X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/mpi-energy2.git/blobdiff_plain/eac9d615d9ae026613914cc0aac04335d39cff5c..c9efa3aa1b816cbed779a8f68048dca4759ed1b1:/mpi-energy2-extension/Heter_paper.tex

diff --git a/mpi-energy2-extension/Heter_paper.tex b/mpi-energy2-extension/Heter_paper.tex
index 82c4e24..5dc876c 100644
--- a/mpi-energy2-extension/Heter_paper.tex
+++ b/mpi-energy2-extension/Heter_paper.tex
@@ -1,5 +1,5 @@
-\documentclass[conference]{IEEEtran}
-
+\documentclass[3p,times]{elsarticle-1}
+\usepackage{ecrc}
 \usepackage[T1]{fontenc}
 \usepackage[utf8]{inputenc}
 \usepackage[english]{babel}
@@ -60,34 +60,182 @@
 \newcommand{\Tnew}{\Xsub{T}{New}}
 \newcommand{\Told}{\Xsub{T}{Old}}
 
+
+%% The ecrc package defines commands needed for running heads and logos.
+%% For running heads, you can set the journal name, the volume, the starting page and the authors
+
+%% set the volume if you know. Otherwise `00'
+\volume{00}
+
+%% set the starting page if not 1
+\firstpage{1}
+
+%% Give the name of the journal
+\journalname{Procedia Computer Science}
+
+%% Give the author list to appear in the running head
+%% Example \runauth{C.V. Radhakrishnan et al.}
+\runauth{}
+
+%% The choice of journal logo is determined by the \jid and \jnltitlelogo commands.
+%% A user-supplied logo with the name <\jid>logo.pdf will be inserted if present.
+%% e.g. if \jid{yspmi} the system will look for a file yspmilogo.pdf
+%% Otherwise the content of \jnltitlelogo will be set between horizontal lines as a default logo
+
+%% Give the abbreviation of the Journal.
+\jid{procs}
+
+%% Give a short journal name for the dummy logo (if needed)
+\jnltitlelogo{Procedia Computer Science}
+
+%% Hereafter the template follows `elsarticle'.
+%% For more details see the existing template files elsarticle-template-harv.tex and elsarticle-template-num.tex.
+
+%% Elsevier CRC generally uses a numbered reference style
+%% For this, the conventions of elsarticle-template-num.tex should be followed (included below)
+%% If using BibTeX, use the style file elsarticle-num.bst
+
+%% End of ecrc-specific commands
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%% The amssymb package provides various useful mathematical symbols
+\usepackage{amssymb}
+%% The amsthm package provides extended theorem environments
+%% \usepackage{amsthm}
+
+%% The lineno packages adds line numbers. Start line numbering with
+%% \begin{linenumbers}, end it with \end{linenumbers}. Or switch it on
+%% for the whole article with \linenumbers after \end{frontmatter}.
+%% \usepackage{lineno}
+
+%% natbib.sty is loaded by default. However, natbib options can be
+%% provided with \biboptions{...} command. Following options are
+%% valid:
+
+%%   round  -  round parentheses are used (default)
+%%   square -  square brackets are used   [option]
+%%   curly  -  curly braces are used      {option}
+%%   angle  -  angle brackets are used    <option>
+%%   semicolon  -  multiple citations separated by semi-colon
+%%   colon  - same as semicolon, an earlier confusion
+%%   comma  -  separated by comma
+%%   numbers-  selects numerical citations
+%%   super  -  numerical citations as superscripts
+%%   sort   -  sorts multiple citations according to order in ref. list
+%%   sort&compress   -  like sort, but also compresses numerical citations
+%%   compress - compresses without sorting
+%%
+%% \biboptions{comma,round}
+
+% \biboptions{}
+
+% if you have landscape tables
+\usepackage[figuresright]{rotating}
+
+% put your own definitions here:
+%   \newcommand{\cZ}{\cal{Z}}
+%   \newtheorem{def}{Definition}[section]
+%   ...
+
+% add words to TeX's hyphenation exception list
+%\hyphenation{author another created financial paper re-commend-ed Post-Script}
+
+% declarations for front matter
+
 \begin{document}
 
