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+\usepackage{xspace}
\usepackage[textsize=footnotesize]{todonotes}
-\newcommand{\AG}[2][inline]{\todo[color=green!50,#1]{\sffamily\textbf{AG:} #2}}
+\newcommand{\AG}[2][inline]{\todo[color=green!50,#1]{\sffamily\textbf{AG:} #2}\xspace}
\begin{document}
The DVFS offline methods are static and are not executed during the runtime of
the program. Some approaches used heuristics to select the best DVFS state
during the compilation phases as an example in Azevedo et al.~\cite{40}. He used
-intra-task algorithm to choose the DVFS setting when there are dependency points
+intra-task algorithm
+\AG{what is an ``intra-task algorithm''?}
+to choose the DVFS setting when there are dependency points
between tasks. While in~\cite{29}, Xie et al. used breadth-first search
algorithm to do that. Their goal is saving energy with time limits. Another
approaches gathers and stores the runtime information for each DVFS state, then
platform. These tasks can exchange the data via synchronous memory passing.
\begin{figure*}[t]
\centering
- \subfloat[Synch. Imbalanced Communications]{\includegraphics[scale=0.67]{synch_tasks}\label{fig:h1}}
- \subfloat[Synch. Imbalanced Computations]{\includegraphics[scale=0.67]{compt}\label{fig:h2}}
+ \subfloat[Sync. Imbalanced Communications]{\includegraphics[scale=0.67]{synch_tasks}\label{fig:h1}}
+ \subfloat[Sync. Imbalanced Computations]{\includegraphics[scale=0.67]{compt}\label{fig:h2}}
\caption{Parallel Tasks on Homogeneous Platform}
\label{fig:homo}
\end{figure*}
+\AG{On fig.~\ref{fig:h1}, how can there be a synchronization point without communications just before ?\\
+Use ``Sync.'' to abbreviate ``Synchronization''}
Therefore, the execution time of a task consists of the computation time and the
communication time. Moreover, the synchronous communications between tasks can
lead to idle time while tasks wait at the synchronous point for others tasks to
the supply voltage $V$ and operational frequency $f$ respectively as follow :
\begin{equation}
\label{eq:pd}
- P_{dyn} = \alpha \cdot C_L \cdot V^2 \cdot f
+ \textit P_{dyn} = \alpha \cdot C_L \cdot V^2 \cdot f
\end{equation}
The static power $P_{static}$ captures the leakage power consumption as well as
the power consumption of peripheral devices like the I/O subsystem.
\begin{equation}
\label{eq:ps}
- P_{static} = V \cdot N \cdot K_{design} \cdot I_{leak}
+ \textit P_{static} = V \cdot N \cdot K_{design} \cdot I_{leak}
\end{equation}
where V is the supply voltage, N is the number of transistors, $K_{design}$ is a
design dependent parameter and $I_{leak}$ is a technology-dependent
parameter. Energy consumed by an individual processor $E_{ind}$ is the summation
of the dynamic and the static power multiply by the execution time for example
-see~\cite{36,15} .
+see~\cite{36,15}.
\begin{equation}
\label{eq:eind}
- E_{ind} = ( P_{dyn} + P_{static} ) \cdot T
+ \textit E_{ind} = ( P_{dyn} + P_{static} ) \cdot T
\end{equation}
The dynamic voltage and frequency scaling (DVFS) is a process that allowed in
modern processors to reduce the dynamic power by scaling down the voltage and
frequency. Its main objective is to reduce the overall energy
consumption~\cite{37}. The operational frequency \emph f depends linearly on the
-supply voltage $V$, i.e., $V = \beta . f$ with some constant $\beta$. This
+supply voltage $V$, i.e., $V = \beta \cdot f$ with some constant $\beta$. This
equation is used to study the change of the dynamic voltage with respect to
various frequency values in~\cite{3}. The reduction process of the frequency are
expressed by scaling factor \emph S. The scale \emph S is the ratio between the
maximum and the new frequency as in EQ~(\ref{eq:s}).
\begin{equation}
\label{eq:s}
- S = \frac{F_{max}}{F_{new}}
+ S = \frac{F_{max}}{F_{new}}
\end{equation}
-The value of the scale \emph S is grater than 1 when changing the frequency to
-any new frequency value(\emph {P-state}) in governor. It is equal to 1 when the
+The value of the scale $S$ is greater than 1 when changing the frequency to
+any new frequency value (\emph {P-state}) in governor.
