X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/mpi-energy.git/blobdiff_plain/cfa074b9eb12b37a1a4aa2c3d4c5ca44f9cc74fb..28ca91b68cbc2f8a08889fe9f5d5307c17e91409:/paper.tex?ds=inline

diff --git a/paper.tex b/paper.tex
index 00d85a2..50ecb90 100644
--- a/paper.tex
+++ b/paper.tex
@@ -10,6 +10,9 @@
 \usepackage{colortbl}
 \usepackage{amsmath}
 
+\usepackage{url}
+\DeclareUrlCommand\email{\urlstyle{same}}
+
 \usepackage[autolanguage,np]{numprint}
 \renewcommand*\npunitcommand[1]{\text{#1}}
 
@@ -33,24 +36,22 @@
     FEMTO-ST Institute\\
     University of Franche-ComtÃ©\\
     IUT de Belfort-MontbÃ©liard, 19 avenue du MarÃ©chal Juin, BP 527, 90016 Belfort cedex, France\\
-    Fax  : +33~3~84~58~77~32\\
-    Email: \{jean-claude.charr, ahmed.fanfakh\_badri\_muslim, raphael.couturier, arnaud.giersch\}@univ-fcomte.fr
+   % Fax  : +33~3~84~58~77~32\\
+    Email: \email{{jean-claude.charr,raphael.couturier,ahmed.fanfakh_badri_muslim,arnaud.giersch}@univ-fcomte.fr}
    }
   }
 
 \maketitle
 
-\AG{Is the fax number correct? Shall we add a telephone number?}
-\JC{Use Capital letters for only the first letter in the title of a section, table, figure, ...} 
 \begin{abstract}
   Dynamic Voltage Frequency Scaling (DVFS) can be applied to modern CPUs. 
 This technique is usually used to reduce the energy consumed by a CPU while
 computing . Indeed, power consumption by a processor at a given instant is
 exponentially related to its frequency. Thus, decreasing the frequency reduces
 the power consumed by the CPU. However, it can also significantly affect the
-performance of the executed program if it is compute bound and a low CPU
+performance of the executed program if it is compute bound and if a low CPU
 frequency is selected. The performance degradation ratio can even be higher than
-the saved energy ratio.Therefore, the chosen scaling factor must give the best possible tradeoff
+the saved energy ratio. Therefore, the chosen scaling factor must give the best possible trade-off
 between energy reduction and performance. 
 
 In this paper we present an algorithm
@@ -104,22 +105,20 @@ benchmarks (NPB v3.3) developed by NASA~\cite{44}. Our experiments are executed
 using the simulator SimGrid/SMPI v3.10~\cite{Casanova:2008:SGF:1397760.1398183}
 over an homogeneous distributed memory architecture. Furthermore, we compare the
 proposed algorithm with Rauber and RÃ¼nger methods~\cite{3}.
-The comparison's results show that our
-algorithm gives better energy-time tradeoff.
-
-This paper is organized as follows: Section~\ref{sec.relwork} presents related works
-from other authors.  Section~\ref{sec.exe} shows the execution of parallel
-tasks and sources of idle times.  It resumes the energy
-model of homogeneous platform. Section~\ref{sec.mpip} evaluates the performance
-of MPI program.  Section~\ref{sec.compet} presents the energy-performance tradeoffs
-objective function. Section~\ref{sec.optim} demonstrates the proposed
-energy-performance algorithm. Section~\ref{sec.expe} verifies the performance prediction
-model and presents the results of the proposed algorithm.  Also, It shows the comparison results. Finally,
-we conclude in Section~\ref{sec.concl}.
-\section{Related Works}
+The comparison's results show that our algorithm gives better energy-time trade-off.
+
+This paper is organized as follows: Section~\ref{sec.relwork} presents some related works
+from other authors.  Section~\ref{sec.exe} explains the execution of parallel
+tasks and the sources of slack times.  It also presents an energy
+model for homogeneous platforms. Section~\ref{sec.mpip} describes how the performance
+of MPI programs can be predicted .  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 energy-performance algorithm. Section~\ref{sec.expe} verifies the accuracy of the performance prediction
+model and presents the results of the proposed algorithm.  It also shows the comparison results between our method and other existing methods. Finally,
+we conclude in Section~\ref{sec.concl} with a summary and some future works.
+\section{Related works}
 \label{sec.relwork}
 
-\AG{Consider introducing the models sec.~\ref{sec.exe} maybe before related works}
+\AG{Consider introducing the models (sec.~\ref{sec.exe}) before related works}
 