-\title{Energy Consumption Reduction with DVFS for \\
-  Message Passing Iterative Applications on \\
-  Heterogeneous Architectures}
-
-\author{%
-  \IEEEauthorblockN{%
-    Jean-Claude Charr,
-    Raphaël Couturier,
-    Ahmed Fanfakh and
-    Arnaud Giersch
-  }
-  \IEEEauthorblockA{%
-    FEMTO-ST Institute, University of Franche-Comté\\
+\begin{frontmatter}
+
+%% Title, authors and addresses
+
+%% use the tnoteref command within \title for footnotes;
+%% use the tnotetext command for the associated footnote;
+%% use the fnref command within \author or \address for footnotes;
+%% use the fntext command for the associated footnote;
+%% use the corref command within \author for corresponding author footnotes;
+%% use the cortext command for the associated footnote;
+%% use the ead command for the email address,
+%% and the form \ead[url] for the home page:
+%%
+%% \title{Title\tnoteref{label1}}
+%% \tnotetext[label1]{}
+%% \author{Name\corref{cor1}\fnref{label2}}
+%% \ead{email address}
+%% \ead[url]{home page}
+%% \fntext[label2]{}
+%% \cortext[cor1]{}
+%% \address{Address\fnref{label3}}
+%% \fntext[label3]{}
+
+\dochead{}
+%% Use \dochead if there is an article header, e.g. \dochead{Short communication}
+\title{Energy Consumption Reduction with DVFS for Message Passing \\
+       Iterative Applications on Grid Architecture} 
+  
+
+%% use optional labels to link authors explicitly to addresses:
+%% \author[label1,label2]{<author name>}
+%% \address[label1]{<address>}
+%% \address[label2]{<address>}
+
+\author{Ahmed Fanfakh,
+        Jean-Claude Charr,
+        Raphaël Couturier,
+        and Arnaud Giersch}
+
+\address{FEMTO-ST Institute, University of Franche-Comté\\
     IUT de Belfort-Montbéliard,
     19 avenue du Maréchal Juin, BP 527, 90016 Belfort cedex, France\\
     % Telephone: \mbox{+33 3 84 58 77 86}, % Raphaël
     % Fax: \mbox{+33 3 84 58 77 81}\\      % Dept Info
-    Email: \email{{jean-claude.charr,raphael.couturier,ahmed.fanfakh_badri_muslim,arnaud.giersch}@univ-fcomte.fr}
+    Email: \email{{ahmed.fanfakh_badri_muslim,jean-claude.charr,raphael.couturier,arnaud.giersch}@univ-fcomte.fr}
    }
-  }
 
-\maketitle
+\begin{abstract}
+  In recent years, green computing topic  has  become an important topic 
+  in the supercomputing research domain. However, the 
+  computing platforms are still  consuming more and
+more energy due to the increasing number of nodes composing
+them. To minimize the operating costs of these platforms many
+techniques have been used. Dynamic voltage and frequency
+scaling (DVFS) is one of them. It can be used to reduce the power consumption of the CPU 
+  while computing, by lowering its frequency. However, 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 grids, composed of heterogeneous clusters, 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  grid. 
+  The proposed algorithm is evaluated on a real grid, the grid'5000 platform, while
+  running the NAS parallel benchmarks.  The experiments show that it reduces the
+  energy consumption on average by \np[\%]{30} while  the performance  is only degraded
+  on average by \np[\%]{3.2}. Finally, the algorithm is 
+  compared to an existing method. The comparison results show that it outperforms the
+  latter in terms of energy consumption reduction and performance.
+\end{abstract}
+
+
+\begin{keyword}
+\textcolor{blue}{
+DVFS \sep heterogeneous grid \sep energy consumption  \sep performance prediction  \sep energy and performance trade-off  \sep frequencies selecting algorithm }
+
+%% keywords here, in the form: keyword \sep keyword
+
+%% MSC codes here, in the form: \MSC code \sep code
+%% or \MSC[2008] code \sep code (2000 is the default)
+
+\end{keyword}
+
+\end{frontmatter}
+
+
 
 \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
@@ -105,9 +253,7 @@ 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
@@ -120,32 +266,31 @@ 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
+The results of the experiments showed 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.}
+Simgrid simulator \cite{SimGrid}, which offers easy tools to create a homogeneous and heterogeneous platforms and run message passing parallel applications over them. In this paper, a new frequencies selecting algorithm,
+adapted to  grid platforms composed of heterogeneous clusters, is presented. It is applied to the NAS parallel benchmarks and evaluated over a real testbed, 
+the grid'5000 platform \cite{grid5000}. It selects  for a grid platform running a message passing iterative
+application the vector of
+frequencies  that simultaneously tries to offer the maximum energy reduction and
+minimum performance degradation ratios. 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
+over a grid platform. 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
+NAS parallel benchmarks and executing them on the grid'5000 testbed. 
+%It shows the results of running different scenarios using multi-cores and one core per node and comparing them. 
+It also evaluates the algorithm over three different power scenarios. 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.}
+in Section~\ref{sec.concl} the paper ends with a summary and some future works.
 
