iteration and $MinTcm$ is the communication time of the slowest processor from
the first iteration. The model computes the maximum computation time
with scaling factor from each node added to the communication time of the \subsection{The verifications of the proposed method}
-\label{sec.verif}
+\label{sec.verif.method}
The precision of the proposed algorithm mainly depends on the execution time prediction model defined in
EQ(\ref{eq:perf}) and the energy model computed by EQ(\ref{eq:energy}).
The energy model is also significantly dependent on the execution time model because the static energy is
equal to the execution time of one iteration as in EQ(\ref{eq:perf}) multiplied
by the number of iterations of that application.
-This prediction model is developed from our model for predicting the execution time of
+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 our method for optimizing both
+The execution time prediction model is used in the method for optimizing both
energy consumption and performance of iterative methods, which is presented in the
following sections.
between the energy curve EQ~(\ref{eq:enorm}) and the performance
curve EQ~(\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 our objective
+performance) at the same time, see figure~(\ref{fig:r1}) or figure~(\ref{fig:r2}). Then the objective
function has the following form:
\begin{equation}
\label{eq:max}
passing iterative synchronous applications, fast nodes have to wait for the slower ones to finish their
computations before being able to synchronously communicate with them as in figure (\ref{fig:heter}).
These periods are called idle or slack times.
-Our algorithm takes into account this problem and tries to reduce these slack times when selecting the
+The algorithm takes into account this problem and tries to reduce these slack times when selecting the
frequency scaling factors vector. At first, it selects initial frequency scaling factors that increase
the execution times of fast nodes and minimize the differences between the computation times of
fast and slow nodes. The value of the initial frequency scaling factor for each node is inversely
\EndWhile
\State Return $Sopt_1,Sopt_2,\dots,Sopt_N$
\end{algorithmic}
- \caption{Heterogeneous scaling algorithm}
+ \caption{frequency scaling factors selection algorithm}
\label{HSA}
\end{algorithm}
\end{algorithm}
\subsection{The verifications of the proposed algorithm}
-\label{sec.verif}
+\label{sec.verif.algo}
The precision of the proposed algorithm mainly depends on the execution time prediction model defined in
EQ(\ref{eq:perf}) and the energy model computed by EQ(\ref{eq:energy}).
The energy model is also significantly dependent on the execution time model because the static energy is
\section{Conclusion}
\label{sec.concl}
-In this paper, a new online frequency selecting algorithm have been presented. It selects the best possible vector of frequency scaling factors for a heterogeneous platform.
-This vector gives the maximum distance (optimal tradeoff) between the predicted energy and
-the predicted performance curves. In addition, we developed a new energy model for measuring
+In this paper, a new online frequency selecting algorithm have 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
-cluster. The proposed method evaluated on Simgrid/SMPI simulator to built a heterogeneous
-platform to executes NAS parallel benchmarks. The results of the experiments showed the ability of
-the proposed algorithm to changes its behaviour to selects different scaling factors when
-the number of computing nodes and both of the static and the dynamic powers are changed.
-
-In the future, we plan to improve this method to apply on asynchronous iterative applications
-where each task does not wait the others tasks to finish there works. This leads us to develop a new
-energy model to an asynchronous iterative applications, where the number of iterations is not
+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.
+
+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
+energy model because the number of iterations is not
known in advance and depends on the global convergence of the iterative system.
\section*{Acknowledgment}
