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+\usepackage[utf8]{inputenc}
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+% \usepackage{sectsty}
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+% \usepackage{secdot}
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+\usepackage{lmodern}
\begin{document}
-\begin{center}
- \Large
- \title*\textbf{Optimal Dynamic Frequency Scaling for Energy-Performance of Parallel MPI Programs}
-\end{center}
-\parskip 0pt
-\linespread{1.18}
-\normalsize
-\makeatletter
-\renewcommand*{\@seccntformat}[1]{\csname the#1\endcsname\hspace{0.01cm}}
-\makeatother
-\sectionfont{\large}
-
-\section{.~Introduction }
+
+\title{Optimal Dynamic Frequency Scaling for Energy-Performance of Parallel MPI Programs}
+\author{A. Badri \and J.-C. Charr \and R. Couturier \and A. Giersch}
+\maketitle
+
+\section{Introduction}
The need for computing power is still increasing and it is not expected to slow
down in the coming years. To satisfy this demand, researchers and supercomputers
memory architecture. Furthermore, we compare the proposed algorithm with
Rauber's methods. The comparison's results show that our algorithm gives better
energy-time trade off.
-\sectionfont{\large}
-\section{.~Related Works }
+\section{Related Works}
In the this section some heuristics, to compute the scaling factor, are
presented and classified in two parts : offline and online methods.
- \sectionfont{\large}
-\subsection{~The offline DVFS orientations}
+\subsection{The offline DVFS orientations}
The DVFS offline methods are static and are not executed during the runtime of
the program. Some approaches used heuristics to select the best DVFS state
algorithm for the same goal. The offline study that shown the DVFS impact on the
communication time of the MPI program is~\cite{17}, Freeh et al. show that these
times not changed when the frequency is scaled down.
-\sectionfont{\large}
-\subsection{~The online DVFS orientations}
+\subsection{The online DVFS orientations}
The objective of these works is to dynamically compute and set the frequency of
the CPU during the runtime of the program for saving energy. Estimating and
\item The proposed algorithm works online without profiling or training as
in~\cite{38,34}.
\end{enumerate}
-\sectionfont{\large}
-\section{.~Parallel Tasks Execution on Homogeneous Platform}
+\section{Parallel Tasks Execution on Homogeneous Platform}
A homogeneous cluster consists of identical nodes in terms of the hardware and
the software. Each node has its own memory and at least one processor which can
Program Time=MAX_{i=1,2,..,N} (T_i) \hfill
\end{equation}
where $T_i$ is the execution time of process $i$.
-\sectionfont{\large}
-\section{.~Energy Model for Homogeneous Platform}
+\section{Energy Model for Homogeneous Platform}
The energy consumption by the processor consists of two powers metric: the
dynamic and the static power. This general power formulation is used by many
S=\:\frac{F_{max}}{F_{new}} \hfill \newline
\end{equation}
The value of the scale \emph S is grater than 1 when changing the frequency to
-any new frequency value(\emph {P-state}) in governor.~It is equal to 1 when the
+any new frequency value(\emph {P-state}) in governor. It is equal to 1 when the
frequency are set to the maximum frequency. The energy consumption model for
parallel homogeneous platform is depending on the scaling factor \emph S. This
factor reduces quadratically the dynamic power. Also, this factor increases the
S_{opt}= {\sqrt [3~]{\frac{2}{n} \frac{P_{dyn}}{P_{static}} \Big(1+\sum\limits_{i=2}^{N}\frac{T_i^3}{T_1^3}\Big) }} \hfill
\end{equation}
%[\Big 3]
-\sectionfont{\large}
-\section{.~Performance Evaluation of MPI Programs}
+\section{Performance Evaluation of MPI Programs}
The performance (execution time) of the parallel MPI applications are depends on
the time of the slowest task as in figure~(\ref{fig:homo}). Normally the
value. Depending on this prediction we can produce our energy-performace scaling
method as we will show in the coming sections. In the next section we make an
investigation study for the EQ~(\ref{eq:tnew}).
-\sectionfont{\large}
-\section{.~Performance Prediction Verification }
+\section{Performance Prediction Verification}
In this section we evaluate the precision of our performance prediction methods
on the NAS benchmark. We use the EQ~(\ref{eq:tnew}) that predicts the execution
the real time (Simgrid time) for all programs is between 0.0032 to 0.0133. AS an
example, we are present the execution times of the NAS benchmarks as in the
figure~(\ref{fig:pred}).
-\sectionfont{\large}
-\section{.~Performance to Energy Competition}
+\section{Performance to Energy Competition}
This section demonstrates our approach for choosing the optimal scaling
factor. This factor gives maximum energy reduction taking into account the
execution time for both computation and communication times . The relation
factor as shown in ~\cite{15,3,19}. Energy measurement model is not the
objective of this paper and we choose Rauber's model as an example with two
reasons that mentioned before.
-\sectionfont{\large}
-\section{.~Optimal Scaling Factor for Performance and Energy }
+\section{Optimal Scaling Factor for Performance and Energy}
In the previous section we described the objective function that satisfy our
goal in discovering optimal scaling factor for both performance and energy at
the same time. Therefore, we develop an energy to performance scaling algorithm
(EPSA). This algorithm is simple and has a direct way to calculate the optimal
-scaling factor for both energy and performance at the same time. \clearpage
-\linespread{1}
-\begin{algorithm}[width=\textwidth,height=\textheight,keepaspectratio]
+scaling factor for both energy and performance at the same time.