 \section{Related works}
 \label{sec.relwork}
@@ -365,11 +510,11 @@ follows:
 \end{equation}
 Replacing $\Fnew$ in (\ref{eq:pd}) as in (\ref{eq:fnew}) gives the following
 equation for dynamic power consumption:
-\begin{multline}
+\begin{equation}
   \label{eq:pdnew}
-   \PdNew = \alpha \cdot \CL \cdot V^2 \cdot \Fnew = \alpha \cdot \CL \cdot \beta^2 \cdot \Fnew^3 \\
-   {} = \alpha \cdot \CL \cdot V^2 \cdot \Fmax \cdot S^{-3} = \PdOld \cdot S^{-3}
-\end{multline}
+   \PdNew = \alpha \cdot \CL \cdot V^2 \cdot \Fnew = \alpha \cdot \CL \cdot \beta^2 \cdot \Fnew^3 
+    = \alpha \cdot \CL \cdot V^2 \cdot \Fmax \cdot S^{-3} = \PdOld \cdot S^{-3}
+\end{equation}
 where $\PdNew$  and $\PdOld$ are the  dynamic power consumed with the
 new frequency and the maximum frequency respectively.
 
@@ -415,13 +560,13 @@ of one iteration multiplied by the static power of each processor.  The overall
 energy consumption of a message passing distributed application executed over a
 heterogeneous grid platform during one iteration is the summation of all dynamic and
 static energies for $M$ processors in $N$ clusters.  It is computed as follows:
-\begin{multline}
+\begin{equation}
   \label{eq:energy}
  E = \sum_{i=1}^{N} \sum_{i=1}^{M} {(S_{ij}^{-2} \cdot \Pd[ij] \cdot  \Tcp[ij])} +  
- \sum_{i=1}^{N} \sum_{j=1}^{M} (\Ps[ij] \cdot {} \\
+ \sum_{i=1}^{N} \sum_{j=1}^{M} (\Ps[ij] \cdot 
   (\mathop{\max_{i=1,\dots N}}_{j=1,\dots,M}({\Tcp[ij]} \cdot S_{ij}) 
   +\mathop{\min_{j=1,\dots M}} (\Tcm[hj]) ))
-\end{multline}
+\end{equation}
 
 Reducing the frequencies of the processors according to the vector of scaling
 factors $(S_{11}, S_{12},\dots, S_{NM})$ may degrade the performance of the application
@@ -446,13 +591,15 @@ appropriate frequency scaling factor for each processor while considering the
 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
-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
+increasing significantly the execution time.
+In our previous
+works, \cite{Our_first_paper} and \cite{pdsec2015}, two methods that select the optimal
+frequency scaling factors for a homogeneous and a heterogeneous cluster respectively, were proposed. 
+Both methods selects the frequencies that gives the best tradeoff between 
+energy consumption reduction and performance for  message passing
+iterative synchronous applications.   In this work we
+are interested in grids that are composed of heterogeneous clusters were the nodes have different characteristics such  as  dynamic power, static power, computation power, frequencies range, network latency and bandwidth. 
+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.
 
@@ -511,13 +658,12 @@ equation, as follows:
   \Pnorm = \frac{\Told}{\Tnew}          
 \end{equation}
 
-\begin{figure}[!t]
+\begin{figure}
   \centering
   \subfloat[Homogeneous cluster]{%
-    \includegraphics[width=.33\textwidth]{fig/homo}\label{fig:r1}}%
-
+    \includegraphics[width=.4\textwidth]{fig/homo}\label{fig:r1}} \hspace{2cm}%
   \subfloat[Heterogeneous grid]{%
-    \includegraphics[width=.33\textwidth]{fig/heter}\label{fig:r2}}
+    \includegraphics[width=.4\textwidth]{fig/heter}\label{fig:r2}}
   \label{fig:rel}
   \caption{The energy and performance relation}
 \end{figure}
@@ -613,7 +759,8 @@ in~\cite{Zhuo_Energy.efficient.Dynamic.Task.Scheduling,Rauber_Analytical.Modelin
 \end{algorithm}
 
 
-In this section, the scaling factors selection algorithm for  grids, algorithm~\ref{HSA}, is presented. It selects the vector of the frequency
+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  grid. It works
@@ -629,7 +776,7 @@ scaling algorithm is called in the iterative MPI program.
 
