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+\documentclass[review]{elsarticle}
+
+\usepackage{lineno,hyperref}
+\modulolinenumbers[5]
+
+\journal{Journal of Computational Science}
+
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+%%%%%%%%%%%%%%%%%%%%%%%
+
\usepackage[T1]{fontenc}
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\usepackage{graphicx}
\usepackage{algorithm}
+\usepackage{setspace}
\usepackage{subfig}
\usepackage{amsmath}
\usepackage{url}
\newcommand{\Told}{\Xsub{T}{Old}}
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\begin{document}
\begin{frontmatter}
-%% Title, authors and addresses
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-\dochead{}
-%% Use \dochead if there is an article header, e.g. \dochead{Short communication}
-\title{Energy Consumption Reduction with DVFS for Message Passing \\
- Iterative Applications on Grid Architecture}
+
+
+\title{Energy Consumption Reduction with DVFS for Message \\
+ Passing Iterative Applications on \\
+ Grid Architecture}
-%% use optional labels to link authors explicitly to addresses:
-%% \author[label1,label2]{<author name>}
-%% \address[label1]{<address>}
-%% \address[label2]{<address>}
+
\author{Ahmed Fanfakh,
Jean-Claude Charr,
Section~\ref{sec.optim} details the proposed frequencies selecting algorithm.
Section~\ref{sec.expe} presents the results of applying the algorithm on the
NAS parallel benchmarks and executing them on the grid'5000 testbed.
-%It shows the results of running different scenarios using multi-cores and one core per node and comparing them.
-It also evaluates the algorithm over three different power scenarios. Moreover, it shows the
+It also evaluates the algorithm over multi-cores per node architectures and over three different power scenarios. Moreover, it shows the
comparison results between the proposed method and an existing method. Finally,
in Section~\ref{sec.concl} the paper ends with a summary and some future works.
-
\section{Related works}
\label{sec.relwork}
\end{equation}
Replacing $\Fnew$ in (\ref{eq:pd}) as in (\ref{eq:fnew}) gives the following
equation for dynamic power consumption:
-\begin{equation}
+\begin{multline}
\label{eq:pdnew}
- \PdNew = \alpha \cdot \CL \cdot V^2 \cdot \Fnew = \alpha \cdot \CL \cdot \beta^2 \cdot \Fnew^3
- = \alpha \cdot \CL \cdot V^2 \cdot \Fmax \cdot S^{-3} = \PdOld \cdot S^{-3}
-\end{equation}
+ \PdNew = \alpha \cdot \CL \cdot V^2 \cdot \Fnew = \alpha \cdot \CL \cdot \beta^2 \cdot \Fnew^3 \\
+ {} = \alpha \cdot \CL \cdot V^2 \cdot \Fmax \cdot S^{-3} = \PdOld \cdot S^{-3}
+\end{multline}
where $\PdNew$ and $\PdOld$ are the dynamic power consumed with the
new frequency and the maximum frequency respectively.
energy consumption of a message passing distributed application executed over a
heterogeneous grid platform during one iteration is the summation of all dynamic and
static energies for $M$ processors in $N$ clusters. It is computed as follows:
-\begin{equation}
+\begin{multline}
\label{eq:energy}
E = \sum_{i=1}^{N} \sum_{i=1}^{M} {(S_{ij}^{-2} \cdot \Pd[ij] \cdot \Tcp[ij])} +
- \sum_{i=1}^{N} \sum_{j=1}^{M} (\Ps[ij] \cdot
+ \sum_{i=1}^{N} \sum_{j=1}^{M} (\Ps[ij] \cdot {} \\
(\mathop{\max_{i=1,\dots N}}_{j=1,\dots,M}({\Tcp[ij]} \cdot S_{ij})
+\mathop{\min_{j=1,\dots M}} (\Tcm[hj]) ))
-\end{equation}
+\end{multline}
+
Reducing the frequencies of the processors according to the vector of scaling
factors $(S_{11}, S_{12},\dots, S_{NM})$ may degrade the performance of the application
\label{sec.optim}
\begin{algorithm}
+\setstretch{1}
\begin{algorithmic}[1]
% \footnotesize
+
\Require ~
\begin{description}
- \item [{$N$}] number of clusters in the grid.
+ \item [{$N$}] number of clusters in the grid.
\item [{$M$}] number of nodes in each cluster.
