became the top of the Green500 list in November 2014 \cite{Green500_List}.
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,
+Besides platform improvements, there are many software and hardware 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
its frequency \cite{Rizvandi_Some.Observations.on.Optimal.Frequency}. However, it also reduces the number of FLOPS
executed by the processor which might increase the execution time of the application running over that processor.
\begin{figure}[t]
\centering
- \includegraphics[scale=0.5]{fig/commtasks}
+ \includegraphics[scale=0.6]{fig/commtasks}
\caption{Parallel tasks on a heterogeneous platform}
\label{fig:heter}
\end{figure}
\end{equation}
Where:\\
\begin{equation}
-\label{eq:perf}
+\label{eq:perf2}
MinTcm = \min_{i=1,2,\dots,N} (Tcm_i)
\end{equation}
where $TcpOld_i$ is the computation time of processor $i$ during the first
if it is communicating with slower nodes, see figure(\ref{fig:heter}). Therefore, all nodes do
not have equal communication times. While the dynamic energy is computed according to the frequency
scaling factor and the dynamic power of each node as in (\ref{eq:Edyn}), the static energy is
-computed as the sum of the execution time of each processor multiplied by its static power.
+computed as the sum of the execution time of one iteration multiplied by static power of each processor.
The overall energy consumption of a message passing distributed application executed over a
heterogeneous platform during one iteration is the summation of all dynamic and static energies
for each processor. It is computed as follows:
reduction with minimum execution time reduction.
This problem can be solved by making the optimization process for energy and
-execution time follow the same direction. Therefore, the equation of the
+execution time following the same direction. Therefore, the equation of the
normalized execution time is inverted which gives the normalized performance equation, as follows:
\begin{multline}
\label{eq:pnorm_inv}
\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.
It uses information gathered during the first iteration such as the computation time and the
communication time in one iteration for each node. The algorithm is executed after the first
iteration and returns a vector of optimal frequency scaling factors that satisfies the objective
-function (\ref{eq:max}). The program apply DVFS operations to change the frequencies of the CPUs
+function (\ref{eq:max}). The program applies DVFS operations to change the frequencies of the CPUs
according to the computed scaling factors. This algorithm is called just once during the execution
of the program. Algorithm~(\ref{dvfs}) shows where and when the proposed scaling algorithm is called
in the iterative MPI program.
toward lower frequencies. The algorithm iterates on all left frequencies, from the higher bound until all
nodes reach their minimum frequencies, to compute their overall energy consumption and performance, and select
the optimal frequency scaling factors vector. At each iteration the algorithm determines the slowest node
-according to (\ref{eq:perf}) and keeps its frequency unchanged, while it lowers the frequency of
+according to the equation (\ref{eq:perf}) and keeps its frequency unchanged, while it lowers the frequency of
all other nodes by one gear.
The new overall energy consumption and execution time are computed according to the new scaling factors.
The optimal set of frequency scaling factors is the set that gives the highest distance according to the objective
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}).
The energy model is also significantly dependent on the execution time model because the static energy is
-linearly related the execution time and the dynamic energy is related to the computation time. So, all of
+linearly related to the execution time and the dynamic energy is related to the computation time. So, all of
the works presented in this paper is based on the execution time model. To verify this model, the predicted
execution time was compared to the real execution time over SimGrid/SMPI simulator, v3.10~\cite{casanova+giersch+legrand+al.2014.versatile},
for all the NAS parallel benchmarks NPB v3.3
\begin{figure}
\centering
\subfloat[Comparison of the results on 8 nodes]{%
- \includegraphics[width=.30\textwidth]{fig/sen_comp}\label{fig:sen_comp}}%
+ \includegraphics[width=.33\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=.34\textwidth]{fig/three_scenarios}\label{fig:scales_comp}}
+ \includegraphics[width=.33\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, the scaling factors selection algorithm
-is compared to Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS}.
+In this section, the scaling factors selection algorithm, called MaxDist,
+is compared to Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS}, called EDP.
They developed a green governor that regularly applies an online frequency selecting algorithm to reduce the energy consumed by a multicore architecture without degrading much its performance. The algorithm selects the frequencies that minimize the energy and delay products, $EDP=Enegry*Delay$ using the predicted overall energy consumption and execution time delay for each frequency.
- To fairly compare both algorithms, the same energy and execution time models, equations (\ref{eq:energy}) and (\ref{eq:fnew}), were used for both algorithms to predict the energy consumption and the execution times. Also Spiliopoulos et al. algorithm was adapted to start the search from the
+To fairly compare both algorithms, the same energy and execution time models, equations (\ref{eq:energy}) and (\ref{eq:fnew}), were used for both algorithms to predict the energy consumption and the execution times. Also Spiliopoulos et al. algorithm was adapted to start the search from the
initial frequencies computed using the equation (\ref{eq:Fint}). The resulting algorithm is an exhaustive search algorithm that minimizes the EDP and has the initial frequencies values as an upper bound.
-Both algorithms were applied to the parallel NAS benchmarks to compare their efficiency. Table \ref{table:compare_EDP} presents the results of comparing the execution times and the energy consumptions for both versions of the NAS benchmarks while running the class C of each benchmark over 8 or 9 heterogeneous nodes. \textcolor{red}{The results show that our algorithm gives better energy savings than Spiliopoulos et al. algorithm,
-on average it is up to 17\% higher for energy saving compared to their algorithm. The average of performance degradation percentage using our method is higher on average by 3.82\%.}
+Both algorithms were applied to the parallel NAS benchmarks to compare their efficiency. Table \ref{table:compare_EDP} presents the results of comparing the execution times and the energy consumptions for both versions of the NAS benchmarks while running the class C of each benchmark over 8 or 9 heterogeneous nodes. The results show that our algorithm gives better energy savings than Spiliopoulos et al. algorithm,
+on average it results in 29.76\% energy saving while their algorithm returns just 25.75\%. The average of performance degradation percentage is approximately the same for both algorithms, about 4\%.
+
For all benchmarks, our algorithm outperforms
-Spiliopoulos et al. algorithm in term of energy and performance tradeoff \textcolor{red}{(on average it has up to 21\% of distance)}, see figure (\ref{fig:compare_EDP}) because it maximizes the distance between the energy saving and the performance degradation values while giving the same weight for both metrics.
+Spiliopoulos et al. algorithm in term of energy and performance tradeoff, see figure (\ref{fig:compare_EDP}), because it maximizes the distance between the energy saving and the performance degradation values while giving the same weight for both metrics.
-\begin{table}[htb]
- \caption{Comparing the proposed algorithm}
- % title of Table
- \centering
- \begin{tabular}{|*{4}{l|}}
- \hline
- Program & Energy & Performance & Distance\% \\
- name & saving\% & degradation\% & \\
- \hline
- CG &13.31 &22.34 &10.89 \\
- \hline
- MG &14.55 &71.39 &6.29 \\
- \hline
- EP &44.4 &0.0 &44.42 \\
- \hline
- LU &-4.79 &-88.58 &10.12 \\
- \hline
- BT &16.76 &22.33 &15.07 \\
- \hline
- SP &20.52 &-46.64 &43.37 \\
- \hline
- FT &14.76 &-7.64 &17.3 \\
-\hline
- \end{tabular}
- \label{table:compare_EDP}
+
+\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}
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
+where each task does not wait for others tasks to finish their works. The development of such method might require a new
energy model because the number of iterations is not
known in advance and depends on the global convergence of the iterative system.
\section*{Acknowledgment}
This work has been partially supported by the Labex
-ACTION project (contract “ANR-11-LABX-01-01”). As a PhD student,
+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.
+Babylon (Iraq) for supporting his work.
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