\usepackage{subfig}
\usepackage{amsmath}
\usepackage{url}
+\usepackage{multirow}
\DeclareUrlCommand\email{\urlstyle{same}}
\usepackage[autolanguage,np]{numprint}
\newcommand{\Sopt}[1][]{\Xsub{S}{opt}_{#1}}
\newcommand{\Tcm}[1][]{\Xsub{T}{cm}_{\fxheight{#1}}}
\newcommand{\Tcp}[1][]{\Xsub{T}{cp}_{#1}}
-\newcommand{\Ppeak}[1][]{\Xsub{P}{peak}_{#1}}
+\newcommand{\Pmax}[1][]{\Xsub{P}{max}_{\fxheight{#1}}}
\newcommand{\Pidle}[1][]{\Xsub{P}{idle}_{\fxheight{#1}}}
\newcommand{\TcpOld}[1][]{\Xsub{T}{cpOld}_{#1}}
\newcommand{\Tnew}{\Xsub{T}{New}}
\maketitle
-\begin{abstract}
-
+\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}{
+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.2015}, 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.
+}
+
+\textcolor{blue}{
+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. All the experimental results were conducted over
+Simgrid simulator \cite{SimGrid}, which offers easy tools to create a homogeneous and heterogeneous platforms. In this paper, a new frequencies selecting algorithm
+adapted for heterogeneous grid platform is presented and executed over real testbed,
+the grid'5000 platform \cite{grid5000}. 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}
-
-\section{The performance and energy consumption measurements on heterogeneous architecture}
+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}
+
+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
In this paper, we are interested in reducing the energy consumption of message
passing distributed iterative synchronous applications running over
-heterogeneous grid platforms. A heterogeneous grid platform is defined as a collection of
-heterogeneous computing clusters interconnected via a long distance network (the internet network). Each computing cluster in the grid composed from homogeneous nodes, where are connected together via high speed homogeneous network. Therefore, each cluster has different characteristics such as computing power (FLOPS), energy consumption, CPU's frequency range, network bandwidth and latency.
+heterogeneous grid platforms. A heterogeneous grid platform could be defined as a collection of
+heterogeneous computing clusters interconnected via a long distance network which has lower bandwidth
+and higher latency than the local networks of the clusters. Each computing cluster in the grid is composed of homogeneous nodes that are connected together via high speed network. Therefore, each cluster has different characteristics such as computing power (FLOPS), energy consumption, CPU's frequency range, network bandwidth and latency.
\begin{figure}[!t]
\centering
+\mathop{\min_{j=1,\dots,M}} (\Tcm[hj])
\end{equation}
-where $N$ is the number of the clusters in the grid, $M$ is the number of the nodes in
+where $N$ is the number of clusters in the grid, $M$ is the number of nodes in
each cluster, $\TcpOld[ij]$ is the computation time of processor $j$ in the cluster $i$
and $\Tcm[hj]$ is the communication time of processor $j$ in the cluster $h$ during the
first iteration. The model computes the maximum computation time with scaling factor
used in the method to optimize both the energy consumption and the performance
of iterative methods, which is presented in the following sections.
-\subsection{Energy model for heterogeneous platform}
+
+\subsection{Energy model for heterogeneous grid platform}
Many researchers~\cite{Malkowski_energy.efficient.high.performance.computing,
Rauber_Analytical.Modeling.for.Energy,Zhuo_Energy.efficient.Dynamic.Task.Scheduling,
characteristics of each processor (computation power, range of frequencies,
dynamic and static powers) and the task executed (computation/communication
ratio). The aim being to reduce the overall energy consumption and to avoid
-increasing significantly the execution time. In our previous
-work~\cite{Our_first_paper,pdsec2015}, we proposed a method that selects the optimal
-frequency scaling factor for a homogeneous and heterogeneous clusters executing a message passing
+increasing significantly the execution time.
+\textcolor{blue}{ In our previous
+works~\cite{Our_first_paper} and \cite{pdsec2015}, we proposed a methods that select the optimal
+frequency scaling factors for a homogeneous and a heterogeneous clusters respectively.
