benchmarks (NPB v3.3) developed by NASA~\cite{44}. Our experiments are executed
using the simulator SimGrid/SMPI v3.10~\cite{Casanova:2008:SGF:1397760.1398183}
over an homogeneous distributed memory architecture. Furthermore, we compare the
-proposed algorithm with Rauber and R\"{u}nger methods~\cite{3}.
+proposed algorithm with Rauber and Rünger methods~\cite{3}.
The comparison's results show that our
algorithm gives better energy-time trade off.
This paper is organized as follows: Section~\ref{sec.relwork} presents the works from other authors.
Section~\ref{sec.ptasks} shows the execution of parallel tasks and sources of idle times. Section~\ref{sec.energy} resumes the
-energy model of homogenous platform. Section~\ref{sec.mpip} evaluates the performance of MPI program.
+energy model of homogeneous platform. Section~\ref{sec.mpip} evaluates the performance of MPI program.
Section~\ref{sec.verif} verifies the performance prediction model. Section~\ref{sec.compet} presents
the energy-performance trade offs objective function. Section~\ref{sec.optim} demonstrates the proposed
energy-performance algorithm. Section~\ref{sec.expe} presents the results of our experiments.
algorithm that detects the communication sections and changes the frequency
during these sections only. This approach changes the frequency many times
because an iteration may contain more than one communication section. The domain
-of analytical modeling used for choosing the optimal frequency as inRauber and R\"{u}nger~\cite{3}. they
+of analytical modeling used for choosing the optimal frequency as in Rauber and Rünger~\cite{3}. they
developed an analytical mathematical model to determine the
optimal frequency scaling factor for any number of concurrent tasks. They set the slowest task to maximum frequency for maintaining performance. In this paper we compare our algorithm with
-Rauber and R\"{u}nger model~\cite{3}, because their model can be used for any number of
+Rauber and Rünger model~\cite{3}, because their model can be used for any number of
concurrent tasks for homogeneous platforms. The primary contributions of this paper are:
\begin{enumerate}
\item Selecting the frequency scaling factor for simultaneously optimizing energy and performance,
The energy consumption model for parallel homogeneous platform depends on the scaling factor \emph S. This factor reduces quadratically the dynamic power. Also, this factor increases the
static energy linearly because the execution time is increased~\cite{36}. The
energy model depending on the frequency scaling factor for homogeneous platform
-for any number of concurrent tasks was developed by Rauber and R\"{u}nger~\cite{3}. This model
+for any number of concurrent tasks was developed by Rauber and Rünger~\cite{3}. This model
considers the two power metrics for measuring the energy of the parallel tasks as
in EQ~(\ref{eq:energy}):
= \frac{F_\textit{max}}{F_\textit{new}} \cdot \frac{T_1}{T_i}
\end{equation}
where $F$ is the number of available frequencies. In this paper we depend on
-Rauber and R\"{u}nger energy model EQ~(\ref{eq:energy}) for two reasons: (1)-this model is used
+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. 2-we compare our
-algorithm with Rauber and R\"{u}nger scaling model. Rauber and R\"{u}nger scaling factor that reduce
+algorithm with Rauber and Rünger scaling model. Rauber and Rünger scaling factor that reduce
energy consumption derived from the EQ~(\ref{eq:energy}). They take the
derivation for this equation (to be minimized) and set it to zero to produce the
scaling factor as in EQ~(\ref{eq:sopt}).
static power values stored in a data file. Moreover, this function works in
optimal way when the energy function has a convex form with frequency scaling
factor as shown in~\cite{15,3,19}. Energy measurement model is not the
-objective of this paper and we choose Rauber and R\"{u}nger model as an example with two
+objective of this paper and we choose Rauber and Rünger model as an example with two
reasons that mentioned before.
\section{Optimal Scaling Factor for Performance and Energy}
\section{Comparing Results}
\label{sec.compare}
-In this section, we compare our EPSA algorithm results with Rauber and R\"{u}nger
+In this section, we compare our EPSA algorithm results with Rauber and Rünger
methods~\cite{3}. He had two scenarios, the first is to reduce energy to optimal
level without considering the performance as in EQ~(\ref{eq:sopt}). We refer to
this scenario as $R_{E}$. The second scenario is similar to the first
to keep the performance from degradation as mush as possible. We refer to this
scenario as $R_{E-P}$. The comparison is made in tables~(\ref{table:compare
Class A},\ref{table:compare Class B},\ref{table:compare Class C}). These
-tables show the results of our EPSA and Rauber and R\"{u}nger scenarios for all the NAS
+tables show the results of our EPSA and Rauber and Rünger scenarios for all the NAS
benchmarks programs for classes A,B and C.
\begin{table}[p]
\caption{Comparing Results for The NAS Class A}
such as Rauber's scaling factor EQ~(\ref{eq:sopt}), but it is optimal for both
the energy and the performance simultaneously. Our $EPSA$ optimal scaling factors
has better simultaneous optimization for both the energy and the performance
-compared to Rauber and R\"{u}nger energy-performance method ($R_{E-P}$). Also, in
+compared to Rauber and Rünger energy-performance method ($R_{E-P}$). Also, in
($R_{E-P}$) method when setting the frequency to maximum value for the
slower task lead to a small improvement of the performance. Also the results
show that this method keep or improve energy saving. Because of the energy
Figure~(\ref{fig:compare}) shows the maximum distance between the energy saving
percent and the performance degradation percent. Therefore, this means it is the
same resultant of our objective function EQ~(\ref{eq:max}). Our algorithm always
-gives positive energy to performance trade offs while Rauber and R\"{u}nger method
+gives positive energy to performance trade offs while Rauber and Rünger method
($R_{E-P}$) gives in some time negative trade offs such as in BT and
EP. The positive trade offs with highest values lead to maximum energy savings
concatenating with less performance degradation and this the objective of this
\includegraphics[width=.33\textwidth]{compare_class_A.pdf}
\includegraphics[width=.33\textwidth]{compare_class_B.pdf}
\includegraphics[width=.33\textwidth]{compare_class_c.pdf}
- \caption{Comparing Our EPSA with Rauber and R\"{u}nger Methods}
+ \caption{Comparing Our EPSA with Rauber and Rünger Methods}
\label{fig:compare}
\end{figure}
%%% ispell-local-dictionary: "american"
%%% End:
-% LocalWords: Badri Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber
-% LocalWords: CMOS EQ $$EPSA$$ Franche Comté Tflop
+% LocalWords: Fanfakh Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber
+% LocalWords: CMOS EQ EPSA Franche Comté Tflop Rünger
