X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/mpi-energy.git/blobdiff_plain/93ccbadf5848d51c30ddfebe0f43794def5225c5..c00a8e3e79d7a39860d4c701f85adff1cc02788b:/paper.tex?ds=inline diff --git a/paper.tex b/paper.tex index a405346..babc12b 100644 --- a/paper.tex +++ b/paper.tex @@ -1,5 +1,4 @@ -\documentclass[12pt]{article} -%\documentclass[12pt,twocolumn]{article} +\documentclass[conference]{IEEEtran} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} @@ -15,14 +14,26 @@ % \usepackage{secdot} %\usepackage[font={footnotesize,bt}]{caption} %\usepackage[font=scriptsize,labelfont=bf]{caption} -\usepackage{lmodern} \usepackage{todonotes} \newcommand{\AG}[2][inline]{\todo[color=green!50,#1]{\sffamily\small\textbf{AG:} #2}} \begin{document} \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} + +\author{% + \IEEEauthorblockN{% + Ahmed Badri, + Jean-Claude Charr, + Raphaël Couturier and + Arnaud Giersch + } + \IEEEauthorblockA{% + FEMTO-ST Institute\\ + University of Franche-Comté + } +} + \maketitle \AG{``Optimal'' is a bit pretentious in the title} @@ -138,13 +149,13 @@ be a multi-core. The nodes are connected via a high bandwidth network. Tasks executed on this model can be either synchronous or asynchronous. In this paper we consider execution of the synchronous tasks on distributed homogeneous platform. These tasks can exchange the data via synchronous memory passing. -\begin{figure}[h] +\begin{figure*}[t] \centering \subfloat[Synch. Imbalanced Communications]{\includegraphics[scale=0.67]{synch_tasks}\label{fig:h1}} \subfloat[Synch. Imbalanced Computations]{\includegraphics[scale=0.67]{compt}\label{fig:h2}} \caption{Parallel Tasks on Homogeneous Platform} \label{fig:homo} -\end{figure} +\end{figure*} Therefore, the execution time of a task consists of the computation time and the communication time. Moreover, the synchronous communications between tasks can lead to idle time while tasks wait at the synchronous point for others tasks to @@ -293,15 +304,15 @@ with all available scaling factors on 8 or 9 nodes to produce real execution time values. These scaling factors are computed by dividing the maximum frequency by the new one see EQ~(\ref{eq:s}). In all tests, we use the simulator SimGrid/SMPI v3.10 to run the NAS programs. -\begin{figure}[width=\textwidth,height=\textheight,keepaspectratio] +\begin{figure*}[t] \centering - \includegraphics[scale=0.60]{cg_per.eps} - \includegraphics[scale=0.60]{mg_pre.eps} - \includegraphics[scale=0.60]{bt_pre.eps} - \includegraphics[scale=0.60]{lu_pre.eps} + \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} \caption{Fitting Predicted to Real Execution Time} \label{fig:pred} -\end{figure} +\end{figure*} %see Figure~\ref{fig:pred} In our cluster there are 18 available frequency states for each processor from 2.5 GHz to 800 MHz, there is 100 MHz difference between two successive @@ -324,15 +335,15 @@ is not straightforward. Moreover, they are not measured using the same metric. For solving this problem, we normalize the energy by calculating the ratio between the consumed energy with scaled frequency and the consumed energy without scaled frequency : -\begin{equation} +\begin{multline} \label{eq:enorm} - E_\textit{Norm} = \frac{E_{Reduced}}{E_{Original}} - = \frac{ P_{dyn} \cdot S_i^{-2} \cdot + E_\textit{Norm} = \frac{E_{Reduced}}{E_{Original}}\\ + {} = \frac{ P_{dyn} \cdot S_i^{-2} \cdot \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) + P_{static} \cdot T_1 \cdot S_i \cdot N }{ P_{dyn} \cdot \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) + P_{static} \cdot T_1 \cdot N } -\end{equation} +\end{multline} \AG{Use \texttt{\textbackslash{}text\{xxx\}} or \texttt{\textbackslash{}textit\{xxx\}} for all subscripted words in equations (e.g. \mbox{\texttt{E\_\{\textbackslash{}text\{Norm\}\}}}). @@ -368,13 +379,16 @@ performance as follows : = \frac{T_{Old}}{T_{\textit{Max Comp Old}} \cdot S + T_{\textit{Max Comm Old}}} \end{equation} -\begin{figure} +\begin{figure*} \centering - \subfloat[Converted Relation.]{\includegraphics[scale=0.70]{file.eps}\label{fig:r1}} - \subfloat[Real Relation.]{\includegraphics[scale=0.70]{file3.eps}\label{fig:r2}} + \subfloat[Converted Relation.]{% + \includegraphics[width=.4\textwidth]{file.eps}\label{fig:r1}}% + \qquad% + \subfloat[Real Relation.]{% + \includegraphics[width=.4\textwidth]{file3.eps}\label{fig:r2}} \label{fig:rel} \caption{The Energy and Performance Relation} -\end{figure} +\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 @@ -518,18 +532,18 @@ programs. In table~(\ref{table:factors results}), we record all optimal scaling factors results for each program on class C. These factors give the maximum energy saving percent and the minimum performance degradation percent in the same time over all available scales. -\begin{figure}[width=\textwidth,height=\textheight,keepaspectratio] +\begin{figure*} \centering - \includegraphics[scale=0.47]{ep.eps} - \includegraphics[scale=0.47]{cg.eps} - \includegraphics[scale=0.47]{sp.eps} - \includegraphics[scale=0.47]{lu.eps} - \includegraphics[scale=0.47]{bt.eps} - \includegraphics[scale=0.47]{ft.eps} + \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 NAS MPI Programs} \label{fig:nas} -\end{figure} -\begin{table}[width=\textwidth,height=\textheight,keepaspectratio] +\end{figure*} +\begin{table} \caption{Optimal Scaling Factors Results} % title of Table \centering @@ -717,15 +731,14 @@ concatenating with less performance degradation and this the objective of this paper. While the negative trade offs refers to improving energy saving (or may be the performance) while degrading the performance (or may be the energy) more than the first. -\begin{figure}[width=\textwidth,height=\textheight,keepaspectratio] +\begin{figure*} \centering - \includegraphics[scale=0.60]{compare_class_A.pdf} - \includegraphics[scale=0.60]{compare_class_B.pdf} - \includegraphics[scale=0.60]{compare_class_c.pdf} - % use scale 35 for all to be in the same line + \includegraphics[width=.33\textwidth]{compare_class_A.pdf}\hfill% + \includegraphics[width=.33\textwidth]{compare_class_B.pdf}\hfill% + \includegraphics[width=.33\textwidth]{compare_class_c.pdf} \caption{Comparing Our EPSA with Rauber's Methods} \label{fig:compare} -\end{figure} +\end{figure*} \section{Conclusion} \label{sec.conc} @@ -737,8 +750,8 @@ than the first. Computations have been performed on the supercomputer facilities of the Mésocentre de calcul de Franche-Comté. -\bibliographystyle{plain} -\bibliography{my_reference} +\bibliographystyle{IEEEtran} +\bibliography{IEEEabrv,my_reference} \end{document} %%% Local Variables: