of the slowest node and the computation time of the node $i$ as follows:
\begin{equation}
\label{eq:Scp}
- \Scp[ij] = \frac{ \mathop{\max_{i=1,\dots N}}_{j=1,\dots,M}(\Tcp[ij])} {\Tcp[ij]}
+ \Scp[ij] = \frac{ \mathop{\max\limits_{i=1,\dots N}}\limits_{j=1,\dots,M}(\Tcp[ij])} {\Tcp[ij]}
\end{equation}
Using the initial frequency scaling factors computed in (\ref{eq:Scp}), the
algorithm computes the initial frequencies for all nodes as a ratio between the
\centering
\begin{tabular}{|*{7}{c|}}
\hline
- Cluster & CPU & Max & Min & Diff. & no. of cores & dynamic power \\
- Name & model & Freq. & Freq. & Freq. & per CPU & of one core \\
- & & GHz & GHz & GHz & & \\
+ & & Max & Min & Diff. & & \\
+ Cluster & CPU & Freq. & Freq. & Freq. & No. of cores & Dynamic power \\
+ Name & model & GHz & GHz & GHz & per CPU & of one core \\
\hline
- & Intel & 2.3 & 1.2 & 0.1 & 6 & \np[W]{35} \\
- Taurus & Xeon & & & & & \\
- & E5-2630 & & & & & \\
+ & Intel & & & & & \\
+ Taurus & Xeon & 2.3 & 1.2 & 0.1 & 6 & \np[W]{35} \\
+ & E5-2630 & & & & & \\
\hline
- & Intel & 2.53 & 1.2 & 0.133 & 4 & \np[W]{23} \\
- Graphene & Xeon & & & & & \\
- & X3440 & & & & & \\
+ & Intel & & & & & \\
+ Graphene & Xeon & 2.53 & 1.2 & 0.133 & 4 & \np[W]{23} \\
+ & X3440 & & & & & \\
\hline
- & Intel & 2.5 & 2 & 0.5 & 4 & \np[W]{46} \\
- Griffon & Xeon & & & & & \\
- & L5420 & & & & & \\
+ & Intel & & & & & \\
+ Griffon & Xeon & 2.5 & 2 & 0.5 & 4 & \np[W]{46} \\
+ & L5420 & & & & & \\
\hline
- & Intel & 2 & 1.2 & 0.1 & 8 & \np[W]{35} \\
- Graphite & Xeon & & & & & \\
- & E5-2650 & & & & & \\
+ & Intel & & & & & \\
+ Graphite & Xeon & 2 & 1.2 & 0.1 & 8 & \np[W]{35} \\
+ & E5-2650 & & & & & \\
\hline
\end{tabular}
\label{table:grid5000}
The overall energy consumption of all the benchmarks solving the class D instance and
using the proposed frequency selection algorithm is measured
using the equation of the reduced energy consumption, equation
-(\ref{eq:energy}). This model uses the measured dynamic power showed in Table \ref{table:grid5000}
-
-and the static
+(\ref{eq:energy}). This model uses the measured dynamic power showed in Table \ref{table:grid5000} and the static
power is assumed to be equal to 20\% of the dynamic power. The execution
time is measured for all the benchmarks over these different scenarios.
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}
+\begin{figure*}[t]
\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}%
\includegraphics[width=.48\textwidth]{fig/dist.eps}\label{fig:dist}}
\label{fig:exp-res}
\caption{The experimental results of different scenarios}
-\end{figure}
+\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 8.3\% or 4.7\% respectively.
More energy reduction can be gained when this ratio is big because it pushes the proposed scaling algorithm to select smaller frequencies that decrease the dynamic power consumption. These experiments also showed that the energy
consumption and the execution times of the EP and MG benchmarks do not change significantly over these two
scenarios because there are no or small communications. Contrary to EP and MG, the energy consumptions and the execution times of the rest of the benchmarks vary according to the communication times that are different from one scenario to the other.
-
+\begin{figure*}[t]
+ \centering
+ \subfloat[The energy saving of running NAS benchmarks over one core and multicores scenarios]{%
+ \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=.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=.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*}
The energy saving percentages of all NAS benchmarks running over these two scenarios are presented in figure \ref{fig:eng-s-mc}.
The figure shows that the energy saving percentages in the one
-\begin{figure}
- \centering
- \subfloat[The energy saving of running NAS benchmarks over one core and multicores scenarios]{%
- \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=.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=.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}
+
In these experiments, class D of the NAS parallel benchmarks are executed over the Nancy site. 16 computing nodes from the three clusters, Graphite, Graphene and Griffon, where used in this experiment.
-\begin{figure}
+\begin{figure*}[t]
\centering
\subfloat[The energy saving percentages for the nodes executing the NAS benchmarks over the three power scenarios]{%
\includegraphics[width=.48\textwidth]{fig/eng_pow.eps}\label{fig:eng-pow}} \hspace{0.4cm}%
\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}
+\end{figure*}
presented in the figures \ref{fig:edp-eng}, \ref{fig:edp-perf} and \ref{fig:edp-dist} respectively.
-\begin{figure}
+\begin{figure*}[t]
\centering
\subfloat[The energy reduction induced by the Maxdist method and the EDP method]{%
\includegraphics[width=.48\textwidth]{fig/edp_eng}\label{fig:edp-eng}} \hspace{0.4cm}%
\includegraphics[width=.48\textwidth]{fig/edp_dist}\label{fig:edp-dist}}
\label{fig:edp-comparison}
\caption{The comparison results}
-\end{figure}
+\end{figure*}
As shown in these figures, the proposed frequencies selection algorithm, Maxdist, outperforms the EDP algorithm in terms of energy consumption reduction and performance for all of the benchmarks executed over the two scenarios.
The proposed algorithm gives better results than EDP because it
In the near future, we would like to develop a similar method that is adapted to
asynchronous iterative applications where iterations are not synchronized and communications are overlapped with computations.
- The development of
-such a method might require a new energy model because the
+The development of such a 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.
