\usepackage{algorithm}
\usepackage{subfig}
\usepackage{amsmath}
-
+\usepackage{multirow}
\usepackage{url}
\DeclareUrlCommand\email{\urlstyle{same}}
works without training or profiling. It uses a new energy model for message passing iterative applications
running on a heterogeneous platform. The proposed algorithm is evaluated on the Simgrid simulator while
running the NAS parallel benchmarks. The experiments demonstrated that it reduces the energy consumption
-up to 35\% while limiting the performance degradation as much as possible.
+up to 35\% while limiting the performance degradation as much as possible. \textcolor{red}{Furthermore, we compare the
+proposed algorithm with other method. The comparison’s results show that our algorithm gives better
+energy-time trade-off.}
+
\end{abstract}
\section{Introduction}
consumption while minimizing the degradation of the program's performance.
Section~\ref{sec.optim} details the proposed frequency selecting algorithm then the precision of the proposed algorithm is verified.
Section~\ref{sec.expe} presents the results of applying the algorithm on the NAS parallel benchmarks and executing them
-on a heterogeneous platform. It also shows the results of running three
-different power scenarios and comparing them.
+on a heterogeneous platform. It shows the results of running three
+different power scenarios and comparing them. \textcolor{red}{Moreover, it also shows the comparison results
+between our method and other method.}
Finally, in Section~\ref{sec.concl} the paper is ended with a summary and some future works.
\section{Related works}
\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=0.5]{fig/compare_EDP.pdf}
+ \caption{Tradeoff comparison for NAS benchmarks class C}
+ \label{fig:compare_EDP}
+\end{figure}
+
\section{Conclusion}
\label{sec.concl}
In this paper, a new online frequency selecting algorithm has been presented. It selects the best possible vector of frequency scaling factors that gives the maximum distance (optimal tradeoff) between the predicted energy and
the predicted performance curves for a heterogeneous platform. This algorithm uses a new energy model for measuring
and predicting the energy of distributed iterative applications running over heterogeneous
-platform. To evaluate the proposed method, it was applied on the NAS parallel benchmarks and executed over a heterogeneous platform simulated by Simgrid. The results of the experiments showed that the algorithm reduces up to 35\% the energy consumption of a message passing iterative method while limiting the degradation of the performance. The algorithm also selects different scaling factors according to the percentage of the computing and communication times, and according to the values of the static and dynamic powers of the CPUs.
+platform. To evaluate the proposed method, it was applied on the NAS parallel benchmarks and executed over a heterogeneous platform simulated by Simgrid. The results of the experiments showed that the algorithm reduces up to 35\% the energy consumption of a message passing iterative method while limiting the degradation of the performance. The algorithm also selects different scaling factors according to the percentage of the computing and communication times, and according to the values of the static and dynamic powers of the CPUs. \textcolor{red}{ We compare our algorithm with Spiliopoulos et al. algorithm, the comparison results showed that our
+algorithm outperforms their algorithm in term of energy-time tradeoff.}
In the near future, this method will be applied to real heterogeneous platforms to evaluate its performance in a real study case. It would also be interesting to evaluate its scalability over large scale heterogeneous platform and measure the energy consumption reduction it can produce. Afterward, we would like to develop a similar method that is adapted to asynchronous iterative applications
where each task does not wait for others tasks to finish there works. The development of such method might require a new
\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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