 \begin{figure}[!t]
   \centering
-  \includegraphics[scale=0.45]{fig/init_freq}
+  \includegraphics[scale=0.6]{fig/init_freq}
   \caption{Selecting the initial frequencies}
   \label{fig:st_freq}
 \end{figure}
@@ -751,22 +898,18 @@ selected clusters and are presented in table  \ref{table:grid5000}.
   \caption{The selected two sites of grid'5000}
   \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. 
-
-
-
-
 \begin{figure}[!t]
   \centering
   \includegraphics[scale=0.6]{fig/power_consumption.pdf}
-  \caption{The power consumption by one core from Taurus cluster}
+  \caption{The power consumption by one core from the Taurus cluster}
   \label{fig:power_cons}
 \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. 
+
 
   
 \begin{table}[!t]
@@ -847,29 +990,16 @@ Table \ref{tab:sc} shows the number of nodes used from each cluster for each sce
                                       & 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                       \\ 
+                                      & Graphene      & Nancy          & 14                     \\ \cline{2-4} 
+                                      & Griffon          & Nancy       & 14                       \\ 
 \hline
 \end{tabular}
  \label{tab:sc}
 \end{table}
 
-\begin{figure}
-  \centering
-  \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}
 
 
 
-\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
@@ -893,28 +1023,7 @@ scenario. Moreover, most of the benchmarks running over the one site scenario th
 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,
@@ -928,8 +1037,31 @@ is exponentially related to the CPU's frequency value. On the other side, the in
 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. 
+\begin{figure}
+  \centering
+  \subfloat[The energy consumption by the nodes wile executing the NAS benchmarks over different scenarios    
+           ]{%
+    \includegraphics[width=.4\textwidth]{fig/eng_con_scenarios.eps}\label{fig:eng_sen}} \hspace{1cm}%
+  \subfloat[The execution times of the NAS benchmarks over different scenarios]{%
+    \includegraphics[width=.4\textwidth]{fig/time_scenarios.eps}\label{fig:time_sen}}
+  \label{fig:exp-time-energy}
+  \caption{The  energy consumption and execution time of NAS  Benchmarks over different scenarios}
+\end{figure}
 
 
+\begin{figure}
+  \centering
+  \subfloat[The energy reduction while executing the NAS benchmarks over different scenarios ]{%
+    \includegraphics[width=.4\textwidth]{fig/eng_s.eps}\label{fig:eng_s}} \hspace{2cm}%
+  \subfloat[The performance degradation of the NAS benchmarks over different scenarios]{%
+    \includegraphics[width=.4\textwidth]{fig/per_d.eps}\label{fig:per_d}}\hspace{2cm}%
+    \subfloat[The tradeoff distance between the energy reduction and the performance of the NAS benchmarks  
+      over different scenarios]{%
+    \includegraphics[width=.4\textwidth]{fig/dist.eps}\label{fig:dist}}
+  \label{fig:exp-res}
+  \caption{The experimental results of different scenarios}
+\end{figure}
+
 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 
@@ -946,9 +1078,9 @@ The best energy saving percentage was obtained in the one site scenario with 16
 
 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. 
+16 or 32  nodes is on average equal to 8.3\% or 4.7\% respectively. 
 For this scenario, the proposed scaling algorithm selects smaller frequencies for the executions with 32 nodes  without significantly degrading their performance because the communication times are higher with 32 nodes which results in smaller  computations to communications ratio.  On the other hand, the performance degradation percentage  for the benchmarks running  on one site  with
-16 or 32  nodes is on average equal to 3\% 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 
+16 or 32  nodes is on average equal to 3.2\% or 10.6\% respectively. In opposition to the two sites scenario, when the number of computing nodes is increased in the one site scenario, the performance degradation percentage is increased. Therefore, doubling the number of computing 
 nodes when the communications occur in high speed network does not decrease the computations to 
 communication ratio. 
 
@@ -960,11 +1092,10 @@ 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, on average it is equal to  26.8\%. The one site scenario using both 16 and 32 nodes had better energy and performance 
 tradeoff comparing to the two sites scenario  because the former has high speed local communications 
 which increase the computations to communications ratio  and the latter uses long distance communications which decrease this ratio. 
 
-
  Finally, the best energy and performance tradeoff depends on all of the following:
 1) the computations to communications ratio when there are  communications and slack times, 2) the heterogeneity of the computing powers of the nodes and 3) the heterogeneity of the consumed  static and dynamic powers of the nodes.
 
