\section{Performance evaluation of MPI programs}
\label{sec.mpip}
-The execution time of parallel synchronous MPI applications depends
-on the time of the slowest task. If there is no
+The execution time of a parallel synchronous iterative application is
+equal to the execution time of the slowest task. If there is no
communication and the application is not data bounded, the execution time of a
parallel program is linearly proportional to the operational frequency and any
DVFS operation for energy reduction increases the execution time of the parallel
\section{Performance and energy reduction trade-off}
\label{sec.compet}
-This section presents our approach for choosing the optimal scaling factor.
-This factor gives maximum energy reduction while taking into account the execution
-times for both computation and communication. The relation between the execution time
-and the energy is nonlinear and complex. Thus, unlike the relation between the execution time and the scaling factor, the relation of energy with the scaling factor is nonlinear, for more details refer to~\cite{17}. Moreover, they are not measured using the same metric. To
-solve this problem, we normalize the energy by calculating the ratio between
+This section presents our method for choosing the optimal scaling factor that gives the best tradeoff between energy reduction and performance. This method takes into account the execution times for both computation and communication to compute the scaling factor. Since, the energy consumption and the performance are not measured using the same metric, a normalized value of both measurements can be used to compare them. The normalized energy is the ratio between
the consumed energy with scaled frequency and the consumed energy without scaled
frequency:
\begin{multline}
\Pdyn \cdot \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
\Pstatic \cdot T_1 \cdot N }
\end{multline}
-In the same way we can normalize the time as follows:
+In the same way, the normalized execution time of a program is computed as follows:
\begin{equation}
\label{eq:pnorm}
\Tnorm = \frac{\Tnew}{\Told}
= \frac{\TmaxCompOld \cdot S + \TmaxCommOld}{
\TmaxCompOld + \TmaxCommOld}
\end{equation}
-The second problem is that the optimization operation for both energy and
-execution time is not in the same direction. In other words, the normalized energy
-and the execution time curves are not at the same direction see
-Figure~\ref{fig:rel}\subref{fig:r2}. While the main goal is to optimize the
-energy and execution time in the same time. According to the
-equations~\eqref{eq:enorm} and~\eqref{eq:pnorm}, the scaling factor $S$ reduce
-both the energy and the execution time simultaneously. But the main objective is
-to produce maximum energy reduction with minimum execution time reduction. Many
-researchers used different strategies to solve this nonlinear problem for
-example see~\cite{19,42}, their methods add big overheads to the algorithm to
-select the suitable frequency. In this paper we present a method to find the
-optimal scaling factor $S$ to optimize both energy and execution time
-simultaneously without adding a big overhead. Our solution for this problem is
-to make the optimization process for energy and execution time follow the same
-direction. Therefore, we inverse the equation of the normalized execution time as
-follows:
+The relation between the execution time and the consumed energy of a program is nonlinear and complex. In consequences, the relation between the consumed energy and the scaling factor is also nonlinear, for more details refer to~\cite{17}. Therefore, the resulting normalized energy consumption curve and execution time curve, for different scaling factors, do not have the same direction see Figure~\ref{fig:rel}\subref{fig:r2}. To tackle this problem and optimize both terms, we inverse the equation of the normalized execution time as follows:
\begin{equation}
\label{eq:pnorm_en}
\Pnorm = \frac{ \Told}{ \Tnew}
\label{fig:rel}
\end{figure}
Then, we can model our objective function as finding the maximum distance
-between the energy curve EQ~\eqref{eq:enorm} and the inverse of execution time (performance)
+between the energy curve EQ~\eqref{eq:enorm} and the inverse of the execution time (performance)
curve EQ~\eqref{eq:pnorm_en} over all available scaling factors. This
represents the minimum energy consumption with minimum execution time (better
performance) at the same time, see Figure~\ref{fig:rel}\subref{fig:r1}. Then
