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+\journal{Journal of Computational Science}
+
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\begin{document}
\begin{frontmatter}
-%% Title, authors and addresses
-
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-\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,
The proposed algorithm is evaluated on a real grid, the grid'5000 platform, while
running the NAS parallel benchmarks. The experiments show that it reduces the
energy consumption on average by \np[\%]{30} while the performance is only degraded
- on average by \np[\%]{3}. Finally, the algorithm is
+ on average by \np[\%]{3.2}. Finally, the algorithm is
compared to an existing method. The comparison results show that it outperforms the
latter in terms of energy consumption reduction and performance.
\end{abstract}
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
\begin{figure}
\centering
\subfloat[Homogeneous cluster]{%
- \includegraphics[width=.33\textwidth]{fig/homo}\label{fig:r1}} \hspace{2cm}%
+ \includegraphics[width=.4\textwidth]{fig/homo}\label{fig:r1}} \hspace{2cm}%
\subfloat[Heterogeneous grid]{%
- \includegraphics[width=.33\textwidth]{fig/heter}\label{fig:r2}}
+ \includegraphics[width=.4\textwidth]{fig/heter}\label{fig:r2}}
\label{fig:rel}
\caption{The energy and performance relation}
\end{figure}
\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 $\Dist \gets \Pnorm - \Enorm$
Name & model & Freq. & Freq. & Freq. & per CPU & of one core \\
& & GHz & GHz & GHz & & \\
\hline
- Taurus & Intel & 2.3 & 1.2 & 0.1 & 6 & \np[W]{35} \\
- & Xeon & & & & & \\
+ & Intel & 2.3 & 1.2 & 0.1 & 6 & \np[W]{35} \\
+ Taurus & Xeon & & & & & \\
& E5-2630 & & & & & \\
\hline
- Graphene & Intel & 2.53 & 1.2 & 0.133 & 4 & \np[W]{23} \\
- & Xeon & & & & & \\
+ & Intel & 2.53 & 1.2 & 0.133 & 4 & \np[W]{23} \\
+ Graphene & Xeon & & & & & \\
& X3440 & & & & & \\
\hline
- Griffon & Intel & 2.5 & 2 & 0.5 & 4 & \np[W]{46} \\
- & Xeon & & & & & \\
+ & Intel & 2.5 & 2 & 0.5 & 4 & \np[W]{46} \\
+ Griffon & Xeon & & & & & \\
& L5420 & & & & & \\
\hline
- Graphite & Intel & 2 & 1.2 & 0.1 & 8 & \np[W]{35} \\
- & Xeon & & & & & \\
+ & Intel & 2 & 1.2 & 0.1 & 8 & \np[W]{35} \\
+ Graphite & Xeon & & & & & \\
& E5-2650 & & & & & \\
\hline
\end{tabular}
\end{table}
-\begin{figure}
- \centering
- \subfloat[The energy consumption by the nodes wile executing the NAS benchmarks over different scenarios
- ]{%
- \includegraphics[width=.4\textwidth]{fig/eng_con_scenarios.eps}\label{fig:eng_sen}} \hspace{1cm}%
- \subfloat[The execution times of the NAS benchmarks over different scenarios]{%
- \includegraphics[width=.4\textwidth]{fig/time_scenarios.eps}\label{fig:time_sen}}
- \label{fig:exp-time-energy}
- \caption{The energy consumption and execution time of NAS Benchmarks over different scenarios}
-\end{figure}
+
The NAS parallel benchmarks are executed over these two platforms
with different number of nodes, as in Table \ref{tab:sc}.
in both scenarios. Even when the number of nodes is doubled. On the other hand, the communications of the rest of the benchmarks increases when using long distance communications between two sites or increasing the number of computing nodes.
