correction

[mpi-energy2.git] / mpi-energy2-extension / Heter_paper.tex

diff --git a/mpi-energy2-extension/Heter_paper.tex b/mpi-energy2-extension/Heter_paper.tex
index 8c6061c8aea45247fd3f4bdff1afaf6521d580e6..b6839ce0402ea1e9596cbbda03b2bc55a284cb3e 100644 (file)
--- a/mpi-energy2-extension/Heter_paper.tex
+++ b/mpi-energy2-extension/Heter_paper.tex
@@ -1,11 +1,49 @@
-\documentclass[3p,times]{elsarticle-1}
-\usepackage{ecrc}
+\documentclass[review]{elsarticle}
+
+\usepackage{lineno,hyperref}
+\modulolinenumbers[5]
+
+\journal{Journal of Computational Science}
+
+%%%%%%%%%%%%%%%%%%%%%%%
+%% Elsevier bibliography styles
+%%%%%%%%%%%%%%%%%%%%%%%
+%% To change the style, put a % in front of the second line of the current style and
+%% remove the % from the second line of the style you would like to use.
+%%%%%%%%%%%%%%%%%%%%%%%
+
+%% Numbered
+%\bibliographystyle{model1-num-names}
+
+%% Numbered without titles
+%\bibliographystyle{model1a-num-names}
+
+%% Harvard
+%\bibliographystyle{model2-names.bst}\biboptions{authoryear}
+
+%% Vancouver numbered
+%\usepackage{numcompress}\bibliographystyle{model3-num-names}
+
+%% Vancouver name/year
+%\usepackage{numcompress}\bibliographystyle{model4-names}\biboptions{authoryear}
+
+%% APA style
+%\bibliographystyle{model5-names}\biboptions{authoryear}
+
+%% AMA style
+%\usepackage{numcompress}\bibliographystyle{model6-num-names}
+
+%% `Elsevier LaTeX' style
+\bibliographystyle{elsarticle-num}
+%%%%%%%%%%%%%%%%%%%%%%%
+

 \usepackage[T1]{fontenc}
 \usepackage[utf8]{inputenc}
 \usepackage[english]{babel}
 \usepackage{algpseudocode}
 \usepackage{graphicx}
 \usepackage{algorithm}
 \usepackage[T1]{fontenc}
 \usepackage[utf8]{inputenc}
 \usepackage[english]{babel}
 \usepackage{algpseudocode}
 \usepackage{graphicx}
 \usepackage{algorithm}

+\usepackage{setspace}

 \usepackage{subfig}
 \usepackage{amsmath}
 \usepackage{url}
 \usepackage{subfig}
 \usepackage{amsmath}
 \usepackage{url}


@@ -61,122 +99,20 @@
 \newcommand{\Told}{\Xsub{T}{Old}}
 
 
 \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}
 
 \begin{frontmatter}
 
 
 \begin{document}
 
 \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} 
+
+
+\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,
 
 \author{Ahmed Fanfakh,
         Jean-Claude Charr,


@@ -192,7 +128,8 @@
    }
 
 \begin{abstract}
    }
 
 \begin{abstract}

-  In recent years, green computing topic  has  become an important topic 
+
+  In recent years, green computing   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
   in the supercomputing research domain. However, the 
   computing platforms are still  consuming more and
 more energy due to the increasing number of nodes composing


@@ -213,15 +150,15 @@ scaling (DVFS) is one of them. It can be used to reduce the power consumption of
   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
   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}. Finally, the algorithm is 
+  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}
   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 }
+
+Dynamic voltage and frequency scaling \sep Grid computing\sep Green computing and  frequency scaling online algorithm.

 
 %% keywords here, in the form: keyword \sep keyword
 
 
 %% keywords here, in the form: keyword \sep keyword
 


@@ -287,11 +224,9 @@ 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 the grid'5000 testbed. 
 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 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
+It also evaluates the algorithm over multi-cores per node architectures and 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.
 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{Related works}
 \label{sec.relwork}
 


@@ -510,11 +445,11 @@ follows:
 \end{equation}
 Replacing $\Fnew$ in (\ref{eq:pd}) as in (\ref{eq:fnew}) gives the following
 equation for dynamic power consumption:
 \end{equation}
 Replacing $\Fnew$ in (\ref{eq:pd}) as in (\ref{eq:fnew}) gives the following
 equation for dynamic power consumption:

-\begin{equation}
+\begin{multline}

   \label{eq:pdnew}
   \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{equation}
+   \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}

 where $\PdNew$  and $\PdOld$ are the  dynamic power consumed with the
 new frequency and the maximum frequency respectively.
 
 where $\PdNew$  and $\PdOld$ are the  dynamic power consumed with the
 new frequency and the maximum frequency respectively.
 