@@ -973,142 +1104,95 @@ which increase the computations to communications ratio  and the latter uses lon
 
 \subsection{The experimental results of multi-cores clusters}
 \label{sec.res-mc}
+\textcolor{blue}{
 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  
+as shown in Table \ref{table:grid5000}. In 
+this section, the proposed scaling algorithm is evaluated over the grid'5000 grid while using multi-core nodes selected according to the one site scenario described in the section \ref{sec.res}.
+The one site scenario, uses  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 14, 
+in the multi-core scenario the selected nodes is equal to  4 nodes while using 
+3 or 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 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 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. 
+in the figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} 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
+                                       & Graphene     & 14              & 1                   \\  \cline{2-4}
+                                       & Griffon      & 14              & 1                   \\ \hline
+\multirow{3}{*}{One site/ multicores}  & Graphite     & 1               &  4              \\  \cline{2-4}
+                                       & Graphene     & 4               & 3 or 4              \\  \cline{2-4}
+                                       & Griffon      & 4               & 3 or 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}
+  \subfloat[Comparing the  execution times of running NAS benchmarks over one core and multicores scenarios]{%
+    \includegraphics[width=.4\textwidth]{fig/time.eps}\label{fig:time-mc}} \hspace{1cm}%
+  \subfloat[Comparing the  energy consumptions of running NAS benchmarks over one core and multi-cores scenarios]{%
+    \includegraphics[width=.4\textwidth]{fig/eng_con.eps}\label{fig:eng-cons-mc}}
+    \label{fig:eng-cons}
+  \caption{The energy consumptions and execution times of NAS benchmarks over one core and multi-cores scenarios}
 \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}
+\textcolor{blue}{
+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. Moreover, the cores of a node share the memory bus which can be also saturated and become a bottleneck.    
+The experiments showed that for most of the NAS benchmarks,      
+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 memory bus.  
+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 ratio of the multi-cores scenario. 
+More energy reduction was achieved when this ratio is increased because the proposed scaling algorithm selects smaller frequencies that decrease the dynamic power consumption. 
+These experiments also showed that the energy 
+consumption and the execution times of the EP and MG benchmarks do not change significantly over these two
+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 two scenarios are presented in the figure \ref{fig:eng-s-mc}. It shows that  the energy saving percentages in the one site one 
+core and one site multi-cores scenarios
+are approximately equivalent, on average they are equal to  25.9\% and 25.1\% respectively. 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 over one site one core is on average equal to 10.6\% and is higher than these executed over the one site multi-cores scenario, which is on average equal to 7.5\%. 
+The performance degradation percentages over one site multi-cores is lower because  the computations to communications ratio is decreased. Therefore, selecting big
+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 the two 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  scenario gives bigger tradeoff distance percentages, on overage equal to 17.6\%  than using one core per node scenario,  on average  equal to 15.3\%.}
 
- \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}
+    \subfloat[The energy saving of running NAS benchmarks over one core and multicores scenarios]{%
+    \includegraphics[width=.4\textwidth]{fig/eng_s_mc.eps}\label{fig:eng-s-mc}} \hspace{2cm}%
+    \subfloat[The performance degradation of running NAS benchmarks over one core and multicores scenarios
+      ]{%
+    \includegraphics[width=.4\textwidth]{fig/per_d_mc.eps}\label{fig:per-d-mc}}\hspace{2cm}%
+    \subfloat[The tradeoff distance of running NAS benchmarks over one core and multicores scenarios]{%
+    \includegraphics[width=.4\textwidth]{fig/dist_mc.eps}\label{fig:dist-mc}}
+  \label{fig:exp-res}
+  \caption{The experimental results of one core and multi-cores scenarios}
 \end{figure}
 
+
+
 \subsection{Experiments with different static and dynamic powers consumption scenarios}
 \label{sec.pow_sen}
 
@@ -1116,176 +1200,138 @@ In section \ref{sec.grid5000}, since it was not possible to measure the static p
 
 The aim of  this section is to evaluate the scaling algorithm while assuming different values of static powers. 
 In addition to the previously used  percentage of static power, two new static power ratios,  10\% and 30\% of the measured dynamic power of the core, are used in this section.
-The experiments have been executed with these two new static power scenarios and over the one site one core per node scenario.
-In these experiments, the class D of the NAS parallel benchmarks are executed over Nancy's site. 16 computing nodes from the three sites, Graphite, Graphene and Griffon, where used in this experiment.  
+The experiments have been executed with these two new static power scenarios  over the one site one core per node scenario.
+In these experiments, the class D of the NAS parallel benchmarks are executed over Nancy's site. 16 computing nodes from the three clusters, Graphite, Graphene and Griffon, where used in this experiment. 
 