 In this section, some heuristics to compute the scaling factor are
 presented and classified into two categories: offline and online methods.
@@ -152,25 +151,25 @@ The main drawback for these methods is that they all require executing a part or
 The online scaling factor selection methods are executed during the runtime of the program. They are usually integrated into iterative programs where the same block of instructions is executed many times.  During the first few iterations, many informations are measured such as the execution time, the energy consumed using a multimeter, the slack times, ... Then a  method will exploit these measurements to compute the scaling factor values for each processor. This operation, measurements and computing new scaling factor, can be repeated as much as needed if the iterations are not regular. Kimura, Peraza, Yu-Liang et al.  ~\cite{11,2,31} used learning methods to select the appropriate scaling factor values  to eliminate the slack times during runtime. However, as seen in ~\cite{39,19}, machine learning methods can take a lot of time to converge when the number of available gears is big. To reduce the impact of slack times,  in~\cite{1}, Lim et al. developed an algorithm that detects the
 communication sections and changes the frequency during these sections
 only. This approach might change the frequency of each processor many times per iteration if an iteration
-contains more than one communication section. In ~\cite{3}, Rauber et al. used an analytical model that after measuring the energy consumed and the execution time with the highest frequency gear, it can predict the energy consumed and the execution time for every frequency gear .   These predictions may be used to choose the optimal gear for each processor executing the parallel program to reduce energy consumption. 
+contains more than one communication section. In ~\cite{3}, Rauber and RÃ¼nger used an analytical model that can predict the consumed energy  and the execution time for every frequency gear after measuring the consumed energy  and the execution time with the highest frequency gear.   These predictions may be used to choose the optimal gear for each processor executing the parallel program to reduce energy consumption. 
 To maintain the performance of the parallel program , they
-set the  processor with the biggest load to the highest gear and then compute the scaling  factor values for the rest pf the processors. Although this model was built for parallel architectures, it can be adapted  to distributed architectures by taking into account the communications. 
-The primary contribution of this paper is presenting a new online scaling factor selection method which has the following characteristics :
+set the  processor with the biggest load to the highest gear and then compute the scaling  factor values for the rest of the processors. Although this model was built for parallel architectures, it can be adapted  to distributed architectures by taking into account the communications. 
+The primary contribution of our paper is presenting a new online scaling factor selection method which has the following characteristics :
 \begin{enumerate}
-\item Based on Rauber's analytical model to predict the energy consumption and the execution time of the application with different frequency gears. 
-\item Selects the frequency scaling factor for simultaneously optimizing energy reduction and maintaining performance.
-\item Well adapted to distributed architectures because it takes into account the communication time.
-\item Well adapted to distributed applications with imbalanced tasks.
-\item Has very small footprint when compared to other
+\item It is based on Rauber and RÃ¼nger analytical model to predict the energy consumption  of the application with different frequency gears. 
+\item It selects the frequency scaling factor for simultaneously optimizing energy reduction and maintaining performance.
+\item It is well adapted to distributed architectures because it takes into account the communication time.
+\item It is well adapted to distributed applications with imbalanced tasks.
+\item it has very small footprint when compared to other
   methods (e.g.,~\cite{19}) and does not require profiling or training as
   in~\cite{38,34}.
 \end{enumerate}
 
 
-\section{Execution and Energy of Parallel Tasks on Homogeneous Platform} 
+\section{Execution and energy of parallel tasks on homogeneous platform} 
 \label{sec.exe}
-\JC{The whole subsection ``Parallel Tasks Execution on Homogeneous Platform'', can be deleted if we need space, we can just say we are interested in this paper in homogeneous clusters}
-\subsection{Parallel Tasks Execution on Homogeneous Platform}
+%\JC{The whole subsection ``Parallel Tasks Execution on Homogeneous Platform'', can be deleted if we need space, we can just say we are interested in this paper in homogeneous clusters}
+\subsection{Parallel tasks execution on homogeneous platform}
 A homogeneous cluster consists of identical nodes in terms of hardware and software. 
 Each node has its own memory and at least one processor which can
 be a multi-core. The nodes are connected via a high bandwidth network. Tasks
@@ -179,9 +178,9 @@ we consider execution of the synchronous tasks on distributed homogeneous
 platform. These tasks can exchange the data via synchronous message passing.
 \begin{figure*}[t]
   \centering
-  \subfloat[Sync. Imbalanced Communications]{\includegraphics[scale=0.67]{commtasks}\label{fig:h1}}
-  \subfloat[Sync. Imbalanced Computations]{\includegraphics[scale=0.67]{compt}\label{fig:h2}}
-  \caption{Parallel Tasks on Homogeneous Platform}
+  \subfloat[Sync. imbalanced communications]{\includegraphics[scale=0.67]{fig/commtasks}\label{fig:h1}}
+  \subfloat[Sync. imbalanced computations]{\includegraphics[scale=0.67]{fig/compt}\label{fig:h2}}
+  \caption{Parallel tasks on homogeneous platform}
   \label{fig:homo}
 \end{figure*}
 Therefore, the execution time of a task consists of the computation time and the
@@ -189,23 +188,23 @@ communication time. Moreover, the synchronous communications between tasks can
 lead to slack times while tasks wait at the synchronization barrier for other tasks to
 finish their tasks (see figure~(\ref{fig:h1})). The imbalanced communications 
 happen when nodes have to send/receive different amount of data or they communicate
-with different number of nodes. Another source of idle times is the imbalanced computations.  
+with different number of nodes. Another source of slack times is the imbalanced computations.  
 This happens when processing different amounts of data on each processor  (see figure~(\ref{fig:h2})).  
 In this case the fastest tasks have to wait at the synchronization barrier for the 
 slowest ones to begin the next task. In both cases the overall execution time 
-of the program is the execution time of the slowest task as in equation \ref{eq:T1}.
+of the program is the execution time of the slowest task as in EQ~(\ref{eq:T1}).
 \begin{equation}
   \label{eq:T1}
   \textit{Program Time} = \max_{i=1,2,\dots,N} T_i
 \end{equation}
 where $T_i$ is the execution time of task $i$ and all the tasks are executed concurrently on different processors.
 
