Remove unused macros.

[mpi-energy2.git] / Heter_paper.tex

diff --git a/Heter_paper.tex b/Heter_paper.tex
index 0491692cc0205522bad90a1a75b8f00057bef0cc..0b545e4ad4f0cc6b0ef10247275210007dc2a614 100644 (file)
--- a/Heter_paper.tex
+++ b/Heter_paper.tex
@@ -41,26 +41,17 @@
 \newcommand{\MaxDist}{\mathit{Max}\Dist}
 \newcommand{\MinTcm}{\mathit{Min}\Tcm}
 \newcommand{\Ntrans}{\Xsub{N}{trans}}
 \newcommand{\MaxDist}{\mathit{Max}\Dist}
 \newcommand{\MinTcm}{\mathit{Min}\Tcm}
 \newcommand{\Ntrans}{\Xsub{N}{trans}}

+\newcommand{\Pd}{\Xsub{P}{d}}

 \newcommand{\PdNew}{\Xsub{P}{dNew}}
 \newcommand{\PdOld}{\Xsub{P}{dOld}}
 \newcommand{\PdNew}{\Xsub{P}{dNew}}
 \newcommand{\PdOld}{\Xsub{P}{dOld}}

-%\newcommand{\Pdyn}{\Xsub{P}{dyn}}
-\newcommand{\Pd}{\Xsub{P}{d}}
-%\newcommand{\PnormInv}{\Xsub{P}{NormInv}}

 \newcommand{\Pnorm}{\Xsub{P}{Norm}}
 \newcommand{\Pnorm}{\Xsub{P}{Norm}}

-%\newcommand{\Pstates}{\Xsub{P}{states}}
-%\newcommand{\Pstatic}{\Xsub{P}{static}}

 \newcommand{\Ps}{\Xsub{P}{s}}
 \newcommand{\Scp}{\Xsub{S}{cp}}
 \newcommand{\Sopt}{\Xsub{S}{opt}}
 \newcommand{\Tcm}{\Xsub{T}{cm}}
 \newcommand{\Ps}{\Xsub{P}{s}}
 \newcommand{\Scp}{\Xsub{S}{cp}}
 \newcommand{\Sopt}{\Xsub{S}{opt}}
 \newcommand{\Tcm}{\Xsub{T}{cm}}

-%\newcommand{\Tcomp}{\Xsub{T}{comp}}
-\newcommand{\TcpOld}{\Xsub{T}{cpOld}}

 \newcommand{\Tcp}{\Xsub{T}{cp}}
 \newcommand{\Tcp}{\Xsub{T}{cp}}

-%\newcommand{\TmaxCommOld}{\Xsub{T}{Max Comm Old}}
-%\newcommand{\TmaxCompOld}{\Xsub{T}{Max Comp Old}}
-%\newcommand{\Tmax}{\Xsub{T}{max}}
+\newcommand{\TcpOld}{\Xsub{T}{cpOld}}

 \newcommand{\Tnew}{\Xsub{T}{New}}
 \newcommand{\Tnew}{\Xsub{T}{New}}

-%\newcommand{\Tnorm}{\Xsub{T}{Norm}}

 \newcommand{\Told}{\Xsub{T}{Old}} 
 
 \begin{document} 
 \newcommand{\Told}{\Xsub{T}{Old}} 
 
 \begin{document} 


@@ -210,14 +201,14 @@ The work presented in this paper concerns the second type of platform, with
 heterogeneous CPUs.  Many methods were conceived to reduce the energy
 consumption of this type of platform.  Naveen et
 al.~\cite{Naveen_Power.Efficient.Resource.Scaling} developed a method that
 heterogeneous CPUs.  Many methods were conceived to reduce the energy
 consumption of this type of platform.  Naveen et
 al.~\cite{Naveen_Power.Efficient.Resource.Scaling} developed a method that

-minimizes the value of $energy\cdot delay^2$ (the delay is the sum of slack
-times that happen during synchronous communications) by dynamically assigning
-new frequencies to the CPUs of the heterogeneous cluster. Lizhe et
-al.~\cite{Lizhe_Energy.aware.parallel.task.scheduling} proposed an algorithm
-that divides the executed tasks into two types: the critical and non critical
-tasks. The algorithm scales down the frequency of non critical tasks
-proportionally to their slack and communication times while limiting the
-performance degradation percentage to less than
+minimizes the value of $\mathit{energy}\times \mathit{delay}^2$ (the delay is
+the sum of slack times that happen during synchronous communications) by
+dynamically assigning new frequencies to the CPUs of the heterogeneous
+cluster. Lizhe et al.~\cite{Lizhe_Energy.aware.parallel.task.scheduling}
+proposed an algorithm that divides the executed tasks into two types: the
+critical and non critical tasks. The algorithm scales down the frequency of non
+critical tasks proportionally to their slack and communication times while
+limiting the performance degradation percentage to less than

 10\%. In~\cite{Joshi_Blackbox.prediction.of.impact.of.DVFS}, they developed a
 heterogeneous cluster composed of two types of Intel and AMD processors. They
 use a gradient method to predict the impact of DVFS operations on performance.
 10\%. In~\cite{Joshi_Blackbox.prediction.of.impact.of.DVFS}, they developed a
 heterogeneous cluster composed of two types of Intel and AMD processors. They
 use a gradient method to predict the impact of DVFS operations on performance.