@@ -560,13 +495,14 @@ 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:
 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{equation}
+\begin{multline}

   \label{eq:energy}
  E = \sum_{i=1}^{N} \sum_{i=1}^{M} {(S_{ij}^{-2} \cdot \Pd[ij] \cdot  \Tcp[ij])} +  
   \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]) ))
   (\mathop{\max_{i=1,\dots N}}_{j=1,\dots,M}({\Tcp[ij]} \cdot S_{ij}) 
   +\mathop{\min_{j=1,\dots M}} (\Tcm[hj]) ))

-\end{equation}
+\end{multline}
+

 
 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
 
 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


@@ -661,9 +597,9 @@ equation, as follows:
 \begin{figure}
   \centering
   \subfloat[Homogeneous cluster]{%
 \begin{figure}
   \centering
   \subfloat[Homogeneous cluster]{%

-    \includegraphics[width=.33\textwidth]{fig/homo}\label{fig:r1}} \hspace{2cm}%
+    \includegraphics[width=.4\textwidth]{fig/homo}\label{fig:r1}} \hspace{2cm}%

   \subfloat[Heterogeneous grid]{%
   \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}
   \label{fig:rel}
   \caption{The energy and performance relation}
 \end{figure}


@@ -693,11 +629,13 @@ in~\cite{Zhuo_Energy.efficient.Dynamic.Task.Scheduling,Rauber_Analytical.Modelin
 \label{sec.optim}
 
 \begin{algorithm}
 \label{sec.optim}
 
 \begin{algorithm}

+\setstretch{1}

   \begin{algorithmic}[1]
     % \footnotesize
   \begin{algorithmic}[1]
     % \footnotesize

+    

     \Require ~
     \begin{description}
     \Require ~
     \begin{description}

-    \item [{$N$}] number of clusters in the grid.
+    \item [{$N$}] number of clusters in the grid. 

     \item [{$M$}] number of nodes in each cluster.
     \item[{$\Tcp[ij]$}] array of all computation times for all nodes during one iteration and with the highest frequency.
     \item[{$\Tcm[ij]$}] array of all communication times for all nodes during one iteration and with the highest frequency.
     \item [{$M$}] number of nodes in each cluster.
     \item[{$\Tcp[ij]$}] array of all computation times for all nodes during one iteration and with the highest frequency.
     \item[{$\Tcm[ij]$}] array of all communication times for all nodes during one iteration and with the highest frequency.


@@ -725,8 +663,7 @@ in~\cite{Zhuo_Energy.efficient.Dynamic.Task.Scheduling,Rauber_Analytical.Modelin
         \EndIf
        \State $\Tnew \gets $ computed as  in equations (\ref{eq:perf}). 
        \State $\Ereduced \gets $ computed as  in equations (\ref{eq:energy}). 
         \EndIf
        \State $\Tnew \gets $ computed as  in equations (\ref{eq:perf}). 
        \State $\Ereduced \gets $ computed as  in equations (\ref{eq:energy}). 

-       \State $\Pnorm \gets \frac{\Told}{\Tnew}$
-       \State $\Enorm\gets \frac{\Ereduced}{\Eoriginal}$
+       \State $\Pnorm \gets \frac{\Told}{\Tnew}$,  $\Enorm\gets \frac{\Ereduced}{\Eoriginal}$

       \If{$(\Pnorm - \Enorm > \Dist)$}
         \State $\Sopt[ij] \gets S_{ij},~i=1,\dots,N,~j=1,\dots,M_i. $
         \State $\Dist \gets \Pnorm - \Enorm$
       \If{$(\Pnorm - \Enorm > \Dist)$}
         \State $\Sopt[ij] \gets S_{ij},~i=1,\dots,N,~j=1,\dots,M_i. $
         \State $\Dist \gets \Pnorm - \Enorm$


@@ -998,16 +935,7 @@ Table \ref{tab:sc} shows the number of nodes used from each cluster for each sce
 \end{table}
 
 
 \end{table}
 
 

-\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}
+

 
 The NAS parallel benchmarks are executed over these two platforms
  with different number of nodes, as in Table \ref{tab:sc}. 
 
 The NAS parallel benchmarks are executed over these two platforms
  with different number of nodes, as in Table \ref{tab:sc}. 


@@ -1033,18 +961,6 @@ However, the  execution times and the energy consumptions of EP and MG benchmark
  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.
 