+Both of the two methods executing a message passing
iterative synchronous application while giving the best trade-off between the
energy consumption and the performance for such applications. In this work we
-are interested in heterogeneous grid as described above. Due to the
+are interested in heterogeneous grid as described above.}
+Due to the
heterogeneity of the processors, a vector of scaling factors should be selected
and it must give the best trade-off between energy consumption and performance.
\end{equation}
Where $\Ereduced$ is computed using (\ref{eq:energy}) and $\Eoriginal$ is
-computed as in ().
+computed as in (\ref{eq:eorginal}).
+
\begin{equation}
\label{eq:eorginal}
energy reduction gain can be achieved when the energy curve has a convex form as shown
in~\cite{Zhuo_Energy.efficient.Dynamic.Task.Scheduling,Rauber_Analytical.Modeling.for.Energy,Hao_Learning.based.DVFS}.
-\section{The scaling factors selection algorithm for heterogeneous grid platforms }
+\section{The scaling factors selection algorithm for grids }
\label{sec.optim}
\begin{algorithm}
\label{dvfs}
\end{algorithm}
-\subsection{The algorithm details}
-In this section, Algorithm~\ref{HSA} is presented. It selects the frequency
-scaling factors vector that gives the best trade-off between minimizing the
+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
-synchronous iterative application executed on a heterogeneous grid platform. It works
+synchronous iterative application executed on a grid. It works
online during the execution time of the iterative message passing program. It
uses information gathered during the first iteration such as the computation
time and the communication time in one iteration for each node. The algorithm is
\label{fig:st_freq}
\end{figure}
-The nodes in a heterogeneous grid have different computing powers, thus
+Nodes from distinct clusters in a grid have different computing powers, thus
while executing message passing iterative synchronous applications, fast nodes
have to wait for the slower ones to finish their computations before being able
to synchronously communicate with them as in Figure~\ref{fig:heter}. These
periods are called idle or slack times. The algorithm takes into account this
-problem and tries to reduce these slack times when selecting the frequency
-scaling factors vector. At first, it selects initial frequency scaling factors
+problem and tries to reduce these slack times when selecting the vector of the frequency
+scaling factors. At first, it selects initial frequency scaling factors
that increase the execution times of fast nodes and minimize the differences
between the computation times of fast and slow nodes. The value of the initial
frequency scaling factor for each node is inversely proportional to its
\end{equation}
If the computed initial frequency for a node is not available in the gears of
that node, it is replaced by the nearest available frequency. In
-Figure~\ref{fig:st_freq}, the nodes are sorted by their computing power in
+Figure~\ref{fig:st_freq}, the nodes are sorted by their computing powers in
ascending order and the frequencies of the faster nodes are scaled down
according to the computed initial frequency scaling factors. The resulting new
frequencies are highlighted in Figure~\ref{fig:st_freq}. This set of
frequencies can be considered as a higher bound for the search space of the
-optimal vector of frequencies because selecting scaling factors higher
+optimal vector of frequencies because selecting higher frequencies
than the higher bound will not improve the performance of the application and it
will increase its overall energy consumption. Therefore the algorithm that
selects the frequency scaling factors starts the search method from these
initial frequencies and takes a downward search direction toward lower
-frequencies or reaching to the lower bound. The lower bound is used to stop
-the algorithm search process when the new computed distance between the energy and performance is less than zero.
-The new negative distance is mean that the performance degradation ratio is higher than energy saving ratio.
-Therefore, the algorithm must stop the iterations before reaching to the end of the search space, the minimum frequencies,
-because the all the coming new distances are negative values.
-The algorithm iterates on all remaining frequencies, from the higher
-bound until all nodes reach their minimum frequencies or to the lower bound, to compute their overall
-energy consumption and performance, and select the optimal frequency scaling
-factors vector. At each iteration the algorithm determines the slowest node
+frequencies until reaching the nodes' minimum frequencies or lower bounds. A node's frequency is considered its lower bound if the computed distance between the energy and performance at this frequency is less than zero.
+A negative distance means that the performance degradation ratio is higher than the energy saving ratio.
+In this situation, the algorithm must stop the downward search because it has reached the lower bound and it is useless to test the lower frequencies. Indeed, they will all give worse distances.