-\subsection{Energy Model for Homogeneous Platform}
+\subsection{Energy model for homogeneous platform}
 
 Many researchers~\cite{9,3,15,26} divide the power consumed by a processor to two power metrics: the
  static and the dynamic power. While the first one is consumed as long as the computing unit is on, the latter is only consumed during computation times. The dynamic power
 $P_{dyn}$  is related to the switching activity $\alpha$, load capacitance $C_L$,
-the supply voltage $V$ and operational frequency $f$, as shown in equation ~\ref{eq:pd}.
+the supply voltage $V$ and operational frequency $f$, as shown in EQ~(\ref{eq:pd}).
 \begin{equation}
   \label{eq:pd}
   P_\textit{dyn} = \alpha \cdot C_L \cdot V^2 \cdot f
@@ -217,12 +216,13 @@ The static power $P_{static}$ captures the leakage power as follows:
 \end{equation}
 where V is the supply voltage, $N_{trans}$ is the number of transistors, $K_{design}$ is a
 design dependent parameter and $I_{leak}$ is a technology-dependent
-parameter. Energy consumed by an individual processor $E_{ind}$ is the summation
-of the dynamic and the static powers multiplied by the execution time~\cite{36,15}.
+parameter. The energy consumed by an individual processor to execute a given program can be computed as:
 \begin{equation}
   \label{eq:eind}
-   E_\textit{ind} = ( P_\textit{dyn} + P_\textit{static} ) \cdot T
+   E_\textit{ind} =  P_\textit{dyn} \cdot T_{Comp} + P_\textit{static} \cdot T
 \end{equation}
+where $T$ is the execution time of the program, $T_{Comp}$ is the computation time and $T_{Comp} \le T$. $T_{Comp}$ may be equal to $T$ if there is no communications, no slack times and no synchronizations. 
+
 DVFS is a process that is allowed in
 modern processors to reduce the dynamic power by scaling down the voltage and
 frequency. Its main objective is to reduce the overall energy
@@ -241,9 +241,8 @@ new frequency value~(\emph {P-state}) in the governor. The CPU governor is an
 interface driver supplied by the operating system's kernel to
 lower a core's frequency.  This factor reduces
 quadratically the dynamic power which may cause degradation in performance and thus, the increase of the static energy because the execution time is increased~\cite{36}. If the tasks are sorted according to their execution times before scaling in a descending order,   the total energy consumption model for a parallel
-homogeneous platform, as  presented by Rauber et al.~\cite{3}, can be written as a function of   the scaling factor \emph S,   as in EQ~(\ref{eq:energy}).
+homogeneous platform, as  presented by Rauber and RÃ¼nger~\cite{3}, can be written as a function of   the scaling factor \emph S,   as in EQ~(\ref{eq:energy}).
 
-\JC{Are you sure of the following equation}
 \begin{equation}
   \label{eq:energy}
   E = P_\textit{dyn} \cdot S_1^{-2} \cdot
@@ -253,29 +252,26 @@ homogeneous platform, as  presented by Rauber et al.~\cite{3}, can be written as
 \end{equation}
 where \emph N is the number of parallel nodes,  $T_i  \  and  \  S_i \  for \  i=1,...,N$ are the execution times and scaling factors of the sorted tasks. Therefore,  $T1$ is the time of the slowest task,  and $S_1$ its scaling factor which should be the highest because they are proportional to
 the time values $T_i$.  The scaling factors are computed as in EQ~(\ref{eq:si}).
-\JC{This equation does not make sense either, what's S? there is no F}
 \begin{equation}
   \label{eq:si}
   S_i = S \cdot \frac{T_1}{T_i}
       = \frac{F_\textit{max}}{F_\textit{new}} \cdot \frac{T_1}{T_i}
 \end{equation}
-\JC{The Rauber model was used for a parallel machine not a homogeneous platform}
-where $F$ is the number of available frequencies. In this paper we depend on
+In this paper we depend on
 Rauber and RÃ¼nger energy model EQ~(\ref{eq:energy}) for two reasons: (1) this
-model is used for homogeneous platform that we work on in this paper, and (2) we
+model is used for any number of concurrent tasks, and (2) we
 compare our algorithm with Rauber and RÃ¼nger scaling factor selection method which is based on
 EQ~(\ref{eq:energy}). The optimal scaling factor is computed by minimizing the derivation for this equation which produces EQ~(\ref{eq:sopt}).
-\JC{what's the small n in the equation}
 