-\begin{figure}
- \centering
- \subfloat[The energy reduction while executing the NAS benchmarks over different scenarios ]{%
- \includegraphics[width=.33\textwidth]{fig/eng_s.eps}\label{fig:eng_s}} \hspace{0.08cm}%
- \subfloat[The performance degradation of the NAS benchmarks over different scenarios]{%
- \includegraphics[width=.33\textwidth]{fig/per_d.eps}\label{fig:per_d}}\hspace{0.08cm}%
- \subfloat[The tradeoff distance between the energy reduction and the performance of the NAS benchmarks
- over different scenarios]{%
- \includegraphics[width=.33\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 computed as the ratio between the reduced
energy consumption, equation (\ref{eq:energy}), and the original energy consumption,
increase the communication times and thus produces less energy saving depending on the
benchmarks being executed. The results of the benchmarks CG, MG, BT and FT show more
energy saving percentage in one site scenario when executed over 16 nodes comparing to 32 nodes. While, LU and SP consume more energy with 16 nodes than 32 in one site because their computations to communications ratio is not affected by the increase of the number of local communications.
+\begin{figure}
+ \centering
+ \subfloat[The energy consumption by the nodes wile executing the NAS benchmarks over different scenarios
+ ]{%
+ \includegraphics[width=.48\textwidth]{fig/eng_con_scenarios.eps}\label{fig:eng_sen}} \hspace{0.4cm}%
+ \subfloat[The execution times of the NAS benchmarks over different scenarios]{%
+ \includegraphics[width=.48\textwidth]{fig/time_scenarios.eps}\label{fig:time_sen}}
+ \label{fig:exp-time-energy}
+ \caption{The energy consumption and execution time of NAS Benchmarks over different scenarios}
+\end{figure}
+
+
The energy saving percentage is reduced for all the benchmarks because of the long distance communications in the two sites
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=.48\textwidth]{fig/eng_s.eps}\label{fig:eng_s}} \hspace{0.4cm}%
+ \subfloat[The performance degradation of the NAS benchmarks over different scenarios]{%
+ \includegraphics[width=.48\textwidth]{fig/per_d.eps}\label{fig:per_d}}\hspace{0.4cm}%
+ \subfloat[The tradeoff distance between the energy reduction and the performance of the NAS benchmarks
+ over different scenarios]{%
+ \includegraphics[width=.48\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\% or 4\% respectively.
+16 or 32 nodes is on average equal to 8.3\% or 4.7\% respectively.
For this scenario, the proposed scaling algorithm selects smaller frequencies for the executions with 32 nodes without significantly degrading their performance because the communication times are higher with 32 nodes which results in smaller computations to communications ratio. On the other hand, the performance degradation percentage for the benchmarks running on one site with
-16 or 32 nodes is on average equal to 3\% or 10\% respectively. In opposition to the two sites scenario, when the number of computing nodes is increased in the one site scenario, the performance degradation percentage is increased. Therefore, doubling the number of computing
+16 or 32 nodes is on average equal to 3.2\% or 10.6\% respectively. In opposition to the two sites scenario, when the number of computing nodes is increased in the one site scenario, the performance degradation percentage is increased. Therefore, doubling the number of computing
nodes when the communications occur in high speed network does not decrease the computations to
communication ratio.
Figure \ref{fig:dist} presents the distance percentage between the energy saving and the performance degradation for each benchmark over both scenarios. The tradeoff distance percentage can be
computed as in equation \ref{eq:max}. The one site scenario with 16 nodes gives the best energy and performance
-tradeoff, on average it is equal to 26\%. The one site scenario using both 16 and 32 nodes had better energy and performance
+tradeoff, on average it is equal to 26.8\%. The one site scenario using both 16 and 32 nodes had better energy and performance
tradeoff comparing to the two sites scenario because the former has high speed local communications
which increase the computations to communications ratio and the latter uses long distance communications which decrease this ratio.