+
+Therefore, the algorithm iterates on all remaining frequencies, from the higher
+bound until all nodes reach their minimum frequencies or their lower bounds, to compute the overall
+energy consumption and performance and selects the optimal vector of the frequency scaling
+factors. At each iteration the algorithm determines the slowest node
according to the equation (\ref{eq:perf}) and keeps its frequency unchanged,
while it lowers the frequency of all other nodes by one gear. The new overall
energy consumption and execution time are computed according to the new scaling
highest distance according to the objective function (\ref{eq:max}).
Figures~\ref{fig:r1} and \ref{fig:r2} illustrate the normalized performance and
-consumed energy for an application running on a homogeneous platform and a
-heterogeneous grid platform respectively while increasing the scaling factors. It can
-be noticed that in a homogeneous platform the search for the optimal scaling
+consumed energy for an application running on a homogeneous cluster and a
+ grid platform respectively while increasing the scaling factors. It can
+be noticed that in a homogeneous cluster the search for the optimal scaling
factor should start from the maximum frequency because the performance and the
consumed energy decrease from the beginning of the plot. On the other hand, in
-the heterogeneous grid platform the performance is maintained at the beginning of the
+the grid platform the performance is maintained at the beginning of the
plot even if the frequencies of the faster nodes decrease until the computing
power of scaled down nodes are lower than the slowest node. In other words,
until they reach the higher bound. It can also be noticed that the higher the
difference between the faster nodes and the slower nodes is, the bigger the
-maximum distance between the energy curve and the performance curve is while the
-scaling factors are varying which results in bigger energy savings.
+maximum distance between the energy curve and the performance curve is, which results in bigger energy savings.
\section{Experimental results}
\label{sec.expe}
+While in~\cite{pdsec2015} the energy model and the scaling factors selection algorithm were applied to a heterogeneous cluster and evaluated over the SimGrid simulator~\cite{SimGrid},
+in this paper real experiments were conducted over the grid'5000 platform.
\subsection{Grid'5000 architature and power consumption}
\label{sec.grid5000}
-The grid'5000 is a large-scale testbed found in France \cite{grid5000}.
-The grid infrastructure consist of ten sites distributed over all France
-metropolitan regions. Each site in the grid'5000 composed from number of heterogeneous
-computing clusters, while each cluster includes a collection of homogeneous nodes.
-In general, the grid'5000 had one thousand of heterogeneous nodes and eight thousand of cores.
-All the sites are connected together via special long distance network called RENATER,
-which is the French National Telecommunication Network for Technology. Whereas inside each site
-the clusters and their nodes are connected throw high speed local area networks.
-There are different types of local networks used such as Ethernet and Infiniband netwoks,
-which allowed different gigabits bandwidth and latencies. On the other hand, the nodes inside each cluster
-are homogeneous, while they are different from the nodes of the other clusters. Therefore, there are
-a wide diversity of processors in grid'5000, that mainly had different processors families
-such as Intel Xeon and AMD Opteron families.
-
-In this paper we are interested to run NAS parallel v3.3 \cite{NAS.Parallel.Benchmarks} over grid'5000.
-We are used seven benchmarks, CG, MG, EP, LU, BT, SP and FT. These benchmarks used seven different types of classes.
-These classes are S, W, A, B, C, D, E, where S represents the smaller problem size that used by benchmark and
-E is represents the biggest class. In this work, the class D is used for all benchmarks in all the experiments that will
-be showed in the coming sections.
-Moreover, the NAS parallel benchmarks have different computations and communications ratios, then it is interested
-to study their energy consumption and their performance on real testbed such as grid'5000.
-In this work, the NAS benchmarks are executed over two sites, Lyon and Nancy sites, of grid'5000.
-These two sites had seven different types of computing clusters as in figure (\ref{fig:grid5000}).
+Grid'5000~\cite{grid5000} is a large-scale testbed that consists of ten sites distributed over all metropolitan France and Luxembourg. All the sites are connected together via a special long distance network called RENATER,
+which is the French National Telecommunication Network for Technology.
+Each site of the grid is composed of few heterogeneous
+computing clusters and each cluster contains many homogeneous nodes. In total,
+grid'5000 has about one thousand heterogeneous nodes and eight thousand cores. In each site,
+the clusters and their nodes are connected via high speed local area networks.
+Two types of local networks are used, Ethernet or Infiniband networks which have different characteristics in terms of bandwidth and latency.
