selection algorithm.
+It works based on objective function that maximized the tradeoff distance
+between the predicted energy consumption and the predicted execution time of the distributed
+iterative applications running over heterogeneous grid. The algorithm selects the best vector of the
+frequencies which maximized the objective function has been used. A new energy model
+used by the proposed algorithm for measuring and predicting the energy consumption
+of the distributed iterative message passing application running over grid architecture.
+To evaluate the proposed method on a real heterogeneous grid platform, it was applied on the
+NAS parallel benchmarks class D instance and executed over grid'5000 testbed platform.
+The experimental results showed that the algorithm saves the energy consumptions on average
+for all NAS benchmarks up to 30\% while gives only 3\% percentage on average for the performance
+degradation for the same instance. The algorithm also selecting different frequencies according to the
+computations and communication times ratio, and according to the values of the static and measured dynamic power of the CPUs. The computations to communications ratio was varied between different scenarios have been used, concerning to the distribution of the computing nodes between different clusters' sites and using one core or multi-cores per node.
+Finally, the proposed algorithm was compared to other algorithm which it
+used the will known energy and delay product as an objective function. The comparison results showed
+that the proposed algorithm outperform the other one in term of energy-time tradeoff.
+In the near future, we would like to develop a similar method that is adapted to
+asynchronous iterative applications where each task does not
+wait for other tasks to finish their works. The development of
+such a method might require a new energy model because the
+number of iterations is not known in advance and depends on
+the global convergence of the iterative system.
+}
\section*{Acknowledgment}
