\usepackage{algorithm}
\usepackage{subfig}
\usepackage{amsmath}
-
+\usepackage{multirow}
\usepackage{url}
\DeclareUrlCommand\email{\urlstyle{same}}
\newcommand{\Told}{\Xsub{T}{Old}}
\begin{document}
-\title{Energy Consumption Reduction in a Heterogeneous Architecture Using DVFS}
+\title{Energy Consumption Reduction for Message Passing Iterative Applications in Heterogeneous Architecture Using DVFS}
\author{%
\IEEEauthorblockN{%
application must be selected.
In this paper, a new online frequencies selecting algorithm for heterogeneous platforms is presented.
-It selects the frequency that give the best tradeoff between energy saving and performance degradation,
+It selects the frequency that try to give the best tradeoff between energy saving and performance degradation,
for each node computing the message passing iterative application. The algorithm has a small overhead and
works without training or profiling. It uses a new energy model for message passing iterative applications
-running on a heterogeneous platform. The proposed algorithm evaluated on the Simgrid simulator while
+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}
The computing platforms must be more energy efficient and offer the highest number of FLOPS per watt possible,
such as the L-CSC from the GSI Helmholtz Center which
became the top of the Green500 list in November 2014 \cite{Green500_List}.
-This heterogeneous platform executes more than 5 GFLOPS per watt while consuming 57.15 kilowatts.
+This heterogeneous platform executes more than 5 GFLOPS per watt while consumed 57.15 kilowatts.
Besides hardware improvements, there are many software techniques to lower the energy consumption of these platforms,
such as scheduling, DVFS, ... DVFS is a widely used process to reduce the energy consumption of a processor by lowering
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.
Moreover, they are not measured using the same metric. To solve this problem, the
execution time is normalized by computing the ratio between the new execution time (after
scaling down the frequencies of some processors) and the initial one (with maximum
-frequency for all nodes,) as follows:
+frequency for all nodes) as follows:
\begin{multline}
\label{eq:pnorm}
P_\textit{Norm} = \frac{T_\textit{New}}{T_\textit{Old}}\\
While the main
goal is to optimize the energy and execution time at the same time, the normalized
energy and execution time curves are not in the same direction. According
-to the equations~(\ref{eq:enorm}) and~(\ref{eq:pnorm}), the vector of frequency
+to the equations~(\ref{eq:pnorm}) and (\ref{eq:enorm}), the vector of frequency
scaling factors $S_1,S_2,\dots,S_N$ reduce both the energy and the execution
time simultaneously. But the main objective is to produce maximum energy
reduction with minimum execution time reduction.
\end{figure}
Then, the objective function can be modeled as finding the maximum distance
-between the energy curve EQ~(\ref{eq:enorm}) and the performance
-curve EQ~(\ref{eq:pnor@+eYd162m_inv}) over all available sets of scaling factors. This
+between the energy curve (\ref{eq:enorm}) and the performance
+curve (\ref{eq:pnorm_inv}) over all available sets of scaling factors. This
represents the minimum energy consumption with minimum execution time (maximum
performance) at the same time, see figure~(\ref{fig:r1}) or figure~(\ref{fig:r2}). Then the objective
function has the following form:
(\overbrace{P_\textit{Norm}(S_{ij})}^{\text{Maximize}} -
\overbrace{E_\textit{Norm}(S_{ij})}^{\text{Minimize}} )
\end{equation}
-where $N$ is the number of nodes and $F$ is the number of available frequencies for each nodes.
-Then, the optimal set of scaling factors that satisfies EQ~(\ref{eq:max}) can be selected.
+where $N$ is the number of nodes and $F$ is the number of available frequencies for each node.
+Then, the optimal set of scaling factors that satisfies (\ref{eq:max}) can be selected.
The objective function can work with any energy model or any power values for each node
(static and dynamic powers). However, the most energy reduction gain can be achieved when
the energy curve has a convex form as shown in~\cite{Zhuo_Energy.efficient.Dynamic.Task.Scheduling,Rauber_Analytical.Modeling.for.Energy,Hao_Learning.based.DVFS}.
\label{sec.optim}
\subsection{The algorithm details}
-In this section algorithm~(\ref{HSA}) is presented. It selects the frequency scaling factors
+In this section algorithm \ref{HSA} is presented. It selects the frequency scaling factors
vector that gives the best trade-off between minimizing the energy consumption and maximizing
the performance of a message passing synchronous iterative application executed on a heterogeneous
platform. It works online during the execution time of the iterative message passing program.
\State Round the computed initial frequencies $F_i$ to the closest one available in each node.
\If{(not the first frequency)}
\State $F_i \gets F_i+Fdiff_i,~i=1,\dots,N.$
- \State where $i=1,\dots,N$ means for loop.
\EndIf
\State $T_\textit{Old} \gets max_{~i=1,\dots,N } (Tcp_i+Tcm_i)$
\State $E_\textit{Original} \gets \sum_{i=1}^{N}{( Pd_i \cdot Tcp_i)} +\sum_{i=1}^{N} {(Ps_i \cdot T_{Old})}$
- \State $Sopt_{i} \gets \frac{Fmax_i}{F_i},~i=1,\dots,N. $
- \State Computing the initial distance $Dist \gets\Pnorm(Sopt_i) - \Enorm(Sopt_i) $
+ \State $Sopt_{i} \gets 1,~i=1,\dots,N. $
+ \State $Dist \gets 0 $
\While {(all nodes not reach their minimum frequency)}
\If{(not the last freq. \textbf{and} not the slowest node)}
\State $F_i \gets F_i - Fdiff_i,~i=1,\dots,N.$
\label{dvfs}
\end{algorithm}
-\subsection{The verifications of the proposed algorithm}
+\subsection{The evaluation of the proposed algorithm}
\label{sec.verif.algo}
The precision of the proposed algorithm mainly depends on the execution time prediction model defined in
(\ref{eq:perf}) and the energy model computed by (\ref{eq:energy}).
different number of nodes. The solutions returned by the brute force algorithm and the proposed algorithm were identical
and the proposed algorithm was on average 10 times faster than the brute force algorithm. It has a small execution time:
for a heterogeneous cluster composed of four different types of nodes having the characteristics presented in
-table~(\ref{table:platform}), it takes on average \np[ms]{0.04} for 4 nodes and \np[ms]{0.15} on average for 144 nodes
+table~\ref{table:platform}, it takes on average \np[ms]{0.04} for 4 nodes and \np[ms]{0.15} on average for 144 nodes
to compute the best scaling factors vector. The algorithm complexity is $O(F\cdot (N \cdot4) )$, where $F$ is the number
of iterations and $N$ is the number of computing nodes. The algorithm needs from 12 to 20 iterations to select the best
vector of frequency scaling factors that gives the results of the next 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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