@@ -648,7 +639,8 @@ maximum distance  between the  energy curve and  the performance curve  is while
           \State $F_i \gets F_i+\Fdiff_i,~i=1,\dots,N.$
     \EndIf 
     \State $\Told \gets max_{~i=1,\dots,N } (\Tcp_i+\Tcm_i)$
           \State $F_i \gets F_i+\Fdiff_i,~i=1,\dots,N.$
     \EndIf 
     \State $\Told \gets max_{~i=1,\dots,N } (\Tcp_i+\Tcm_i)$

-    \State $\Eoriginal \gets \sum_{i=1}^{N}{( \Pd_i \cdot  \Tcp_i)} +\sum_{i=1}^{N} {(\Ps_i \cdot \Told)}$
+    % \State $\Eoriginal \gets \sum_{i=1}^{N}{( \Pd_i \cdot  \Tcp_i)} +\sum_{i=1}^{N} {(\Ps_i \cdot \Told)}$
+    \State $\Eoriginal \gets \sum_{i=1}^{N}{( \Pd_i \cdot  \Tcp_i + \Ps_i \cdot \Told)}$

     \State $\Sopt_{i} \gets 1,~i=1,\dots,N. $
     \State $\Dist \gets 0 $
     \While {(all nodes not reach their  minimum  frequency)}
     \State $\Sopt_{i} \gets 1,~i=1,\dots,N. $
     \State $\Dist \gets 0 $
     \While {(all nodes not reach their  minimum  frequency)}


@@ -657,7 +649,8 @@ maximum distance  between the  energy curve and  the performance curve  is while
         \State $S_i \gets \frac{\Fmax_i}{F_i},~i=1,\dots,N.$
         \EndIf
        \State $\Tnew \gets max_\textit{~i=1,\dots,N} (\Tcp_{i} \cdot S_{i}) + \MinTcm $
         \State $S_i \gets \frac{\Fmax_i}{F_i},~i=1,\dots,N.$
         \EndIf
        \State $\Tnew \gets max_\textit{~i=1,\dots,N} (\Tcp_{i} \cdot S_{i}) + \MinTcm $

-       \State $\Ereduced \gets \sum_{i=1}^{N}{(S_i^{-2} \cdot \Pd_i \cdot  \Tcp_i)} + \sum_{i=1}^{N} {(\Ps_i \cdot \rlap{\Tnew)}} $
+%       \State $\Ereduced \gets \sum_{i=1}^{N}{(S_i^{-2} \cdot \Pd_i \cdot  \Tcp_i)} + \sum_{i=1}^{N} {(\Ps_i \cdot \rlap{\Tnew)}} $
+       \State $\Ereduced \gets \sum_{i=1}^{N}{(S_i^{-2} \cdot \Pd_i \cdot  \Tcp_i + \Ps_i \cdot \rlap{\Tnew)}} $

        \State $\Pnorm \gets \frac{\Told}{\Tnew}$
        \State $\Enorm\gets \frac{\Ereduced}{\Eoriginal}$
       \If{$(\Pnorm - \Enorm > \Dist)$}
        \State $\Pnorm \gets \frac{\Told}{\Tnew}$
        \State $\Enorm\gets \frac{\Ereduced}{\Eoriginal}$
       \If{$(\Pnorm - \Enorm > \Dist)$}


@@ -1137,6 +1130,24 @@ degradation.
   \label{table:res_s2}
 \end{table}
 
   \label{table:res_s2}
 \end{table}
 

+\begin{table}[!t]
+ \caption{Comparing the proposed algorithm}
+ \centering
+\begin{tabular}{|*{7}{r|}}
+\hline
+Program & \multicolumn{2}{c|}{Energy saving \%} & \multicolumn{2}{c|}{Perf.  degradation \%} & \multicolumn{2}{c|}{Distance} \\ \cline{2-7} 
+name    & EDP             & MaxDist          & EDP            & MaxDist           & EDP          & MaxDist        \\ \hline
+CG      & 27.58           & 31.25            & 5.82           & 7.12              & 21.76        & 24.13          \\ \hline
+MG      & 29.49           & 33.78            & 3.74           & 6.41              & 25.75        & 27.37          \\ \hline
+LU      & 19.55           & 28.33            & 0.0            & 0.01              & 19.55        & 28.22          \\ \hline
+EP      & 28.40           & 27.04            & 4.29           & 0.49              & 24.11        & 26.55          \\ \hline
+BT      & 27.68           & 32.32            & 6.45           & 7.87              & 21.23        & 24.43          \\ \hline
+SP      & 20.52           & 24.73            & 5.21           & 2.78              & 15.31         & 21.95         \\ \hline
+FT      & 27.03           & 31.02            & 2.75           & 2.54              & 24.28        & 28.48           \\ \hline
+
+\end{tabular}
+\label{table:compare_EDP}
+\end{table}

 
 \begin{figure}[!t]
   \centering
 
 \begin{figure}[!t]
   \centering


@@ -1149,16 +1160,31 @@ degradation.
   \caption{The comparison of the three power scenarios}
 \end{figure}  
 