 
  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
-  \subfloat[The energy reduction while executing the NAS benchmarks over different scenarios ]{%
-    \includegraphics[width=.33\textwidth]{fig/eng_s.eps}\label{fig:eng_s}} \hspace{0.08cm}%
-  \subfloat[The performance degradation of the NAS benchmarks over different scenarios]{%
-    \includegraphics[width=.33\textwidth]{fig/per_d.eps}\label{fig:per_d}}\hspace{0.08cm}%
-    \subfloat[The tradeoff distance between the energy reduction and the performance of the NAS benchmarks  
-      over different scenarios]{%
-    \includegraphics[width=.33\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 computed as the ratio between the reduced 
 energy consumption, equation (\ref{eq:energy}), and the original energy consumption,
 
 The energy saving percentage is computed as the ratio between the reduced 
 energy consumption, equation (\ref{eq:energy}), and the original energy consumption,


@@ -1058,6 +974,18 @@ 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. 
 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}
+
+

 
 
 The energy saving percentage is reduced for all the benchmarks because of the long distance communications in the two sites 
 
 
 The energy saving percentage is reduced for all the benchmarks because of the long distance communications in the two sites 


@@ -1073,12 +1001,23 @@ 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\%.
 
 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\%.
 

-
+\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}

 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
 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
 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. 
 
 nodes when the communications occur in high speed network does not decrease the computations to 
 communication ratio. 
 


@@ -1090,7 +1029,7 @@ 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 
 
 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. 
 
 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. 
 


@@ -1100,20 +1039,20 @@ which increase the computations to communications ratio  and the latter uses lon
 
 
 
 
 
 

-\subsection{The experimental results of multi-cores clusters}
+\subsection{The experimental results over multi-cores clusters}

 \label{sec.res-mc}
 \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}. In 
 The  clusters of grid'5000 have different number of cores embedded in their nodes
 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 
+this section, the proposed scaling algorithm is evaluated over the  grid'5000 platform  while using multi-cores 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 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 energy consumptions and execution times of running the class D of the NAS parallel 
+benchmarks over these four different scenarios are presented 
+in the figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.

 
 \begin{table}[]
 \centering
 
 \begin{table}[]
 \centering


@@ -1122,10 +1061,10 @@ in the figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.}
 \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
 \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}{*}{One site/ one core}    & Graphite     & 4               & 1                   \\  \cline{2-4}
+\multirow{3}{*}{One core per node}    & Graphite     & 4               & 1                   \\  \cline{2-4}

                                        & Graphene     & 14              & 1                   \\  \cline{2-4}
                                        & Griffon      & 14              & 1                   \\ \hline
                                        & Graphene     & 14              & 1                   \\  \cline{2-4}
                                        & Griffon      & 14              & 1                   \\ \hline

-\multirow{3}{*}{One site/ multicores}  & Graphite     & 1               &  4              \\  \cline{2-4}
+\multirow{3}{*}{Multi-cores per node}  & Graphite     & 1               &  4              \\  \cline{2-4}

                                        & Graphene     & 4               & 3 or 4              \\  \cline{2-4}
                                        & Griffon      & 4               & 3 or 4                   \\ \hline
 \end{tabular}
                                        & Graphene     & 4               & 3 or 4              \\  \cline{2-4}
                                        & Griffon      & 4               & 3 or 4                   \\ \hline
 \end{tabular}


@@ -1140,51 +1079,48 @@ Scenario name                          & Cluster name & \begin{tabular}[c]{@{}c@
   \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}
   \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}
+  \caption{The energy consumptions and execution times of NAS benchmarks over one core and multi-cores per node architectures}

 \end{figure}
 
 
 \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 execution times for most of  the NAS  benchmarks are higher over the multi-cores per node scenario 
+than over 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 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 
 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 
+ one core scenario  than over the 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. 
 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 
+More energy reduction can be gained when this ratio is big because it pushes the proposed scaling algorithm to select 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
 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.  
+scenarios  because there are no or small communications. 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}. 
+The figure shows that  the energy saving percentages in the one 
+core and the multi-cores scenarios
+are approximately equivalent, on average they are equal to  25.9\% and 25.1\% respectively.
+The energy consumption is reduced at the same rate in the two scenarios when compared to the energy consumption of the executions without DVFS. 
+
+

 The performance degradation percentages of the NAS benchmarks are presented in
 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.
+figure \ref{fig:per-d-mc}. It shows that the performance degradation percentages is higher for the NAS benchmarks over the  one core per node scenario  (on average equal to 10.6\%)  than over the  multi-cores scenario (on average equal to 7.5\%). The performance degradation percentages over the multi-cores scenario is lower because  the computations to communications ratio is smaller than the ratio of the other scenario. 
+

 The tradeoff distance percentages of the NAS benchmarks over the two scenarios are presented 
 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\%.}
+in the figure \ref{fig:dist-mc}. These  tradeoff distance between energy consumption reduction and performance  are used to verify which scenario is the best in both terms  at the same time. The figure shows that  the  tradeoff distance percentages are on average   bigger over the multi-cores scenario  (17.6\%) than over the  one core per node scenario  (15.3\%).