- \begin{figure}
-  \centering
-  \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}
+  \subfloat[The energy saving percentages for the nodes executing the NAS benchmarks over the three power scenarios]{%
+    \includegraphics[width=.4\textwidth]{fig/eng_pow.eps}\label{fig:eng-pow}} \hspace{2cm}%
+  \subfloat[The performance degradation percentages for the NAS benchmarks over the three power scenarios]{%
+    \includegraphics[width=.4\textwidth]{fig/per_pow.eps}\label{fig:per-pow}}\hspace{2cm}%
+    \subfloat[The tradeoff distance between the energy reduction and the performance of the NAS benchmarks over the three power scenarios]{%
+      
+    \includegraphics[width=.4\textwidth]{fig/dist_pow.eps}\label{fig:dist-pow}}
+  \label{fig:exp-pow}
+  \caption{The experimental results of different static power scenarios}
 \end{figure}
 
 
-\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}
+  \includegraphics[scale=0.5]{fig/three_scenarios.pdf}
+  \caption{Comparing the selected frequency scaling factors for the MG benchmark over the 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 
+gives the biggest energy saving percentages in comparison to the 20\% and 30\% static power 
+scenarios. The small value of the static power consumption makes the proposed 
 scaling algorithm  select smaller frequencies for the CPUs. 
 These smaller frequencies reduce the dynamic energy consumption more than increasing the consumed static energy which gives 		less overall energy consumption. 
 The energy saving percentages of the 30\% static power scenario is the smallest between the other scenarios, because the scaling algorithm selects bigger frequencies for the CPUs which increases the energy consumption. Figure \ref{fig:fre-pow} demonstrates that the proposed scaling algorithm selects   the best frequency scaling factors   according to the static power consumption ratio being used.
 
-\textcolor{blue}{ 
-The performance degradation percentages are presented in the figure \ref{fig:per-pow},
-the 30\% of static power scenario had less performance degradation percentage. This  because
-bigger frequencies are selected for the CPUs by the scaling algorithm. While, 
-the inverse happens in the 20\% and 30\% scenarios, because the scaling algorithm selects  bigger 
-frequencies. 
-The tradeoff distance percentage for the NAS benchmarks with these three static power scenarios 
-are presented in the figure \ref{fig:dist}. It shows that the tradeoff
-distance percentage is the best when the  10\% of static power scenario is used, and this percentage 
-is decreased for the other two scenarios because of  different frequencies have being selected by the scaling algorithm.
-In EP benchmark, the results of energy saving, performance degradation and tradeoff 
-distance are showed small differences when the these static power scenarios are used.
-In this benchmark there are no communications which leads  the proposed scaling algorithm to select similar frequencies even if the static power values are different. While, the 
-inverse has been shown  for the rest of the benchmarks, which have  different communication times.
-This makes the scaling algorithm proportionally selects big or small frequencies for each benchmark,
-because the communication times  proportionally increase or decrease the static energy consumption. }
+The performance degradation percentages are presented in the figure \ref{fig:per-pow}.
+The 30\% static power scenario had less performance degradation percentage  because the scaling algorithm
+had  selected big frequencies for the CPUs. While, 
+the inverse happens in the 10\% and 20\% scenarios because the scaling algorithm had selected  CPUs' frequencies smaller than those of the 30\% scenario. The tradeoff distance percentage for the NAS benchmarks with these three static power scenarios 
+are presented in the figure \ref{fig:dist}. 
+It shows that the best  tradeoff
+distance percentage is obtained with  the  10\% static power scenario  and this percentage 
+is decreased for the other two scenarios because the scaling algorithm had selected different frequencies according to the static power values.
+
+In the EP benchmark, the energy saving, performance degradation and tradeoff 
+distance percentages for the these static power scenarios are not significantly different because there is no communication in this benchmark. Therefore, the static power is only consumed during computation and   the proposed scaling algorithm selects similar frequencies for the three scenarios.  On the other hand,  for the rest of the benchmarks,  the scaling algorithm  selects  the values of the frequencies according to the communication times of each benchmark because the static energy consumption increases  proportionally to the  communication times.
+
 
