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University of Franche-Comté\\
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
+ Email: \email{{jean-claude.charr,raphael.couturier,ahmed.fanfakh_badri_muslim,arnaud.giersch}@univ-fcomte.fr}
}
}
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 this 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 Based on Rauber and Rünger 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.
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}}
+ \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*}
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 Rünger~\cite{3}, can be written as a function of the scaling factor \emph S, as in EQ~(\ref{eq:energy}).
\begin{equation}
\label{eq:energy}
\begin{figure*}
\centering
\subfloat[Converted relation.]{%
- \includegraphics[width=.4\textwidth]{file.eps}\label{fig:r1}}%
+ \includegraphics[width=.4\textwidth]{fig/file}\label{fig:r1}}%
\qquad%
\subfloat[Real relation.]{%
- \includegraphics[width=.4\textwidth]{file3.eps}\label{fig:r2}}
+ \includegraphics[width=.4\textwidth]{fig/file3}\label{fig:r2}}
\label{fig:rel}
\caption{The energy and performance relation}
\end{figure*}
frequency by the new one see EQ~(\ref{eq:s}).
\begin{figure*}[t]
\centering
- \includegraphics[width=.328\textwidth]{cg_per.eps}\hfill%
- \includegraphics[width=.328\textwidth]{mg_pre.eps}\hfill%
- % \includegraphics[width=.4\textwidth]{bt_pre.eps}\qquad%
- \includegraphics[width=.328\textwidth]{lu_pre.eps}\hfill%
+ \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*}
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 Rünger in~\cite{3}. The results showed that the algorithm selected
+used by Rauber and Rünger 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
same time from all available scaling factors.
\begin{figure*}[t]
\centering
- \includegraphics[width=.328\textwidth]{ep.eps}\hfill%
- \includegraphics[width=.328\textwidth]{cg.eps}\hfill%
- \includegraphics[width=.328\textwidth]{sp.eps}
- \includegraphics[width=.328\textwidth]{lu.eps}\hfill%
- \includegraphics[width=.328\textwidth]{bt.eps}\hfill%
- \includegraphics[width=.328\textwidth]{ft.eps}
+ \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*}
EP.
\begin{figure*}[t]
\centering
- \includegraphics[width=.328\textwidth]{compare_class_A.pdf}
- \includegraphics[width=.328\textwidth]{compare_class_B.pdf}
- \includegraphics[width=.328\textwidth]{compare_class_c.pdf}
+ \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 Rünger methods}
\label{fig:compare}
\end{figure*}
\section*{Acknowledgment}
-\AG{Jean-Claude, why did you remove the Mésocentre here?}
-As a PhD student, M. Ahmed Fanfakh, would like to thank the University of
+Computations have been performed on the supercomputer facilities of the
+Mésocentre de calcul de Franche-Comté. As a PhD student, M. Ahmed Fanfakh, would like to thank the University of
Babylon (Iraq) for supporting his work.
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