 \begin{equation}
   \label{eq:sopt}
-  S_\textit{opt} = \sqrt[3]{\frac{2}{n} \cdot \frac{P_\textit{dyn}}{P_\textit{static}} \cdot
+  S_\textit{opt} = \sqrt[3]{\frac{2}{N} \cdot \frac{P_\textit{dyn}}{P_\textit{static}} \cdot
     \left( 1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^3} \right) }
 \end{equation}
 
 \JC{The following 2 sections can be merged easily}
 
-\section{Performance Evaluation of MPI Programs}
+\section{Performance evaluation of MPI programs}
 \label{sec.mpip}
 
 The performance (execution time) of  parallel synchronous MPI applications depend on
@@ -296,8 +292,7 @@ the new scaling factor as in EQ~(\ref{eq:tnew}).
 \end{equation}
  In this paper, this prediction method is used to select the best scaling factor for each processor as presented in the next section.
 
-
-\section{Performance to Energy Competition}
+\section{Performance to energy competition}
 \label{sec.compet}
 
 This section demonstrates our approach for choosing the optimal scaling
@@ -312,9 +307,9 @@ without scaled frequency:
 \begin{multline}
   \label{eq:enorm}
   E_\textit{Norm} = \frac{ E_\textit{Reduced}}{E_\textit{Original}} \\
-        {} = \frac{P_\textit{dyn} \cdot S_i^{-2} \cdot
+        {} = \frac{P_\textit{dyn} \cdot S_1^{-2} \cdot
                \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
-               P_\textit{static} \cdot T_1 \cdot S_i \cdot N  }{
+               P_\textit{static} \cdot T_1 \cdot S_1 \cdot N  }{
               P_\textit{dyn} \cdot \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
               P_\textit{static} \cdot T_1 \cdot N }
 \end{multline}
@@ -344,39 +339,40 @@ performance as follows:
 \begin{equation}
   \label{eq:pnorm_en}
   P^{-1}_\textit{Norm} = \frac{ T_\textit{Old}}{ T_\textit{New}}
-               = \frac{ T_\textit{Old}}{T_\textit{Max Comp Old} \cdot S +
+               = \frac{T_\textit{Max Comp Old} +
+                 T_\textit{Max Comm Old}}{T_\textit{Max Comp Old} \cdot S +
                  T_\textit{Max Comm Old}}
 \end{equation}
 \begin{figure*}
   \centering
-  \subfloat[Converted Relation.]{%
-    \includegraphics[width=.4\textwidth]{file.eps}\label{fig:r1}}%
+  \subfloat[Converted relation.]{%
+    \includegraphics[width=.4\textwidth]{fig/file}\label{fig:r1}}%
   \qquad%
-  \subfloat[Real Relation.]{%
-    \includegraphics[width=.4\textwidth]{file3.eps}\label{fig:r2}}
+  \subfloat[Real relation.]{%
+    \includegraphics[width=.4\textwidth]{fig/file3}\label{fig:r2}}
   \label{fig:rel}
-  \caption{The Energy and Performance Relation}
+  \caption{The energy and performance relation}
 \end{figure*}
 Then, we can modelize our objective function as finding the maximum distance
 between the energy curve EQ~(\ref{eq:enorm}) and the inverse of performance
-curve EQ~(\ref{eq:pnorm_en}) over all available scaling factors. This represent
+curve EQ~(\ref{eq:pnorm_en}) over all available scaling factors. This represents
 the minimum energy consumption with minimum execution time (better performance)
 at the same time, see figure~(\ref{fig:r1}). Then our objective function has the
 following form:
 \begin{equation}
   \label{eq:max}
-  \textit{MaxDist} = \max (\overbrace{P^{-1}_\textit{Norm}}^{\text{Maximize}} -
-                           \overbrace{E_\textit{Norm}}^{\text{Minimize}} )
+ Max Dist = \max_{j=1,2,\dots,F} (\overbrace{P^{-1}_\textit{Norm}(S_j)}^{\text{Maximize}} -
+                        \overbrace{E_\textit{Norm}(S_j)}^{\text{Minimize}} )
 \end{equation}
-Then we can select the optimal scaling factor that satisfy
+where F is the number of available frequencies. Then we can select the optimal scaling factor that satisfies
 EQ~(\ref{eq:max}).  Our objective function can work with any energy model or
 static power values stored in a data file. Moreover, this function works in
 optimal way when the energy curve has a convex form over the available frequency scaling
 factors as shown in~\cite{15,3,19}. 
 