\item[{$\Tcp[ij]$}] array of all computation times for all nodes during one iteration and with the highest frequency.
\item[{$\Tcm[ij]$}] array of all communication times for all nodes during one iteration and with the highest frequency.
\EndIf
\State $\Tnew \gets $ computed as in equations (\ref{eq:perf}).
\State $\Ereduced \gets $ computed as in equations (\ref{eq:energy}).
- \State $\Pnorm \gets \frac{\Told}{\Tnew}$
- \State $\Enorm\gets \frac{\Ereduced}{\Eoriginal}$
+ \State $\Pnorm \gets \frac{\Told}{\Tnew}$, $\Enorm\gets \frac{\Ereduced}{\Eoriginal}$
\If{$(\Pnorm - \Enorm > \Dist)$}
\State $\Sopt[ij] \gets S_{ij},~i=1,\dots,N,~j=1,\dots,M_i. $
\State $\Dist \gets \Pnorm - \Enorm$
\end{figure}
-\begin{figure}
- \centering
- \subfloat[The energy reduction while executing the NAS benchmarks over different scenarios ]{%
- \includegraphics[width=.4\textwidth]{fig/eng_s.eps}\label{fig:eng_s}} \hspace{2cm}%
- \subfloat[The performance degradation of the NAS benchmarks over different scenarios]{%
- \includegraphics[width=.4\textwidth]{fig/per_d.eps}\label{fig:per_d}}\hspace{2cm}%
- \subfloat[The tradeoff distance between the energy reduction and the performance of the NAS benchmarks
- over different scenarios]{%
- \includegraphics[width=.4\textwidth]{fig/dist.eps}\label{fig:dist}}
- \label{fig:exp-res}
- \caption{The experimental results of different scenarios}
-\end{figure}
+
The energy saving percentage is reduced for all the benchmarks because of the long distance communications in the two sites
scenario, except for the EP benchmark which has no communications. Therefore, the energy saving percentage of this benchmark is
produces less energy consumption and thus more energy saving.
The best energy saving percentage was obtained in the one site scenario with 16 nodes, the energy consumption was on average reduced up to 30\%.
-
+\begin{figure}
+ \centering
+ \subfloat[The energy reduction while executing the NAS benchmarks over different scenarios ]{%
+ \includegraphics[width=.4\textwidth]{fig/eng_s.eps}\label{fig:eng_s}} \hspace{2cm}%
+ \subfloat[The performance degradation of the NAS benchmarks over different scenarios]{%
+ \includegraphics[width=.4\textwidth]{fig/per_d.eps}\label{fig:per_d}}\hspace{2cm}%
+ \subfloat[The tradeoff distance between the energy reduction and the performance of the NAS benchmarks
+ over different scenarios]{%
+ \includegraphics[width=.4\textwidth]{fig/dist.eps}\label{fig:dist}}
+ \label{fig:exp-res}
+ \caption{The experimental results of different scenarios}
+\end{figure}
Figure \ref{fig:per_d} presents the performance degradation percentages for all benchmarks over the two scenarios.
The performance degradation percentage for the benchmarks running on two sites with
16 or 32 nodes is on average equal to 8.3\% or 4.7\% respectively.
NAS parallel benchmarks and the class D instance was executed over the grid'5000 testbed platform.
The experimental results showed that the algorithm reduces on average 30\% of the energy consumption
for all the NAS benchmarks while only degrading by 3.2\% on average the performance.
-The Maxdist algorithm was also evaluated in different scenarios that vary in the distribution of the computing nodes between different clusters' sites or \textcolor{blue}{between using one core and multi-cores per node} or in the values of the consumed static power. The algorithm selects different vector of frequencies according to the
+The Maxdist algorithm was also evaluated in different scenarios that vary in the distribution of the computing nodes between different clusters' sites or use multi-cores per node architecture or consume different static power values. The algorithm selects different vector of frequencies according to the
computations and communication times ratios, and the values of the static and measured dynamic powers of the CPUs.
Finally, the proposed algorithm was compared to another method that uses
the well known energy and delay product as an objective function. The comparison results showed
Mr. Ahmed Fanfakh, would like to thank the University of Babylon (Iraq) for
supporting his work.
-
-\bibliographystyle{elsarticle-num}
+\section*{References}
\bibliography{my_reference}
\end{document}
