\usepackage{colortbl}
\usepackage{amsmath}
+\usepackage{url}
+\DeclareUrlCommand\email{\urlstyle{same}}
+
\usepackage[autolanguage,np]{numprint}
\renewcommand*\npunitcommand[1]{\text{#1}}
\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
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b
+ Email: \email{{jean-claude.charr,raphael.couturier,ahmed.fanfakh_badri_muslim,arnaud.giersch}@univ-fcomte.fr}
}
}
\maketitle
-<<<<<<< HEAD
-=======
\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, ...}
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b
\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
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
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
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 Rünger methods~\cite{3}.
-The comparison's results show that our algorithm gives better energy-time tradeoff.
+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 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
+of MPI program. Section~\ref{sec.compet} presents the energy-performance trade-offs
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}.
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.
\section{Execution and energy of parallel tasks on homogeneous platform}
\label{sec.exe}
-<<<<<<< HEAD
-%\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}
+%\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}
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b
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
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}).
-<<<<<<< HEAD
-=======
-\JC{Are you sure of the following equation}
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b
\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}).
-<<<<<<< HEAD
-=======
-\JC{This equation does not make sense either, what's S? there is no F}
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b
\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}
-<<<<<<< HEAD
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
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b
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}).
-<<<<<<< HEAD
-=======
-\JC{what's the small n in the equation}
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b
\begin{equation}
\label{eq:sopt}
\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*}
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
-<<<<<<< HEAD
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}
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b
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
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*}
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
-<<<<<<< HEAD
-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
-=======
-scenario as $R_{E-P}$. The comparison is made in tables~(\ref{table:compareA},
-\ref{table:compareB}, and \ref{table:compareC}). These
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b
+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},
+and~\ref{table:compareC}. These
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]
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
+Negative values 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 Rünger 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 Rünger method
+($R_{E-P}$) gives in some time negative trade-offs such as in BT and
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{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 and Rünger methods while being executed on the simulator SimGrid. The results showed that our method, outperforms Rauber and Rünger 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 Rünger methods while being executed on the simulator SimGrid. The results showed that our method, outperforms Rauber and Rünger 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
+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.
-<<<<<<< HEAD
-=======
-\JC{delete the online paths for each reference\AG{except for TOP500 and the NPB}}
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% 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
%%% End:
% LocalWords: Fanfakh Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber
-% LocalWords: CMOS EQ EPSA Franche Comté Tflop Rünger
+% LocalWords: CMOS EQ EPSA Franche Comté Tflop Rünger IUT Maréchal Juin cedex