+
+Since grid'5000 is dedicated for testing, contrary to production grids it allows a user to deploy its own customized operating system on all the booked nodes. The user could have root rights and thus apply DVFS operations while executing a distributed application. Moreover, the grid'5000 testbed provides at some sites a power measurement tool to capture
+the power consumption for each node in those sites. The measured power is the overall consumed power by by all the components of a node at a given instant, such as CPU, hard drive, main-board, memory, ... For more details refer to
+\cite{Energy_measurement}. To just measure the CPU power of one core in a node $j$,
+ firstly, the power consumed by the node while being idle at instant $y$, noted as $\Pidle[jy]$, was measured. Then, the power was measured while running a single thread benchmark with no communication (no idle time) over the same node with its CPU scaled to the maximum available frequency. The latter power measured at time $x$ with maximum frequency for one core of node $j$ is noted $\Pmax[jx]$. The difference between the two measured power consumption represents the
+dynamic power consumption of that core with the maximum frequency, see figure(\ref{fig:power_cons}).
+
+
+The dynamic power $\Pd[j]$ is computed as in equation (\ref{eq:pdyn})
+\begin{equation}
+ \label{eq:pdyn}
+ \Pd[j] = \max_{x=\beta_1,\dots \beta_2} (\Pmax[jx]) - \min_{y=\Theta_1,\dots \Theta_2} (\Pidle[jy])
+\end{equation}
+
+where $\Pd[j]$ is the dynamic power consumption for one core of node $j$,
+$\lbrace \beta_1,\beta_2 \rbrace$ is the time interval for the measured maximum power values,
+$\lbrace\Theta_1,\Theta_2\rbrace$ is the time interval for the measured idle power values.
+Therefore, the dynamic power of one core is computed as the difference between the maximum
+measured value in maximum powers vector and the minimum measured value in the idle powers vector.
+
+On the other hand, the static power consumption by one core is a part of the measured idle power consumption of the node. Since in grid'5000 there is no way to measure precisely the consumed static power and in~\cite{Our_first_paper,pdsec2015,Rauber_Analytical.Modeling.for.Energy} it was assumed that the static power represents a ratio of the dynamic power, the value of the static power is assumed as 20\% of dynamic power consumption of the core.
+
+In the experiments presented in the following sections, two sites of grid'5000 were used, Lyon and Nancy sites. These two sites have in total seven different clusters as in figure (\ref{fig:grid5000}).
+
+Four clusters from the two sites were selected in the experiments: one cluster from
+Lyon's site, Taurus cluster, and three clusters from Nancy's site, Graphene,
+Griffon and Graphite. Each one of these clusters has homogeneous nodes inside, while nodes from different clusters are heterogeneous in many aspects such as: computing power, power consumption, available
+frequency ranges and local network features: the bandwidth and the latency. Table \ref{table:grid5000} shows
+the details characteristics of these four clusters. Moreover, the dynamic powers were computed using the equation (\ref{eq:pdyn}) for all the nodes in the
+selected clusters and are presented in table \ref{table:grid5000}.
+
\begin{figure}[!t]
\centering
\label{fig:grid5000}
\end{figure}
-Four clusters from the two sites are selected in the experiments, one cluster from
-Lyon site, Taurus cluster, and three clusters from Nancy site where are Graphene,
-Griffon and Graphite. Each one of these clusters has homogeneous nodes inside, while their nodes are
-different from the nodes of other clusters in many aspects such as: computing power, power consumption, available
-frequencies ranges and the network features, the bandwidth and the latency. The Table \ref{table:grid5000} shows
-the details characteristics of these four clusters.
+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.
+
+
+
+
+\begin{figure}[!t]
+ \centering
+ \includegraphics[scale=0.6]{fig/power_consumption.pdf}
+ \caption{The power consumption by one core from Taurus cluster}
+ \label{fig:power_cons}
+\end{figure}
+
+
\begin{table}[!t]
\label{table:grid5000}
\end{table}
-The grid'5000 testbed provided some monitoring and measurements features to captured
-the power consumption values for each node in any cluster of Lyon and Nancy sites.
-The power consumed for each node from the selected four clusters is measured.