   \caption{The comparison of the three power scenarios}
 \end{figure}  
 

-
+\begin{figure}[!t]
+  \centering
+   \includegraphics[scale=0.5]{fig/compare_EDP.pdf}
+  \caption{Trade-off comparison for NAS benchmarks class C}
+  \label{fig:compare_EDP}
+\end{figure}

 
 
 \subsection{The comparison of the proposed scaling algorithm }
 \label{sec.compare_EDP}
 
 
 \subsection{The comparison of the proposed scaling algorithm }
 \label{sec.compare_EDP}

-In this section, the scaling  factors selection algorithm, called $\MaxDist$,
-is compared to Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS}, called EDP. 
-They developed a green governor that regularly applies an online frequency selecting algorithm to reduce the energy consumed by a multicore architecture without degrading much its performance. The algorithm selects the frequencies that minimize the energy and delay products, $EDP=Energy\cdot Delay$ using the predicted overall energy consumption and execution time delay for each frequency.
-To fairly compare both algorithms, the same energy and execution time models, equations (\ref{eq:energy}) and  (\ref{eq:fnew}), were used for both algorithms to predict the energy consumption and the execution times. Also Spiliopoulos et al. algorithm was adapted to  start the search from the 
-initial frequencies computed using the equation (\ref{eq:Fint}). The resulting algorithm is an exhaustive search algorithm that minimizes the EDP and has the initial frequencies values as an upper bound.
+In this section, the scaling factors selection algorithm, called MaxDist, is
+compared to Spiliopoulos et al. algorithm
+\cite{Spiliopoulos_Green.governors.Adaptive.DVFS}, called EDP.  They developed a
+green governor that regularly applies an online frequency selecting algorithm to
+reduce the energy consumed by a multicore architecture without degrading much
+its performance. The algorithm selects the frequencies that minimize the energy
+and delay products, $\mathit{EDP}=\mathit{energy}\times \mathit{delay}$ using
+the predicted overall energy consumption and execution time delay for each
+frequency.  To fairly compare both algorithms, the same energy and execution
+time models, equations (\ref{eq:energy}) and (\ref{eq:fnew}), were used for both
+algorithms to predict the energy consumption and the execution times. Also
+Spiliopoulos et al. algorithm was adapted to start the search from the initial
+frequencies computed using the equation (\ref{eq:Fint}). The resulting algorithm
+is an exhaustive search algorithm that minimizes the EDP and has the initial
+frequencies values as an upper bound.

 
 Both algorithms were applied to the parallel NAS benchmarks to compare their
 efficiency. Table~\ref{table:compare_EDP} presents the results of comparing the
 
 Both algorithms were applied to the parallel NAS benchmarks to compare their
 efficiency. Table~\ref{table:compare_EDP} presents the results of comparing the


@@ -1176,39 +1202,6 @@ because it maximizes the distance  between the energy saving and the performance
 degradation values while giving the same weight for both metrics.
 
 
 degradation values while giving the same weight for both metrics.
 
 

-
-
-\begin{table}[!t]
- \caption{Comparing the proposed algorithm}
- \centering
-\begin{tabular}{|*{7}{r|}}
-\hline
-Program & \multicolumn{2}{c|}{Energy saving \%} & \multicolumn{2}{c|}{Perf.  degradation \%} & \multicolumn{2}{c|}{Distance} \\ \cline{2-7} 
-name    & EDP             & MaxDist          & EDP            & MaxDist           & EDP          & MaxDist        \\ \hline
-CG      & 27.58           & 31.25            & 5.82           & 7.12              & 21.76        & 24.13          \\ \hline
-MG      & 29.49           & 33.78            & 3.74           & 6.41              & 25.75        & 27.37          \\ \hline
-LU      & 19.55           & 28.33            & 0.0            & 0.01              & 19.55        & 28.22          \\ \hline
-EP      & 28.40           & 27.04            & 4.29           & 0.49              & 24.11        & 26.55          \\ \hline
-BT      & 27.68           & 32.32            & 6.45           & 7.87              & 21.23        & 24.43          \\ \hline
-SP      & 20.52           & 24.73            & 5.21           & 2.78              & 15.31         & 21.95         \\ \hline
-FT      & 27.03           & 31.02            & 2.75           & 2.54              & 24.28        & 28.48           \\ \hline
-
-\end{tabular}
-\label{table:compare_EDP}
-\end{table}
-
-
-
-
-
-\begin{figure}[!t]
-  \centering
-   \includegraphics[scale=0.5]{fig/compare_EDP.pdf}
-  \caption{Trade-off comparison for NAS benchmarks class C}
-  \label{fig:compare_EDP}
-\end{figure}
-
-

 \section{Conclusion}
 \label{sec.concl} 
 In this paper, a new online frequency selecting algorithm has been presented. It
 \section{Conclusion}
 \label{sec.concl} 
 In this paper, a new online frequency selecting algorithm has been presented. It