*a* homogeneous

[mpi-energy.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 9c374ba8c8b4d56d6ca1346ca15f2942f2f41b28..da3fb812cc81531afc8ff4ec5448488cf6fe2b94 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -136,7 +136,7 @@ the MPI program to choose the scaling factor.  This algorithm has the ability to
 predict both energy consumption and execution time over all available scaling
 factors.  The prediction achieved depends on some computing time information,
 gathered at the beginning of the runtime.  We apply this algorithm to the NAS parallel benchmarks (NPB v3.3)~\cite{44}.  Our experiments are executed using the simulator
 predict both energy consumption and execution time over all available scaling
 factors.  The prediction achieved depends on some computing time information,
 gathered at the beginning of the runtime.  We apply this algorithm to the NAS parallel benchmarks (NPB v3.3)~\cite{44}.  Our experiments are executed using the simulator

-SimGrid/SMPI v3.10~\cite{Casanova:2008:SGF:1397760.1398183} over an homogeneous
+SimGrid/SMPI v3.10~\cite{Casanova:2008:SGF:1397760.1398183} over a homogeneous

 distributed memory architecture.  Furthermore, we compare the proposed algorithm
 with Rauber and Rünger methods~\cite{3}.  The comparison's results show that our
 algorithm gives better energy-time trade-off.
 distributed memory architecture.  Furthermore, we compare the proposed algorithm
 with Rauber and Rünger methods~\cite{3}.  The comparison's results show that our
 algorithm gives better energy-time trade-off.


@@ -228,7 +228,7 @@ our paper is to present a new online scaling factor selection method which has t
 %   paper in homogeneous clusters}
 
 
 %   paper in homogeneous clusters}
 
 

-\section{Energy model for homogeneous platform}
+\section{Energy model for a homogeneous platform}

 \label{sec.exe}
 Many researchers~\cite{9,3,15,26} divide the power consumed by a processor into
 two power metrics: the static and the dynamic power.  While the first one is
 \label{sec.exe}
 Many researchers~\cite{9,3,15,26} divide the power consumed by a processor into
 two power metrics: the static and the dynamic power.  While the first one is


@@ -285,11 +285,11 @@ function of the scaling factor $S$, as in EQ~\eqref{eq:energy}.
     \left( T_1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^2} \right) +
       \Pstatic \cdot T_1 \cdot S_1 \cdot N
 \end{equation}
     \left( T_1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^2} \right) +
       \Pstatic \cdot T_1 \cdot S_1 \cdot N
 \end{equation}

-where $N$ is the number of parallel nodes, $T_i$ and $S_i$ for $i=1,\dots,N$ are
-the execution times and scaling factors of the sorted tasks.  Therefore, $T_1$ is
+where $N$ is the number of parallel nodes, $T_i$ for $i=1,\dots,N$ are
+the execution times of the sorted tasks.  Therefore, $T_1$ 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
 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~\eqref{eq:si}.
+factors $S_i$ are computed as in EQ~\eqref{eq:si}.

 \begin{equation}
   \label{eq:si}
   S_i = S \cdot \frac{T_1}{T_i}
 \begin{equation}
   \label{eq:si}
   S_i = S \cdot \frac{T_1}{T_i}


@@ -345,18 +345,18 @@ the consumed energy with scaled frequency and the consumed energy without scaled
 frequency:
 \begin{multline}
   \label{eq:enorm}
 frequency:
 \begin{multline}
   \label{eq:enorm}

-  \Enorm(S) = \frac{ \Ereduced}{\Eoriginal} \\
-         {} = \frac{\Pdyn \cdot S^{-2} \cdot
+  \Enorm = \frac{ \Ereduced}{\Eoriginal} \\
+      {} = \frac{\Pdyn \cdot S_1^{-2} \cdot

              \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
              \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +

-               \Pstatic \cdot T_1 \cdot S \cdot N}{
+               \Pstatic \cdot T_1 \cdot S_1 \cdot N}{

              \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 performance as follows:
 \begin{equation}
   \label{eq:pnorm}
              \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 performance as follows:
 \begin{equation}
   \label{eq:pnorm}

-  \Pnorm(S) = \frac{\Tnew}{\Told}
-            = \frac{\TmaxCompOld \cdot S + \TmaxCommOld}{
+  \Pnorm = \frac{\Tnew}{\Told}
+         = \frac{\TmaxCompOld \cdot S + \TmaxCommOld}{

              \TmaxCompOld + \TmaxCommOld}
 \end{equation}
 The second problem is that the optimization operation for both energy and
              \TmaxCompOld + \TmaxCommOld}
 \end{equation}
 The second problem is that the optimization operation for both energy and


@@ -377,7 +377,7 @@ direction.  Therefore, we inverse the equation of the normalized performance as
 follows:
 \begin{equation}
   \label{eq:pnorm_en}
 follows:
 \begin{equation}
   \label{eq:pnorm_en}

-  \Pnorm^{-1}(S) = \frac{ \Told}{ \Tnew}
+  \Pnorm^{-1} = \frac{ \Told}{ \Tnew}

                = \frac{\TmaxCompOld +
                  \TmaxCommOld}{\TmaxCompOld \cdot S +
                  \TmaxCommOld}
                = \frac{\TmaxCompOld +
                  \TmaxCommOld}{\TmaxCompOld \cdot S +
                  \TmaxCommOld}


@@ -433,10 +433,13 @@ the objective function described above.
     \For {$j = 2$ to $\Pstates$}
       \State $\Fnew \gets \Fnew - \Fdiff$
       \State $S \gets \Fmax / \Fnew$
     \For {$j = 2$ to $\Pstates$}
       \State $\Fnew \gets \Fnew - \Fdiff$
       \State $S \gets \Fmax / \Fnew$

+      \State $S_i \gets S \cdot \frac{T_1}{T_i}
+                  = \frac{\Fmax}{\Fnew} \cdot \frac{T_1}{T_i}$
+             for $i=1,\dots,N$

       \State $\Enorm \gets
       \State $\Enorm \gets

-          \frac{\Pdyn \cdot S^{-2} \cdot
+          \frac{\Pdyn \cdot S_1^{-2} \cdot

                   \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
                   \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +

-                  \Pstatic \cdot T_1 \cdot S \cdot N }{
+                  \Pstatic \cdot T_1 \cdot S_1 \cdot N }{

                 \Pdyn \cdot
                   \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
                   \Pstatic \cdot T_1 \cdot N }$
                 \Pdyn \cdot
                   \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
                   \Pstatic \cdot T_1 \cdot N }$


@@ -679,7 +682,7 @@ trade-offs such as in BT and EP.
 
 In this paper, we have presented a new online scaling factor selection method
 that optimizes simultaneously the energy and performance of a distributed
 
 In this paper, we have presented a new online scaling factor selection method
 that optimizes simultaneously the energy and performance of a distributed

-application running on an homogeneous cluster.  It uses the computation and
+application running on a homogeneous cluster.  It uses the computation and

 communication times measured at the first iteration to predict energy
 consumption and the performance of the parallel application at every available
 frequency.  Then, it selects the scaling factor that gives the best trade-off
 communication times measured at the first iteration to predict energy
 consumption and the performance of the parallel application at every available
 frequency.  Then, it selects the scaling factor that gives the best trade-off