  
 \subsection{The comparison of the proposed frequencies selecting algorithm }
 \label{sec.compare_EDP}
-\textcolor{blue}{
-The tradeoff between the energy consumption and the performance of the parallel 
-applications had significant importance in the domain of the research. 
-Many researchers, \cite{EDP_for_multi_processors,Energy_aware_application_scheduling,Exploring_Energy_Performance_TradeOffs},
-have optimized the tradeoff between the energy and the performance using the well known  energy and delay product, $EDP=energy \times delay$. 
-This model is also used by Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS},
-the  objective is to select the frequencies that minimized EDP product for the multi-cores 
-architecture when DVFS is used. Moreover, their algorithm is applied online, which synchronously optimized the energy consumption 
-and the execution time. Both energy consumption and execution time of a processor are predicted by the their algorithm.
-In this section the proposed frequencies selection algorithm, called Maxdist is compared with Spiliopoulos et al. algorithm, called EDP.
-To make both of the algorithms follow the same direction and  fairly  comparing them, the same energy model,  equation \ref{eq:energy} and
-the execution time model, equation \ref{eq:perf}, are used in the prediction process to select the best vector of the frequencies. 
-In contrast, the proposed algorithm starts the search space from the lower bound computed as in equation the  \ref{eq:Fint}. Also, the algorithm
-stops  the search process when it is reached to the lower bound as mentioned before. In the same way, the EDP algorithm is developed to start from the 
-same upper bound used in Maxdist algorithm, and it stops the search process when  a minimum available frequencies is reached. 
-Finally, the resulting EDP algorithm is an exhaustive search algorithm that test all possible frequencies, starting from the initial frequencies, 
-and selecting those minimized the EDP product.
-Both algorithms were applied to NAS benchmarks, class D, over 16 nodes selected from grid'5000 clusters.
-The participating computing nodes are distributed between two sites and one site to have two different scenarios that used in the section \ref{sec.res}. 
-The experimental results: the energy saving, performance degradation and tradeoff distance percentages are 
-presented in the figures \ref{fig:edp-eng}, \ref{fig:edp-perf} and \ref{fig:edp-dist} respectively. 
-\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}
+
+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 a method that uses the well known  energy and delay product objective function, $EDP=energy \times delay$, that has been used by many researchers  \cite{EDP_for_multi_processors,Energy_aware_application_scheduling,Exploring_Energy_Performance_TradeOffs}. 
+This objective function  was also used by Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS} where they select the frequencies that minimize the EDP product and apply them with DVFS operations to  the multi-cores 
+architecture. Their online algorithm predicts the energy consumption and execution time of a processor before using the EDP method.
+
+To fairly compare the proposed frequencies scaling algorithm to  Spiliopoulos et al. algorithm, called Maxdist and EDP respectively, both algorithms use the same energy model,  equation \ref{eq:energy} and
+execution time model, equation \ref{eq:perf}, to predict the energy consumption and the execution time for each computing node.
+Moreover, both algorithms start the search space from the upper bound computed as in equation   \ref{eq:Fint}.
+Finally, the resulting EDP algorithm is an exhaustive search algorithm that tests all the possible frequencies, starting from the initial frequencies (upper bound), 
+and selects the vector of frequencies that minimize the EDP product.
+
+Both algorithms were applied to the class D of the NAS benchmarks over 16 nodes.
+The participating computing nodes are distributed  according to the two scenarios described in  section \ref{sec.res}. 
+The experimental results, the energy saving, performance degradation and tradeoff distance percentages, are 
+presented in the figures \ref{fig:edp-eng}, \ref{fig:edp-perf} and \ref{fig:edp-dist} respectively.
+
+
 \begin{figure}
   \centering
-  \includegraphics[scale=0.5]{fig/edp_dist}
-  \caption{Comparing of the tradeoff distance for the proposed method with EDP method}
-  \label{fig:edp-dist}
+  \subfloat[The energy reduction induced by the Maxdist method and the EDP method]{%
+    \includegraphics[width=.4\textwidth]{fig/edp_eng}\label{fig:edp-eng}} \hspace{2cm}%
+    \subfloat[The performance degradation induced by  the Maxdist method and the EDP method]{%
+    \includegraphics[width=.4\textwidth]{fig/edp_per}\label{fig:edp-perf}}\hspace{2cm}%
+    \subfloat[The tradeoff distance between the energy consumption reduction and the performance for the Maxdist method and the  EDP method]{%
+    \includegraphics[width=.4\textwidth]{fig/edp_dist}\label{fig:edp-dist}}
+  \label{fig:edp-comparison}
+  \caption{The comparison results}
 \end{figure}
-As shown form these figures, the proposed frequencies selection algorithm, Maxdist, outperform the EDP algorithm in term of energy and performance for all of the benchmarks executed over the two scenarios. 
-Generally, the proposed algorithm gives better results for all benchmarks because it is
-optimized the distance between the energy saving and the performance degradation in the same time. 
+
+As shown in these figures, the proposed frequencies selection algorithm, Maxdist, outperforms the EDP algorithm in terms of energy consumption reduction and performance for all of the benchmarks executed over the two scenarios. 
+The proposed algorithm gives better results than EDP  because it 
+maximizes the energy saving and the performance at the same time. 
 Moreover, the proposed scaling algorithm gives the same weight for these two metrics.
-Whereas, the EDP algorithm gives some times negative tradeoff values for some benchmarks in the two sites scenarios.
+Whereas, the EDP algorithm gives sometimes negative tradeoff values for some benchmarks in the two sites scenarios.
 These negative tradeoff values mean that the performance degradation percentage is higher than energy saving percentage.
-The higher positive value of the tradeoff distance percentage mean that the  energy saving percentage is much higher than the performance degradation percentage. 
+The high positive values of the tradeoff distance percentage mean that the  energy saving percentage is much higher than the performance degradation percentage. 
 The time complexity of both Maxdist and EDP algorithms are $O(N \cdot M \cdot F)$ and 
-$O(N \cdot M \cdot F^2)$ respectively. Where $N$ is the number of the clusters, $M$ is the number of nodes and $F$ is the 
-maximum number of available frequencies. The proposed algorithm, Maxdist, has selected the best frequencies in a small execution time, 
-on average is equal to  0.01 $ms$, when it is executed over 32 nodes distributed between Nancy and Lyon sites.
-While the EDP algorithm was slower than Maxdist algorithm by ten times over the same number of nodes and same distribution, its execution time on average 
-is equal to 0.1 $ms$. 
-}
+$O(N \cdot M \cdot F^2)$ respectively, where $N$ is the number of the clusters, $M$ is the number of nodes and $F$ is the 
+maximum number of available frequencies. When Maxdist is applied to a benchmark that is being executed over 32 nodes distributed between Nancy and Lyon sites, it takes on average  $0.01 ms$  to compute the best frequencies while EDP is on average ten times slower over the same architecture.  
 