+\AG{Explain what's a governor}
+It is equal to 1 when the
frequency are set to the maximum frequency. The energy consumption model for
parallel homogeneous platform is depending on the scaling factor \emph S. This
factor reduces quadratically the dynamic power. Also, this factor increases the
scaling factor as in EQ~(\ref{eq:sopt}).
\begin{equation}
\label{eq:sopt}
- S_{opt} = \sqrt[3]{\frac{2}{n} \cdot \frac{P_{dyn}}{P_{static}} \cdot
+ \textit S_{opt} = \sqrt[3]{\frac{2}{n} \cdot \frac{P_{dyn}}{P_{static}} \cdot
\left( 1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^3} \right) }
\end{equation}
EQ~(\ref{eq:tnew}).
\begin{equation}
\label{eq:tnew}
- T_{new} = T_{\textit{Max Comp Old}} \cdot S + T_{\textit{Max Comm Old}}
+ \textit T_{new} = T_{\textit{Max Comp Old}} \cdot S + T_{\textit{Max Comm Old}}
\end{equation}
The above equation shows that the scaling factor \emph S has linear relation
with the computation time without affecting the communication time. The
This section demonstrates our approach for choosing the optimal scaling
factor. This factor gives maximum energy reduction taking into account the
-execution time for both computation and communication times . The relation
+execution time for both computation and communication times. The relation
between the energy and the performance are nonlinear and complex, because the
relation of the energy with scaling factor is nonlinear and with the performance
it is linear see~\cite{17}. The relation between the energy and the performance
without scaled frequency :
\begin{multline}
\label{eq:enorm}
- E_\textit{Norm} = \frac{E_{Reduced}}{E_{Original}}\\
- {} = \frac{ P_{dyn} \cdot S_i^{-2} \cdot
+ \textit E_{Norm} = \frac{\textit E_{Reduced}}{\textit E_{Original}} \\
+ {} = \frac{ P_{dyn} \cdot S_i^{-2} \cdot
\left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
P_{static} \cdot T_1 \cdot S_i \cdot N }{
P_{dyn} \cdot \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
By the same way we can normalize the performance as follows :
\begin{equation}
\label{eq:pnorm}
- P_{Norm} = \frac{T_{New}}{T_{Old}}
+\textit P_{Norm} = \frac{\textit T_{New}}{\textit T_{Old}}
= \frac{T_{\textit{Max Comp Old}} \cdot S +
- T_{\textit{Max Comm Old}}}{T_{Old}}
+ T_{\textit{Max Comm Old}}}{\textit T_{Old}}
\end{equation}
The second problem is the optimization operation for both energy and performance
is not in the same direction. In other words, the normalized energy and the
performance as follows :
\begin{equation}
\label{eq:pnorm_en}
- P^{-1}_{Norm} = \frac{T_{Old}}{T_{New}}
- = \frac{T_{Old}}{T_{\textit{Max Comp Old}} \cdot S +
+\textit P^{-1}_{Norm} = \frac{\textit T_{Old}}{\textit T_{New}}
+ = \frac{\textit T_{Old}}{T_{\textit{Max Comp Old}} \cdot S +
T_{\textit{Max Comm Old}}}
\end{equation}
\begin{figure*}
following form:
\begin{equation}
\label{eq:max}
- \textit{MaxDist} = \max (\overbrace{P^{-1}_{Norm}}^{\text{Maximize}} -
- \overbrace{E_{Norm}}^{\text{Minimize}} )
+ \textit{MaxDist} = \max (\overbrace{\textit P^{-1}_{Norm}}^{\text{Maximize}} -
+ \overbrace{\textit E_{Norm}}^{\text{Minimize}} )
\end{equation}
Then we can select the optimal scaling factor that satisfy the
EQ~(\ref{eq:max}). Our objective function can works with any energy model or
\State -Computations Section.
\State -Communications Section.
\If {$(J==1)$}
- \State -Gather all times of computation and\par
- \State communication from each node.
+ \State -Gather all times of computation and communication from\par each node.
\State -Call EPSA with these times.
\State -Calculate the new frequency from optimal scale.
\State -Set the new frequency to the system.
\hline
Max & Min & Backbone & Backbone&Link &Link& Sharing \\
Freq. & Freq. & Bandwidth & Latency & Bandwidth& Latency&Policy \\ \hline
- 2.5 &800 & 2.25 GBps &$5\times 10^{-7} s$& 1 GBps & $5\times 10^{-5}$ s&Full \\
+ 2.5 &800 & 2.25 GBps &$5\times 10^{-7} s$& 1 GBps & $5\times 10^{-5} s$ &Full \\
GHz& MHz& & & & &Duplex \\\hline
\end{tabular}
\label{table:platform}
BT & 1.31 &29.60&21.28 &8.32\\ \hline
SP & 1.38 &33.48&21.36 &12.12\\ \hline
FT & 1.47 &34.72&19.00 &15.72\\ \hline
- \end{tabular}
+ \end{tabular}
\label{table:factors results}
% is used to refer this table in the text
\end{table}
Computations have been performed on the supercomputer facilities of the
Mésocentre de calcul de Franche-Comté.
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+% number - used to balance the columns on the last page
+% adjust value as needed - may need to be readjusted if
+% the document is modified later
+%\IEEEtriggeratref{15}
+
\bibliographystyle{IEEEtran}
\bibliography{IEEEabrv,my_reference}
\end{document}
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-%%%ispell-local-dictionary: "american"
+%%% ispell-local-dictionary: "american"
%%% End:
% LocalWords: Badri Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber
-% LocalWords: CMOS EQ EPSA
+% LocalWords: CMOS EQ EPSA Franche Comté Tflop
