\usepackage{algorithm}
\usepackage{subfig}
\usepackage{amsmath}
-
+\usepackage{multirow}
\usepackage{url}
\DeclareUrlCommand\email{\urlstyle{same}}
\begin{figure}[t]
\centering
- \includegraphics[scale=0.6]{fig/commtasks}
+ \includegraphics[scale=0.5]{fig/commtasks}
\caption{Parallel tasks on a heterogeneous platform}
\label{fig:heter}
\end{figure}
This prediction model is developed from the model for predicting the execution time of
message passing distributed applications for homogeneous architectures~\cite{Our_first_paper}.
-The execution time prediction model is used in the method for optimizing both
+The execution time prediction model is uSpiliopoulossed in the method for optimizing both
energy consumption and performance of iterative methods, which is presented in the
following sections.
& & GHz & GHz &GHz & & \\
\hline
1 &40 & 2.5 & 1.2 & 0.1 & 20~w &4~w \\
- & & & & & & \\
+
\hline
2 &50 & 2.66 & 1.6 & 0.133 & 25~w &5~w \\
- & & & & & & \\
+
\hline
3 &60 & 2.9 & 1.2 & 0.1 & 30~w &6~w \\
- & & & & & & \\
+
\hline
4 &70 & 3.4 & 1.6 & 0.133 & 35~w &7~w \\
- & & & & & & \\
+
\hline
\end{tabular}
\label{table:platform}
\centering
\begin{tabular}{|*{7}{l|}}
\hline
- Method & Execution & Energy & Energy & Performance & Distance \\
+ Program & Execution & Energy & Energy & Performance & Distance \\
name & time/s & consumption/J & saving\% & degradation\% & \\
\hline
CG & 64.64 & 3560.39 &34.16 &6.72 &27.44 \\
\centering
\begin{tabular}{|*{7}{l|}}
\hline
- Method & Execution & Energy & Energy & Performance & Distance \\
+ Program & Execution & Energy & Energy & Performance & Distance \\
name & time/s & consumption/J & saving\% & degradation\% & \\
\hline
CG &36.11 &3263.49 &31.25 &7.12 &24.13 \\
\centering
\begin{tabular}{|*{7}{l|}}
\hline
- Method & Execution & Energy & Energy & Performance & Distance \\
+ Program & Execution & Energy & Energy & Performance & Distance \\
name & time/s & consumption/J & saving\% & degradation\% & \\
\hline
CG &31.74 &4373.90 &26.29 &9.57 &16.72 \\
\centering
\begin{tabular}{|*{7}{l|}}
\hline
- Method & Execution & Energy & Energy & Performance & Distance \\
+ Program & Execution & Energy & Energy & Performance & Distance \\
name & time/s & consumption/J & saving\% & degradation\% & \\
\hline
CG &32.35 &6704.21 &16.15 &5.30 &10.85 \\
\centering
\begin{tabular}{|*{7}{l|}}
\hline
- Method & Execution & Energy & Energy & Performance & Distance \\
+ Program & Execution & Energy & Energy & Performance & Distance \\
name & time/s & consumption/J & saving\% & degradation\% & \\
\hline
CG &46.65 &17521.83 &8.13 &1.68 &6.45 \\
\centering
\begin{tabular}{|*{7}{l|}}
\hline
- Method & Execution & Energy & Energy & Performance & Distance \\
+ Program & Execution & Energy & Energy & Performance & Distance \\
name & time/s & consumption/J & saving\% & degradation\% & \\
\hline
CG &56.92 &41163.36 &4.00 &1.10 &2.90 \\
\centering
\begin{tabular}{|*{6}{l|}}
\hline
- Method & Energy & Energy & Performance & Distance \\
+ Program & Energy & Energy & Performance & Distance \\
name & consumption/J & saving\% & degradation\% & \\
\hline
CG &4144.21 &22.42 &7.72 &14.70 \\
\centering
\begin{tabular}{|*{6}{l|}}
\hline
- Method & Energy & Energy & Performance & Distance \\
+ Program & Energy & Energy & Performance & Distance \\
name & consumption/J & saving\% & degradation\% & \\
\hline
CG &2812.38 &36.36 &6.80 &29.56 \\
\begin{figure}
\centering
- \subfloat[Comparison the average of the results on 8 nodes]{%
- \includegraphics[width=.33\textwidth]{fig/sen_comp}\label{fig:sen_comp}}%
+ \subfloat[Comparison of the results on 8 nodes]{%
+ \includegraphics[width=.30\textwidth]{fig/sen_comp}\label{fig:sen_comp}}%
\subfloat[Comparison the selected frequency scaling factors of MG benchmark class C running on 8 nodes]{%
- \includegraphics[width=.33\textwidth]{fig/three_scenarios}\label{fig:scales_comp}}
+ \includegraphics[width=.34\textwidth]{fig/three_scenarios}\label{fig:scales_comp}}
\label{fig:comp}
\caption{The comparison of the three power scenarios}
\end{figure}
+\subsection{The comparison of the proposed scaling algorithm }
+\label{sec.compare_EDP}
+
+In this section, we compare our scaling factors selection algorithm
+with Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS}.