-While the power consumed by any computing node is a collection of the powers consumed by
-hard drive, main-board, memory and node's computing cores, for more detail refer to
-\cite{Energy_measurement}. Therefore, the dynamic power consumed
-by one core is not allowed to measured alone. To overcome this problem, firstly,
-we measured the power consumed by one node when there is no computation, when
-the CPU is in the idle state. The second step, we run EP benchmark, there is no communications
-in this benchmarks, over one core with maximum frequency of the desired node and
-capturing the power consumed by a node, this representing the peak power of the node with one core.
-The difference between the peak power and the idle power representing the
-dynamic power consumption of that core with maximum frequency, for example see figure(\ref{fig:power_cons}).
-The $\Ppeak[jx]$ is the peak power value in time $x$ with maximum frequency for one core of node $j$,
-and $\Pidle[jy]$ is the idle power value in time $y$ for the one core of the node $j$ .
-The dynamic power $\Pd[j]$ is computed as in equation (\ref{eq:pdyn})
-\begin{equation}
- \label{eq:pdyn}
- \Pd[j] = \max_{x=\beta_1,\dots \beta_2} (\Ppeak[jx]) - \min_{y=\Theta_1,\dots \Theta_2} (\Pidle[jy])
-\end{equation}
-where $\Pd[j]$ is the dynamic power consumption for one core of node $j$,
-$\lbrace \beta_1,\beta_2 \rbrace$ is the time interval for the measured peak power values,
-$\lbrace\Theta_1,\Theta_2\rbrace$ is the time interval for the measured idle power values.
-Therefore, the dynamic power of one core is computed as the difference between the maximum
-measured value in peak powers vector and the minimum measured value in the idle powers vector.
-We are computed the dynamic powers, using the equation (\ref{eq:pdyn}), for all nodes in the
-selected clusters, which is recorded in table \ref{table:grid5000}.
-On the other side, the static power consumption by one core is embedded with whole idle power consumption of the node.
-Indeed, the static power is represents as ratio from dynamic power. So, we supposed
-the static power consumption represented as \np[\%]{20} of dynamic power consumption of the core,
-the same assumption was made in \cite{Our_first_paper,pdsec2015,Rauber_Analytical.Modeling.for.Energy}.
-\begin{figure}[!t]
+
+\subsection{The experimental results of the scaling algorithm}
+\label{sec.res}
+In this section, the results of the application of the scaling factors selection algorithm \ref{HSA}
+to the NAS parallel benchmarks are presented.
+
+As mentioned previously, the experiments
+were conducted over two sites of grid'5000, Lyon and Nancy sites.
+Two scenarios were considered while selecting the clusters from these two sites :
+\begin{itemize}
+\item In the first scenario, nodes from two sites and three heterogeneous clusters were selected. The two sites are connected
+ via a long distance network.
+\item In the second scenario nodes from three clusters that are located in one site, Nancy site.
+\end{itemize}
+
+The main reason
+behind using these two scenarios is to evaluate the influence of long distance communications (higher latency) on the performance of the
+scaling factors selection algorithm. Indeed, in the first scenario the computations to communications ratio
+is very low due to the higher communication times which reduces the effect of DVFS operations.
+
+The NAS parallel benchmarks are executed over
+16 and 32 nodes for each scenario. The number of participating computing nodes form each cluster
+are different because all the selected clusters do not have the same available number of nodes and all benchmarks do not require the same number of computing nodes.
+Table \ref{tab:sc} shows the number of nodes used from each cluster for each scenario.