-\section{Optimal Scaling Factor for Performance and Energy}
+\section{Optimal scaling factor for performance and energy}
 \label{sec.optim}
- Algorithm~\ref{EPSA} compute the optimal scaling factor according to the objective function described above.
+ Algorithm~\ref{EPSA} computes the optimal scaling factor according to the objective function described above.
 \begin{algorithm}[tp]
   \caption{Scaling factor selection algorithm}
   \label{EPSA}
@@ -386,45 +382,59 @@ factors as shown in~\cite{15,3,19}.
     \State Set $P_{states}$ to the number of available frequencies.
     \State Set the variable $F_{new}$ to max. frequency,  $F_{new} = F_{max} $
     \State Set the variable $F_{diff}$ to the difference between two successive frequencies.
-    \For {$i=1$   to   $P_{states} $}
+    \For {$j:=1$   to   $P_{states} $}
       \State - $F_{new}=F_{new} - F_{diff} $
       \State - $S = \frac{F_\textit{max}}{F_\textit{new}}$
-      \State - $S_i = S \cdot \frac{T_1}{T_i}= \frac{F_\textit{max}}{F_\textit{new}} \cdot \frac{T_1}{T_i} \  for \  i=1,...,N$
-      \State - $E_\textit{Norm} = \frac{P_\textit{dyn} \cdot S_i^{-2} \cdot
+      \State - $S_i = S \cdot \frac{T_1}{T_i}= \frac{F_\textit{max}}{F_\textit{new}} \cdot \frac{T_1}{T_i} \                   
+       for \  i=1,...,N$
+      \State - $E_\textit{Norm} = \frac{P_\textit{dyn} \cdot S_1^{-2} \cdot
                \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
-               P_\textit{static} \cdot T_1 \cdot S_i \cdot N  }{
+               P_\textit{static} \cdot T_1 \cdot S_1 \cdot N  }{
               P_\textit{dyn} \cdot \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
               P_\textit{static} \cdot T_1 \cdot N }$
       \State -  $P_{NormInv}=T_{old}/T_{new}$ 
       \If{  $(P_{NormInv}-E_{Norm} > Dist$) }
-        \State $S_{optimal} = S$
+        \State $S_{opt} = S$
         \State $Dist = P_{NormInv} - E_{Norm}$
       \EndIf
     \EndFor
-    \State  Return $S_{optimal}$
+    \State  Return $S_{opt}$
   \end{algorithmic}
 \end{algorithm}
 
 The proposed algorithm works online during the execution time of the MPI
 program. It selects the optimal scaling factor after gathering the computation and communication times 
-from the program after one iteration. Then the program changes the new frequencies of the CPUs according to the computed scaling factors. This algorithm has small execution time
-(between 0.00152 $ms$ for 4 nodes to 0.00665 $ms$ for 32 nodes). The algorithm complexity is O(F$\cdot$N), 
+from the program after one iteration. Then the program changes the new frequencies of the CPUs according to the computed scaling factors. This algorithm has a small execution time: for a homogeneous cluster composed of nodes having the characteristics presented in table~\ref{table:platform}, it takes  0.00152 $ms$ on average for 4 nodes and 0.00665 $ms$ on average for 32 nodes. The algorithm complexity is O(F$\cdot$N), 
 where F is the number of available frequencies and N is the number of computing nodes.  The algorithm is called just 
 once during the execution of the program. The DVFS algorithm~(\ref{dvfs}) shows where and when the algorithm is called
 in the MPI program.
+\begin{table}[htb]
+  \caption{Platform file parameters}
+  % title of Table
+  \centering
+  \begin{tabular}{|*{7}{l|}}
+    \hline
+    Max & Min & Backbone & Backbone&Link &Link& Sharing  \\
+    Freq. & Freq. & Bandwidth & Latency & Bandwidth& Latency&Policy  \\ \hline
+    \np{2.5} & \np{800} & \np[GBps]{2.25} &\np[$\mu$s]{0.5}& \np[GBps]{1} & \np[$\mu$s]{50} &Full  \\
+    GHz& MHz&  & & &  &Duplex  \\\hline
+  \end{tabular}
+  \label{table:platform}
+\end{table}
+
 %\begin{minipage}{\textwidth}
 
 \begin{algorithm}[tp]
   \caption{DVFS}
   \label{dvfs}
   \begin{algorithmic}[1]
- \For {$J:=1$ to $Some-Iterations \; $}
-  \State -Computations Section.
-   \State -Communications Section.
-   \If {$(J=1)$} 
+ \For {$k:=1$ to $Some-Iterations \; $}
+  \State -Computations section.
+   \State -Communications section.
+   \If {$(k=1)$} 
      \State -Gather all times of computation and\par\hspace{13 pt} communication from each node.
      \State -Call algorithm~\ref{EPSA} with these times.
-     \State -Compute the new frequency from the returned optimal scaling factor.
+     \State -Compute the new frequency from the \par\hspace{13 pt} returned optimal scaling factor.
      \State -Set the new frequency to the CPU.
    \EndIf
 \EndFor
@@ -442,10 +452,10 @@ According to this equation all the nodes may have the same frequency value if
 they have balanced workloads, otherwise, they take different frequencies when
 having imbalanced workloads. Thus, EQ~(\ref{eq:fi}) adapts the frequency of the CPU to the nodes' workloads to maintain performance.
 