 
 
 
 \begin{figure}
   \centering
     \subfloat[The energy saving of running NAS benchmarks over one core and multicores scenarios]{%
 
 
 
 \begin{figure}
   \centering
     \subfloat[The energy saving of running NAS benchmarks over one core and multicores scenarios]{%

-    \includegraphics[width=.33\textwidth]{fig/eng_s_mc.eps}\label{fig:eng-s-mc}} \hspace{0.08cm}%
+    \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
       ]{%
     \subfloat[The performance degradation of running NAS benchmarks over one core and multicores scenarios
       ]{%

-    \includegraphics[width=.33\textwidth]{fig/per_d_mc.eps}\label{fig:per-d-mc}}\hspace{0.08cm}%
+    \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]{%
     \subfloat[The tradeoff distance of running NAS benchmarks over one core and multicores scenarios]{%

-    \includegraphics[width=.33\textwidth]{fig/dist_mc.eps}\label{fig:dist-mc}}
+    \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}
   \label{fig:exp-res}
   \caption{The experimental results of one core and multi-cores scenarios}
 \end{figure}


@@ -1205,11 +1141,12 @@ In these experiments, the class D of the NAS parallel benchmarks are executed ov
 \begin{figure}
   \centering
   \subfloat[The energy saving percentages for the nodes executing the NAS benchmarks over the three power scenarios]{%
 \begin{figure}
   \centering
   \subfloat[The energy saving percentages for the nodes executing the NAS benchmarks over the three power scenarios]{%

-    \includegraphics[width=.33\textwidth]{fig/eng_pow.eps}\label{fig:eng-pow}} \hspace{0.08cm}%
+    \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]{%
   \subfloat[The performance degradation percentages for the NAS benchmarks over the three power scenarios]{%

-    \includegraphics[width=.33\textwidth]{fig/per_pow.eps}\label{fig:per-pow}}\hspace{0.08cm}%
+    \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]{%
     \subfloat[The tradeoff distance between the energy reduction and the performance of the NAS benchmarks over the three power scenarios]{%

-    \includegraphics[width=.33\textwidth]{fig/dist_pow.eps}\label{fig:dist-pow}}
+      
+    \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}
   \label{fig:exp-pow}
   \caption{The experimental results of different static power scenarios}
 \end{figure}


@@ -1269,11 +1206,11 @@ presented in the figures \ref{fig:edp-eng}, \ref{fig:edp-perf} and \ref{fig:edp-
 \begin{figure}
   \centering
   \subfloat[The energy reduction induced by the Maxdist method and the EDP method]{%
 \begin{figure}
   \centering
   \subfloat[The energy reduction induced by the Maxdist method and the EDP method]{%

-    \includegraphics[width=.33\textwidth]{fig/edp_eng}\label{fig:edp-eng}} \hspace{0.08cm}%
+    \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]{%
     \subfloat[The performance degradation induced by  the Maxdist method and the EDP method]{%

-    \includegraphics[width=.33\textwidth]{fig/edp_per}\label{fig:edp-perf}}\hspace{0.08cm}%
+    \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]{%
     \subfloat[The tradeoff distance between the energy consumption reduction and the performance for the Maxdist method and the  EDP method]{%

-    \includegraphics[width=.33\textwidth]{fig/edp_dist}\label{fig:edp-dist}}
+    \includegraphics[width=.4\textwidth]{fig/edp_dist}\label{fig:edp-dist}}

   \label{fig:edp-comparison}
   \caption{The comparison results}
 \end{figure}
   \label{fig:edp-comparison}
   \caption{The comparison results}
 \end{figure}


@@ -1302,8 +1239,8 @@ of the distributed iterative message passing application running over a grid arc
 To evaluate the proposed method on a real heterogeneous grid platform, it was applied on the  
  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
 To evaluate the proposed method on a real heterogeneous grid platform, it was applied on the  
  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\% 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 
+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  use multi-cores per node architecture or consume different static power values. 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 
 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 


@@ -1325,8 +1262,7 @@ This work  has been  partially supported by  the Labex ACTION  project (contract
 Mr. Ahmed  Fanfakh, would  like to  thank the University  of Babylon  (Iraq) for
 supporting his work.
 
 Mr. Ahmed  Fanfakh, would  like to  thank the University  of Babylon  (Iraq) for
 supporting his work.
 

-
-\bibliographystyle{elsarticle-num}
+\section*{References}

 \bibliography{my_reference}
 
 \end{document}
 \bibliography{my_reference}
 
 \end{document}