+\begin{algorithm}[t]
\caption{EPSA}
\label{EPSA}
\begin{algorithmic}[1]
\State $ Return \; \; (S_{optimal})$
\end{algorithmic}
\end{algorithm}
-\linespread{1.2} The proposed EPSA algorithm works online during the execution
-time of the MPI program. It selects the optimal scaling factor by gathering some
-information from the program after one iteration. This algorithm has small
-execution time (between 0.00152 $ms$ for 4 nodes to 0.00665 $ms$ for 32
-nodes). The data required by this algorithm is the computation time and the
-communication time for each task from the first iteration only. When these times
-are measured, the MPI program calls the EPSA algorithm to choose the new
-frequency using the optimal scaling factor. Then the program set the new
-frequency to the system. The algorithm is called just one time during the
-execution of the program. The following example shows where and when the EPSA
-algorithm is called in the MPI program : \clearpage
-\begin{lstlisting}
+The proposed EPSA algorithm works online during the execution time of the MPI
+program. It selects the optimal scaling factor by gathering some information
+from the program after one iteration. This algorithm has small execution time
+(between 0.00152 $ms$ for 4 nodes to 0.00665 $ms$ for 32 nodes). The data
+required by this algorithm is the computation time and the communication time
+for each task from the first iteration only. When these times are measured, the
+MPI program calls the EPSA algorithm to choose the new frequency using the
+optimal scaling factor. Then the program set the new frequency to the
+system. The algorithm is called just one time during the execution of the
+program. The following example shows where and when the EPSA algorithm is called
+in the MPI program :
+\begin{minipage}{\textwidth}
+\begin{lstlisting}[frame=tb]
FOR J:=1 to Some_iterations Do
-Computations Section.
-Communications Section.
ENDIF
ENDFOR
\end{lstlisting}
+\end{minipage}
After obtaining the optimal scale factor from the EPSA algorithm. The program
calculates the new frequency $F_i$ for each task proportionally to its time
value $T_i$. By substitution of the EQ~(\ref{eq:s}) in the EQ~(\ref{eq:si}), we
they have balanced workloads. Otherwise, they take different frequencies when
have imbalanced workloads. Then EQ~(\ref{eq:fi}) works in adaptive way to change
the freguency according to the nodes workloads.
-\sectionfont{\large}
-\section{.~Experimental Results}
+\section{Experimental Results}
The proposed ESPA algorithm was applied to seven MPI programs of the NAS
benchmarks (EP ,CG , MG ,FT , BT, LU and SP). We work on three classes (A, B and
\caption{Optimal scaling factors for The NAS MPI Programs}
\label{fig:nas}
\end{figure}
-\linespread{1.1}
\begin{table}[width=\textwidth,height=\textheight,keepaspectratio]
\caption{Optimal Scaling Factors Results}
% title of Table
\label{table:factors results}
% is used to refer this table in the text
\end{table}
-\linespread{1.2}
As shown in the table~(\ref{table:factors results}), when the optimal scaling
factor has big value we can gain more energy savings for example as in CG and
cases. In EP there are no communications inside the iterations. This make our
EPSA to selects smaller scaling factor values (inducing smaller energy savings).
-% \clearpage
-\sectionfont{\large}
-
-\section{.~Comparing Results}
+\section{Comparing Results}
In this section, we compare our EPSA algorithm results with Rauber's
methods~\cite{3}. He had two scenarios, the first is to reduce energy to optimal
Class A},\ref{table:compare Class B},\ref{table:compare Class C}). These
tables show the results of our EPSA and Rauber's two scenarios for all the NAS
benchmarks programs for classes A,B and C.
-%\linespread{1}
\begin{table}[ht]
\caption{Comparing Results for The NAS Class A}
% title of Table
\label{table:compare Class C}
% is used to refer this table in the text
\end{table}
-%\linespread{1.2}
-\clearpage As shown in these tables our scaling factor is not optimal for energy
-saving such as Rauber's scaling factor EQ~(\ref{eq:sopt}), but it is optimal for
-both the energy and the performance simultaneously. Our EPSA optimal scaling
-factors has better simultaneous optimization for both the energy and the
-performance compared to Rauber's energy-performance method
-($Rauber_{E-P}$). Also, in ($Rauber_{E-P}$) method when setting the frequency to
-maximum value for the slower task lead to a small improvement of the
-performance. Also the results show that this method keep or improve energy
-saving. Because of the energy consumption decrease when the execution time
-decreased while the frequency value increased.
+As shown in these tables our scaling factor is not optimal for energy saving
+such as Rauber's scaling factor EQ~(\ref{eq:sopt}), but it is optimal for both
+the energy and the performance simultaneously. Our EPSA optimal scaling factors
+has better simultaneous optimization for both the energy and the performance
+compared to Rauber's energy-performance method ($Rauber_{E-P}$). Also, in
+($Rauber_{E-P}$) method when setting the frequency to maximum value for the
+slower task lead to a small improvement of the performance. Also the results
+show that this method keep or improve energy saving. Because of the energy
+consumption decrease when the execution time decreased while the frequency value
+increased.
Figure~(\ref{fig:compare}) shows the maximum distance between the energy saving
percent and the performance degradation percent. Therefore, this means it is the
\label{fig:compare}
\end{figure}
-\clearpage
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\end{document}