-\section{Experimental Results}
+\section{Experimental results}
 \label{sec.expe}
 Our experiments are executed on the simulator SimGrid/SMPI
-v3.10. We configure the simulator to use a a homogeneous cluster with one core per
+v3.10. We configure the simulator to use a homogeneous cluster with one core per
 node. The
 detailed characteristics of our platform file are shown in the
 table~(\ref{table:platform}).
@@ -453,20 +463,8 @@ Each node in the cluster has 18 frequency values
 from 2.5 GHz to 800 MHz with 100 MHz difference between each two successive
 frequencies. The simulated network link is 1 GB Ethernet (TCP/IP). 
 The backbone of the cluster simulates a high performance switch.
-\begin{table}[htb]
-  \caption{Platform File Parameters}
-  % title of Table
-  \centering
-  \begin{tabular}{|*{7}{l|}}
-    \hline
-    Max & Min & Backbone & Backbone&Link &Link& Sharing  \\
-    Freq. & Freq. & Bandwidth & Latency & Bandwidth& Latency&Policy  \\ \hline
-    \np{2.5} & \np{800} & \np[GBps]{2.25} &\np[$\mu$s]{0.5}& \np[GBps]{1} & \np[$\mu$s]{50} &Full  \\
-    GHz& MHz&  & & &  &Duplex  \\\hline
-  \end{tabular}
-  \label{table:platform}
-\end{table}
-\subsection{Performance Prediction Verification}
+
+\subsection{Performance prediction verification}
 
 In this section we evaluate the precision of our performance prediction method based on EQ~(\ref{eq:tnew}) by applying it the NAS benchmarks. The NAS programs are executed with the class B option for comparing the
 real execution time with the predicted execution time. Each program runs offline
@@ -475,21 +473,19 @@ time values. These scaling factors are computed by dividing the maximum
 frequency by the new one see EQ~(\ref{eq:s}). 
 \begin{figure*}[t]
   \centering
-  \includegraphics[width=.4\textwidth]{cg_per.eps}\qquad%
-  \includegraphics[width=.4\textwidth]{mg_pre.eps}
-  \includegraphics[width=.4\textwidth]{bt_pre.eps}\qquad%
-  \includegraphics[width=.4\textwidth]{lu_pre.eps}
+  \includegraphics[width=.328\textwidth]{fig/cg_per}\hfill%
+  \includegraphics[width=.328\textwidth]{fig/mg_pre}\hfill%
+ % \includegraphics[width=.4\textwidth]{fig/bt_pre}\qquad%
+  \includegraphics[width=.328\textwidth]{fig/lu_pre}\hfill%
   \caption{Comparing predicted to real execution time}
   \label{fig:pred}
 \end{figure*}
 %see Figure~\ref{fig:pred}
 In our cluster there are 18 available frequency states for each processor. 
-This lead to 18 run states for each program. We use seven MPI programs of the
+This leads to 18 run states for each program. We use seven MPI programs of the
  NAS parallel benchmarks: CG, MG, EP, FT, BT, LU
-and SP. Figure~(\ref{fig:pred}) presents plots of the real execution times and the simulated ones. The average normalized errors between the predicted execution time and
-the real time (SimGrid time) for all programs is between 0.0032 to 0.0133. 
-\JC{why compute the average error not the max}
-\subsection{The  experimental results}
+and SP. Figure~(\ref{fig:pred}) presents plots of the real execution times and the simulated ones. The maximum normalized error between the predicted execution time and the real time (SimGrid time) for all programs is between 0.0073 to 0.031. The  better case is for CG and the worse case is for LU. 
+\subsection{The experimental results for the scaling algorithm }
 The proposed algorithm was applied to seven MPI programs of the NAS
 benchmarks (EP, CG, MG, FT, BT, LU and SP) which were run with three classes (A, B and
 C). For each instance the benchmarks were executed on a number of processors
@@ -500,7 +496,7 @@ respectively.
 Depending on EQ~(\ref{eq:energy}), we measure the energy consumption for all
 the NAS MPI programs while assuming the power dynamic with the highest frequency is equal to \np[W]{20} and
 the power static is equal to \np[W]{4} for all experiments. These power values were also
-used by Rauber and RÃ¼nger in~\cite{3}.   The results showed that the algorithm selected
+used by Rauber and RÃ¼nger in~\cite{3}.  The results showed that the algorithm selected
 different scaling factors for each program depending on the communication
 features of the program as in the plots~(\ref{fig:nas}). These plots illustrate that
 there are different distances between the normalized energy and the normalized
@@ -518,17 +514,17 @@ energy saving percent and the minimum performance degradation percent at the
 same time from all available scaling factors.
 \begin{figure*}[t]
   \centering
-  \includegraphics[width=.33\textwidth]{ep.eps}\hfill%
-  \includegraphics[width=.33\textwidth]{cg.eps}\hfill%
-  \includegraphics[width=.33\textwidth]{sp.eps}
-  \includegraphics[width=.33\textwidth]{lu.eps}\hfill%
-  \includegraphics[width=.33\textwidth]{bt.eps}\hfill%
-  \includegraphics[width=.33\textwidth]{ft.eps}
-  \caption{Optimal scaling factors for The parallel NAS benchmarks}
+  \includegraphics[width=.328\textwidth]{fig/ep}\hfill%
+  \includegraphics[width=.328\textwidth]{fig/cg}\hfill%
+  \includegraphics[width=.328\textwidth]{fig/sp}
+  \includegraphics[width=.328\textwidth]{fig/lu}\hfill%
+  \includegraphics[width=.328\textwidth]{fig/bt}\hfill%
+  \includegraphics[width=.328\textwidth]{fig/ft}
+  \caption{Optimal scaling factors for the predicted energy and performance of NAS benchmarks}
   \label{fig:nas}
 \end{figure*}
 \begin{table}[htb]
-  \caption{The Scaling Factors Results}
+  \caption{The scaling factors results}
   % title of Table
   \centering
   \begin{tabular}{|l|*{4}{r|}}
@@ -552,9 +548,9 @@ FT. The opposite happens when the optimal scaling factor is small value as
 example BT and EP. Our algorithm selects big scaling factor value when the
 communication and the other slacks times are big and smaller ones in opposite
 cases. In EP there are no communications inside the iterations. This make our
-EPSA to selects smaller scaling factor values (inducing smaller energy savings).
+algorithm to selects smaller scaling factor values (inducing smaller energy savings).
 