+They developed an online frequency selecting algorithm running over multicore architecture.
+The algorithm predicted both the energy and performance during the runtime of the program, then
+selecting the frequencies that minimized the energy and delay products (EDP), $EDP=Enegry * Delay$.
+To be able to compare with this algorithm, we used our energy and execution time models in prediction process,
+equations (\ref{eq:energy}) and (\ref{eq:fnew}). Also their algorithm is adapted to taking into account
+the heterogeneous platform to starts selecting the
+initial frequencies using the equation (\ref{eq:Fint}). The algorithm built to test all possible frequencies as
+a brute-force search algorithm.
+
+The comparison results of running NAS benchmarks class C on 8 or 9 nodes are
+presented in table \ref{table:compare_EDP}. The results show that our algorithm has a biggest energy saving percentage,
+on average it has 29.76\% and thier algorithm has 25.75\%,
+while the average of performance degradation percentage is approximately the same, the average for our algorithm is
+equal to 3.89\% and for their algorithm is equal to 4.03\%. In general, our algorithm outperforms
+Spiliopoulos et al. algorithm in term of energy and performance tradeoff see figure (\ref{fig:compare_EDP}).
+This because our algorithm maximized the difference (the distance) between the energy saving and the performance degradation
+comparing to their EDP optimization function. It is also keeps the frequency of the slowest node without change
+that gave some enhancements to the energy and performance tradeoff.
+
+
+\begin{table}[h]
+ \caption{Comparing the proposed algorithm}
+ \centering
+\begin{tabular}{|l|l|l|l|l|l|l|l|}
+\hline
+\multicolumn{2}{|l|}{\multirow{2}{*}{\begin{tabular}[c]{@{}l@{}}Program \\ name\end{tabular}}} & \multicolumn{2}{l|}{Energy saving \%} & \multicolumn{2}{l|}{Perf. degradation \%} & \multicolumn{2}{l|}{Distance} \\ \cline{3-8}
+\multicolumn{2}{|l|}{} & EDP & MaxDist & EDP & MaxDist & EDP & MaxDist \\ \hline
+\multicolumn{2}{|l|}{CG} & 27.58 & 31.25 & 5.82 & 7.12 & 21.76 & 24.13 \\ \hline
+\multicolumn{2}{|l|}{MG} & 29.49 & 33.78 & 3.74 & 6.41 & 25.75 & 27.37 \\ \hline
+\multicolumn{2}{|l|}{LU} & 19.55 & 28.33 & 0.0 & 0.01 & 19.55 & 28.22 \\ \hline
+\multicolumn{2}{|l|}{EP} & 28.40 & 27.04 & 4.29 & 0.49 & 24.11 & 26.55 \\ \hline
+\multicolumn{2}{|l|}{BT} & 27.68 & 32.32 & 6.45 & 7.87 & 21.23 & 24.43 \\ \hline
+\multicolumn{2}{|l|}{SP} & 20.52 & 24.73 & 5.21 & 2.78 & 15.31 & 21.95 \\ \hline
+\multicolumn{2}{|l|}{FT} & 27.03 & 31.02 & 2.75 & 2.54 & 24.28 & 28.48 \\ \hline
+
+\end{tabular}
+\label{table:compare_EDP}
+\end{table}
+
+
+
+\begin{figure}[t]
+ \centering
+ \includegraphics[scale=0.6]{fig/compare_EDP.pdf}
+ \caption{Tradeoff comparison for NAS benchmarks class C}
+ \label{fig:compare_EDP}
+\end{figure}
+
\section{Conclusion}
\label{sec.concl}
\section*{Acknowledgment}
+This work has been partially supported by the Labex
+ACTION project (contract “ANR-11-LABX-01-01”). As a PhD student,
+Mr. Ahmed Fanfakh, would like to thank the University of
+Babylon (Iraq) for supporting his work.
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