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\begin{document}
\maketitle
-\AG{Use Capital letters for only the first letter in the title of a section, table, figure, ...}
+\JC{Use Capital letters for only the first letter in the title of a section, table, figure, ...}
\begin{abstract}
Dynamic Voltage Frequency Scaling (DVFS) can be applied to modern CPUs.
This technique is usually used to reduce the energy consumed by a CPU while
\section{Execution and Energy of Parallel Tasks on Homogeneous Platform}
\label{sec.exe}
-\AG{The whole subsection ``Parallel Tasks Execution on Homogeneous Platform'', can be deleted if we need space, we can just say we are interested in this paper in homogeneous clusters}
+\JC{The whole subsection ``Parallel Tasks Execution on Homogeneous Platform'', can be deleted if we need space, we can just say we are interested in this paper in homogeneous clusters}
\subsection{Parallel Tasks Execution on Homogeneous Platform}
A homogeneous cluster consists of identical nodes in terms of hardware and software.
Each node has its own memory and at least one processor which can
quadratically the dynamic power which may cause degradation in performance and thus, the increase of the static energy because the execution time is increased~\cite{36}. If the tasks are sorted according to their execution times before scaling in a descending order, the total energy consumption model for a parallel
homogeneous platform, as presented by Rauber et al.~\cite{3}, can be written as a function of the scaling factor \emph S, as in EQ~(\ref{eq:energy}).
-\AG{Are you sure of the following equation}
+\JC{Are you sure of the following equation}
\begin{equation}
\label{eq:energy}
E = P_\textit{dyn} \cdot S_1^{-2} \cdot
\end{equation}
where \emph N is the number of parallel nodes, $T_i \ and \ S_i \ for \ i=1,...,N$ are the execution times and scaling factors of the sorted tasks. Therefore, $T1$ is the time of the slowest task, and $S_1$ its scaling factor which should be the highest because they are proportional to
the time values $T_i$. The scaling factors are computed as in EQ~(\ref{eq:si}).
-\AG{This equation does not make sense either, what's S? there is no F}
+\JC{This equation does not make sense either, what's S? there is no F}
\begin{equation}
\label{eq:si}
S_i = S \cdot \frac{T_1}{T_i}
= \frac{F_\textit{max}}{F_\textit{new}} \cdot \frac{T_1}{T_i}
\end{equation}
-\AG{The Rauber model was used for a parallel machine not a homogeneous platform}
+\JC{The Rauber model was used for a parallel machine not a homogeneous platform}
where $F$ is the number of available frequencies. In this paper we depend on
Rauber and Rünger energy model EQ~(\ref{eq:energy}) for two reasons: (1) this
model is used for homogeneous platform that we work on in this paper, and (2) we
compare our algorithm with Rauber and Rünger scaling factor selection method which is based on
EQ~(\ref{eq:energy}). The optimal scaling factor is computed by minimizing the derivation for this equation which produces EQ~(\ref{eq:sopt}).
-\AG{what's the small n in the equation}
+\JC{what's the small n in the equation}
\begin{equation}
\label{eq:sopt}
\left( 1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^3} \right) }
\end{equation}
-\AG{The following 2 sections can be merged easily}
+\JC{The following 2 sections can be merged easily}
\section{Performance Evaluation of MPI Programs}
\label{sec.mpip}
NAS parallel benchmarks: CG, MG, EP, FT, BT, LU
and SP. Figure~(\ref{fig:pred}) presents plots of the real execution times and the simulated ones. The average normalized errors between the predicted execution time and
the real time (SimGrid time) for all programs is between 0.0032 to 0.0133.
-\AG{why compute the average error not the max}
+\JC{why compute the average error not the max}
\subsection{The experimental results}
The proposed algorithm was applied to seven MPI programs of the NAS
benchmarks (EP, CG, MG, FT, BT, LU and SP) which were run with three classes (A, B and
As a PhD student, M. Ahmed Fanfakh, would like to thank the University of
Babylon (Iraq) for supporting his work.
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