\begin{figure}
\centering
\subfloat[Comparing the execution times of running NAS benchmarks over one core and multicores scenarios]{%
- \includegraphics[width=.4\textwidth]{fig/time.eps}\label{fig:time-mc}} \hspace{1cm}%
+ \includegraphics[width=.48\textwidth]{fig/time.eps}\label{fig:time-mc}} \hspace{0.4cm}%
\subfloat[Comparing the energy consumptions of running NAS benchmarks over one core and multi-cores scenarios]{%
- \includegraphics[width=.4\textwidth]{fig/eng_con.eps}\label{fig:eng-cons-mc}}
+ \includegraphics[width=.48\textwidth]{fig/eng_con.eps}\label{fig:eng-cons-mc}}
\label{fig:eng-cons}
\caption{The energy consumptions and execution times of NAS benchmarks over one core and multi-cores per node architectures}
\end{figure}
\begin{figure}
\centering
\subfloat[The energy saving of running NAS benchmarks over one core and multicores scenarios]{%
- \includegraphics[width=.33\textwidth]{fig/eng_s_mc.eps}\label{fig:eng-s-mc}} \hspace{0.08cm}%
+ \includegraphics[width=.48\textwidth]{fig/eng_s_mc.eps}\label{fig:eng-s-mc}} \hspace{0.4cm}%
\subfloat[The performance degradation of running NAS benchmarks over one core and multicores scenarios
]{%
- \includegraphics[width=.33\textwidth]{fig/per_d_mc.eps}\label{fig:per-d-mc}}\hspace{0.08cm}%
+ \includegraphics[width=.48\textwidth]{fig/per_d_mc.eps}\label{fig:per-d-mc}}\hspace{0.4cm}%
\subfloat[The tradeoff distance of running NAS benchmarks over one core and multicores scenarios]{%
- \includegraphics[width=.33\textwidth]{fig/dist_mc.eps}\label{fig:dist-mc}}
+ \includegraphics[width=.48\textwidth]{fig/dist_mc.eps}\label{fig:dist-mc}}
\label{fig:exp-res}
\caption{The experimental results of one core and multi-cores scenarios}
\end{figure}
\begin{figure}
\centering
\subfloat[The energy saving percentages for the nodes executing the NAS benchmarks over the three power scenarios]{%
- \includegraphics[width=.33\textwidth]{fig/eng_pow.eps}\label{fig:eng-pow}} \hspace{0.08cm}%
+ \includegraphics[width=.48\textwidth]{fig/eng_pow.eps}\label{fig:eng-pow}} \hspace{0.4cm}%
\subfloat[The performance degradation percentages for the NAS benchmarks over the three power scenarios]{%
- \includegraphics[width=.33\textwidth]{fig/per_pow.eps}\label{fig:per-pow}}\hspace{0.08cm}%
+ \includegraphics[width=.48\textwidth]{fig/per_pow.eps}\label{fig:per-pow}}\hspace{0.4cm}%
\subfloat[The tradeoff distance between the energy reduction and the performance of the NAS benchmarks over the three power scenarios]{%
- \includegraphics[width=.33\textwidth]{fig/dist_pow.eps}\label{fig:dist-pow}}
+
+ \includegraphics[width=.48\textwidth]{fig/dist_pow.eps}\label{fig:dist-pow}}
\label{fig:exp-pow}
\caption{The experimental results of different static power scenarios}
\end{figure}
\begin{figure}
\centering
\subfloat[The energy reduction induced by the Maxdist method and the EDP method]{%
- \includegraphics[width=.33\textwidth]{fig/edp_eng}\label{fig:edp-eng}} \hspace{0.08cm}%
+ \includegraphics[width=.48\textwidth]{fig/edp_eng}\label{fig:edp-eng}} \hspace{0.4cm}%
\subfloat[The performance degradation induced by the Maxdist method and the EDP method]{%
- \includegraphics[width=.33\textwidth]{fig/edp_per}\label{fig:edp-perf}}\hspace{0.08cm}%
+ \includegraphics[width=.48\textwidth]{fig/edp_per}\label{fig:edp-perf}}\hspace{0.4cm}%
\subfloat[The tradeoff distance between the energy consumption reduction and the performance for the Maxdist method and the EDP method]{%
- \includegraphics[width=.33\textwidth]{fig/edp_dist}\label{fig:edp-dist}}
+ \includegraphics[width=.48\textwidth]{fig/edp_dist}\label{fig:edp-dist}}
\label{fig:edp-comparison}
\caption{The comparison results}
\end{figure}
To evaluate the proposed method on a real heterogeneous grid platform, it was applied on the
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\% 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
+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 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}