+
+\begin{table}[h]
+
+\caption{The different clusters scenarios}
+\centering
+\begin{tabular}{|*{4}{c|}}
+\hline
+\multirow{2}{*}{Scenario name} & \multicolumn{3}{c|} {The participating clusters} \\ \cline{2-4}
+ & Cluster & Site & No. of nodes \\
+\hline
+\multirow{3}{*}{Two sites / 16 nodes} & Taurus & Lyon & 5 \\ \cline{2-4}
+ & Graphene & Nancy & 5 \\ \cline{2-4}
+ & Griffon & Nancy & 6 \\
+\hline
+\multirow{3}{*}{Tow sites / 32 nodes} & Taurus & Lyon & 10 \\ \cline{2-4}
+ & Graphene & Nancy & 10 \\ \cline{2-4}
+ & Griffon &Nancy & 12 \\
+\hline
+\multirow{3}{*}{One site / 16 nodes} & Graphite & Nancy & 4 \\ \cline{2-4}
+ & Graphene & Nancy & 6 \\ \cline{2-4}
+ & Griffon & Nancy & 6 \\
+\hline
+\multirow{3}{*}{One site / 32 nodes} & Graphite & Nancy & 4 \\ \cline{2-4}
+ & Graphene & Nancy & 12 \\ \cline{2-4}
+ & Griffon & Nancy & 12 \\
+\hline
+\end{tabular}
+ \label{tab:sc}
+\end{table}
+
+\begin{figure}
\centering
- \includegraphics[scale=0.6]{fig/power_consumption.pdf}
- \caption{The power consumption by one core from Taurus cluster}
- \label{fig:power_cons}
+ \includegraphics[scale=0.5]{fig/eng_con_scenarios.eps}
+ \caption{The energy consumptions of NAS benchmarks over different scenarios }
+ \label{fig:eng_sen}
\end{figure}
-\subsection{The experimental results of the scaling algorithm}
-\label{sec.res}
+
+\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. 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.
+
+\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 bigger 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 their 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 sites 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 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\% or 4\% 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\% or 10\% 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\%. 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.
+
+
+
\subsection{The experimental results of multi-cores clusters}
-\label{sec.res}
+\label{sec.res-mc}
+The clusters of grid'5000 have different number of cores embedded in their nodes
+as shown in Table \ref{table:grid5000}. The cores of each node can exchange
+data via the shared memory \cite{rauber_book}. In
+this section, the proposed scaling algorithm is evaluated over the grid'5000 grid while using multi-core nodes
+selected according to the two platform scenarios described in the section \ref{sec.res}.
+The two platform scenarios, the two sites and one site scenarios, use 32
+cores from multi-cores nodes instead of 32 distinct nodes. For example if
+the participating number of cores from a certain cluster is equal to 12,
+in the multi-core scenario the selected nodes is equal to 3 nodes while using
+4 cores from each node. The platforms with one
+core per node and multi-cores nodes are shown 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 presented
+in the figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.
+
+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.
+
+ \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.
+Indeed, in this scenario each core has a dedicated network link and all the communications are local.
+Moreover, the energy consumptions of the NAS benchmarks are lower over the
+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.
+
+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
+consumption and the execution times of the EP and MG benchmarks do not change significantly over these four
+scenarios because there are no or small communications,
+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.
+
+
+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
+are approximately equivalent, on average they are up to 25\%. In both scenarios there
+are a small difference in the computations to communications ratios, which leads
+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 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.
+
+
+When the benchmarks are executed over the one
+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 bigger
+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 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
+\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}
-\subsection{The results for different power consumption scenarios}
-\label{sec.compare}
+ \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}
+\subsection{Experiments with different static and dynamic powers consumption scenarios}
+\label{sec.pow_sen}
+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 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.
+
+ \begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/eng_pow.eps}
+ \caption{The energy saving percentages for NAS benchmarks of the three power scenario}
+ \label{fig:eng-pow}
+\end{figure}
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/per_pow.eps}
+ \caption{The performance degradation percentages for NAS benchmarks of the three power scenario}
+ \label{fig:per-pow}
+\end{figure}
-\subsection{The comparison of the proposed scaling algorithm }
-\label{sec.compare_EDP}
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/dist_pow.eps}
+ \caption{The tradeoff distance for NAS benchmarks of the three power scenario}
+ \label{fig:dist-pow}
+\end{figure}
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.47]{fig/three_scenarios.pdf}
+ \caption{Comparing the selected frequency scaling factors of MG benchmark for three static power scenarios}
+ \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
+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. }
+
+
+\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.
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/edp_eng}
+ \caption{Comparing of the energy saving for the proposed method with EDP method}
+ \label{fig:edp-eng}
+\end{figure}
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/edp_per}
+ \caption{Comparing of the performance degradation for the proposed method with EDP method}
+ \label{fig:edp-perf}
+\end{figure}
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/edp_dist}
+ \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.
+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.
+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 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 $ms$.
+}
\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}