-\subsection{Comparing Results}
+\subsection{Results comparison}
 
 In this section, we compare our scaling factor selection method with Rauber and RÃ¼nger
 methods~\cite{3}. They had two scenarios, the first is to reduce energy to the
@@ -562,12 +558,13 @@ optimal level without considering the performance as in EQ~(\ref{eq:sopt}). We
 refer to this scenario as $R_{E}$. The second scenario is similar to the first
 except setting the slower task to the maximum frequency (when the scale $S=1$)
 to keep the performance from degradation as mush as possible. We refer to this
-scenario as $R_{E-P}$. The comparison is made in tables~(\ref{table:compare
-  Class A},\ref{table:compare Class B},\ref{table:compare Class C}). These
+scenario as $R_{E-P}$. While we refer to our algorithm as EPSA (Energy to Performance Scaling Algorithm). The comparison
+is made in tables \ref{table:compareA}, \ref{table:compareB},
+and~\ref{table:compareC}. These
 tables show the results of our method and Rauber and RÃ¼nger scenarios for all the
-NAS benchmarks programs for classes A,B and C.
+NAS benchmarks programs for classes A, B and C.
 \begin{table}[p]
-  \caption{Comparing Results for  The NAS Class A}
+  \caption{Comparing results for  the NAS class A}
   % title of Table
   \centering
   \begin{tabular}{|l|l|*{4}{r|}}
@@ -608,7 +605,7 @@ NAS benchmarks programs for classes A,B and C.
   % is used to refer this table in the text
 \end{table}
 \begin{table}[p]
-  \caption{Comparing Results for The NAS Class B}
+  \caption{Comparing results for the NAS class B}
   % title of Table
   \centering
   \begin{tabular}{|l|l|*{4}{r|}}
@@ -650,7 +647,7 @@ NAS benchmarks programs for classes A,B and C.
 \end{table}
 