 
 \section{Conclusion}
 \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 
+This paper has presented a new online frequencies selection algorithm.
+ The algorithm selects the best vector of 
+frequencies that maximizes  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.
+iterative applications running over a heterogeneous grid. A new energy model 
+is used by the proposed algorithm to predict the energy consumption 
+of the distributed iterative message passing application running over a 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.
+ NAS parallel benchmarks   and the  class D instance was executed over the  grid'5000 testbed platform. 
+ The experimental results showed that the algorithm reduces  on average 30\% of the energy consumption
+for all the NAS benchmarks   while  only degrading by 3.2\% on average  the performance. 
+The Maxdist algorithm was also evaluated in different scenarios that vary in the distribution of the computing nodes between different clusters' sites or \textcolor{blue}{between using one core and multi-cores per node} or in the values of the consumed static power. The algorithm selects different vector of frequencies according to the 
+computations and communication times ratios, and  the values of the static and measured dynamic powers of the CPUs. 
+Finally, the proposed algorithm was compared to another method that uses
+the well known energy and delay product as an objective function. The comparison results showed 
+that the proposed algorithm outperforms the latter by selecting a vector of frequencies that gives a better tradeoff  between energy consumption reduction and performance. 
+
 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
+asynchronous iterative applications where iterations are not synchronized and communications are overlapped with computations. 
+ 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}
 
 This work  has been  partially supported by  the Labex ACTION  project (contract
-``ANR-11-LABX-01-01'').  Computations  have been performed  on the supercomputer
-facilities  of the  Mésocentre de  calcul de  Franche-Comté. As  a  PhD student,
+``ANR-11-LABX-01-01'').  Computations  have been performed  on the Grid'5000 platform. As  a  PhD student,
 Mr. Ahmed  Fanfakh, would  like to  thank the University  of Babylon  (Iraq) for
 supporting his work.
 
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-%\IEEEtriggeratref{15}
 
-\bibliographystyle{IEEEtran}
-\bibliography{IEEEabrv,my_reference}
+\bibliographystyle{elsarticle-num}
+\bibliography{my_reference}
+
 \end{document}
 
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: t
-%%% fill-column: 80
-%%% ispell-local-dictionary: "american"
-%%% End:
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-% LocalWords:  Fanfakh Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber
-% LocalWords:  CMOS EPSA Franche Comté Tflop Rünger IUT Maréchal Juin cedex GPU
-% LocalWords:  de badri muslim MPI SimGrid GFlops Xeon EP BT GPUs CPUs AMD
-%  LocalWords:  Spiliopoulos scalability
+