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\begin{document}
\IEEEauthorblockA{%
FEMTO-ST Institute\\
University of Franche-Comté\\
-<<<<<<< HEAD
IUT de Belfort-Montb\'{e}liard, Rue Engel Gros, BP 27, 90016 Belfort, France\\
Fax : (+33)~3~84~58~77~32\\
- Email: \{jean-claude.charr, raphael.couturier, ahmed.fanfakh, arnaud.giersch\}@univ-fcomte.fr
-=======
- IUT de Belfort-Montbéliard, 19 avenue du Maréchal Juin, BP 527, 90016 Belfort cedex, France\\
- Fax : +33~3~84~58~77~32\\
- Email: \{jean-claude.charr,raphael.couturier,ahmed.fanfakh\_badri\_muslim,arnaud.giersch\}@univ-fcomte.fr
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+ Email: \{jean-claude.charr, raphael.couturier, ahmed.fanfakh\_badri\_muslim, arnaud.giersch\}@univ-fcomte.fr
}
}
\maketitle
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-\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, ...}
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\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
\section{Related works}
\label{sec.relwork}
-\AG{Consider introducing the models (sec.~\ref{sec.exe}) before related works}
+\AG{Consider introducing the models sec.~\ref{sec.exe} maybe before related works}
In this section, some heuristics to compute the scaling factor are
presented and classified into two categories: offline and online methods.
\section{Execution and energy of parallel tasks on homogeneous platform}
\label{sec.exe}
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%\AG{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}
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-\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}
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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
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}).
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-\JC{Are you sure of the following equation}
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\begin{equation}
\label{eq:energy}
E = P_\textit{dyn} \cdot S_1^{-2} \cdot
\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}).
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-\JC{This equation does not make sense either, what's S? there is no F}
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\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}
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In this paper we depend on
-=======
-\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
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Rauber and Rünger energy model EQ~(\ref{eq:energy}) for two reasons: (1) this
model is used for any number of concurrent tasks, and (2) we
compare our algorithm with Rauber and Rünger 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}).
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-=======
-\JC{what's the small n in the equation}
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\begin{equation}
\label{eq:sopt}
\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}
+\AG{The following 2 sections can be merged easily}
\section{Performance evaluation of MPI programs}
\label{sec.mpip}
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
NAS parallel benchmarks: CG, MG, EP, FT, BT, LU
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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 }
-=======
-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}
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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
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
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scenario as $R_{E-P}$. While we refer to our algorithm as EPSA. The comparison is made in tables~(\ref{table:compareA},\ref{table:compareB},\ref{table:compareC}). These
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-scenario as $R_{E-P}$. The comparison is made in tables~(\ref{table:compareA},
-\ref{table:compareB}, and \ref{table:compareC}). These
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tables show the results of our method and Rauber and Rünger scenarios for all the
NAS benchmarks programs for classes A,B and C.
\begin{table}[p]
As a PhD student, M. Ahmed Fanfakh, would like to thank the University of
Babylon (Iraq) for supporting his work.
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