 \begin{table}[p]
-  \caption{Comparing Results for The NAS Class C}
+  \caption{Comparing results for the NAS class C}
   % title of Table
   \centering
   \begin{tabular}{|l|l|*{4}{r|}}
@@ -690,35 +687,31 @@ NAS benchmarks programs for classes A,B and C.
 \label{table:compareC}
 % is used to refer this table in the text
 \end{table}
-As shown in tables~\ref{table:compareA},~\ref{table:compareB} and~\ref{table:compareC}, the ($R_{E-P}$) method outperforms the ($R_{E}$) method in terms of performance and energy reduction. The ($R_{E-P}$) method also gives better energy savings than our method. However, although our scaling factor is not optimal for energy reduction, the results in these tables prove that our algorithm returns the best scaling factor that satisfy our objective method : the largest distance between energy reduction and performance degradation. 
-
-Figure~(\ref{fig:compare}) shows the maximum distance between the energy saving
-percent and the performance degradation percent.  
-Negative values mean that one of the two objectives (energy or performance) have been degraded more than the other. The positive tradeoffs with the highest values lead to maximum energy savings
+As shown in tables~\ref{table:compareA},~\ref{table:compareB} and~\ref{table:compareC}, the ($R_{E-P}$) method outperforms the ($R_{E}$) method in terms of performance and energy reduction. The ($R_{E-P}$) method also gives better energy savings than our method. However, although our scaling factor is not optimal for energy reduction, the results in these tables prove that our algorithm returns the best scaling factor that satisfy our objective method : the largest distance between energy reduction and performance degradation. Negative values in the energy-performance column mean that one of the two objectives (energy or performance) have been degraded more than the other. The positive trade-offs with the highest values lead to maximum energy savings
 while keeping the performance degradation as low as possible. Our algorithm always
-gives the highest positive energy to performance tradeoffs while Rauber and RÃ¼nger method
-($R_{E-P}$) gives in some time negative tradeoffs such as in BT and
+gives the highest positive energy to performance trade-offs while Rauber and RÃ¼nger method
+($R_{E-P}$) gives in some time negative trade-offs such as in BT and
 EP.
-\begin{figure}[t]
-  \centering
-  \includegraphics[width=.33\textwidth]{compare_class_A.pdf}
-  \includegraphics[width=.33\textwidth]{compare_class_B.pdf}
-  \includegraphics[width=.33\textwidth]{compare_class_c.pdf}
-  \caption{Comparing our method to Rauber and RÃ¼nger Methods}
-  \label{fig:compare}
-\end{figure}
+%\begin{figure*}[t]
+%  \centering
+%  \includegraphics[width=.328\textwidth]{fig/compare_class_A}
+%  \includegraphics[width=.328\textwidth]{fig/compare_class_B}
+%  \includegraphics[width=.328\textwidth]{fig/compare_class_C}
+%  \caption{Comparing our method to Rauber and RÃ¼nger methods}
+%  \label{fig:compare}
+%\end{figure*}
 \section{Conclusion}
 \label{sec.concl}
-In this paper, we have presented a new online scaling factor selection method that optimizes simultaneously the energy and performance of a distributed application running on an homogeneous cluster. It uses the computation and communication times measured at the first iteration to predict energy consumption and the performance of the parallel application at every available frequency. Then, it selects the scaling factor that gives the best tradeoff between energy reduction and performance which is the maximum distance between the energy and the inverted performance curves. To evaluate this method, we have applied it to the NAS benchmarks and it was compared to Rauber's methods while being executed on the simulator SimGrid. The results showed that our method, outperforms Rauber's methods in terms of energy-performance ratio. 
+In this paper, we have presented a new online scaling factor selection method that optimizes simultaneously the energy and performance of a distributed application running on an homogeneous cluster. It uses the computation and communication times measured at the first iteration to predict energy consumption and the performance of the parallel application at every available frequency. Then, it selects the scaling factor that gives the best trade-off between energy reduction and performance which is the maximum distance between the energy and the inverted performance curves. To evaluate this method, we have applied it to the NAS benchmarks and it was compared to Rauber and RÃ¼nger methods while being executed on the simulator SimGrid. The results showed that our method, outperforms Rauber and RÃ¼nger methods in terms of energy-performance ratio. 
 
 In the near future, we would like to adapt this scaling factor selection method to heterogeneous platforms where each node has different characteristics. In particular, each CPU has different available frequencies, energy consumption and performance. It would be also interesting to develop a new energy model for asynchronous parallel iterative methods where the number of iterations is not known in advance and depends on the global convergence of the iterative system.
 
 
 \section*{Acknowledgment}
-As a PhD student, M. Ahmed Fanfakh, would like to thank the University of
+This work has been supported by the Labex ACTION project (contract ``ANR-11-LABX-01-01'').Computations have been performed on the supercomputer facilities of the
+MÃ©socentre de calcul de Franche-ComtÃ©. As a PhD student, M. Ahmed Fanfakh, would like to thank the University of
 Babylon (Iraq) for supporting his work.
 
-\JC{delete the online paths for each reference}
 % trigger a \newpage just before the given reference
 % number - used to balance the columns on the last page
 % adjust value as needed - may need to be readjusted if
@@ -737,4 +730,4 @@ Babylon (Iraq) for supporting his work.
 %%% End:
 
 %  LocalWords:  Fanfakh Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber
-%  LocalWords:  CMOS EQ EPSA Franche ComtÃ© Tflop RÃ¼nger
+%  LocalWords:  CMOS EQ EPSA Franche ComtÃ© Tflop RÃ¼nger IUT MarÃ©chal Juin cedex
