X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/mpi-energy2.git/blobdiff_plain/6b321df326acc4bb4e33b94f8a963c553fbea89a..fb261c12d6ff09c93a38f3185cedc05431bf7d8c:/Heter_paper.tex

diff --git a/Heter_paper.tex b/Heter_paper.tex
index ec89460..077de95 100644
--- a/Heter_paper.tex
+++ b/Heter_paper.tex
@@ -132,7 +132,7 @@ Section~\ref{sec.optim} details the proposed frequency selecting algorithm then
 Section~\ref{sec.expe} presents the results of applying the algorithm on  the NAS parallel benchmarks and executing them 
 on a heterogeneous platform. It also shows the results of running three 
 different power scenarios and comparing them. 
-Finally, we conclude in Section~\ref{sec.concl} with a summary and some future works.
+Finally, in Section~\ref{sec.concl} the paper is ended with a summary and some future works.
 
 \section{Related works}
 \label{sec.relwork}
@@ -196,7 +196,7 @@ In contrast to the above described papers, this paper presents the following con
 
 In this paper, we are interested in reducing the energy consumption of message
 passing distributed iterative synchronous applications running over
-heterogeneous platforms. We define a heterogeneous platform as a collection of
+heterogeneous platforms. A heterogeneous platform is defined as a collection of
 heterogeneous computing nodes interconnected via a high speed homogeneous
 network. Therefore, each node has different characteristics such as computing
 power (FLOPS), energy consumption, CPU's frequency range, \dots{} but they all
@@ -260,7 +260,7 @@ where $TcpOld_i$ is the computation time  of processor $i$ during the first
 iteration and $MinTcm$ is the communication time of the slowest processor from 
 the first iteration.  The model computes the maximum computation time 
 with scaling factor from each node  added to the communication time of the \subsection{The verifications of the proposed method}
-\label{sec.verif}
+\label{sec.verif.method}
 The precision of the proposed algorithm mainly depends on the execution time prediction model defined in 
 EQ(\ref{eq:perf}) and the energy model computed by EQ(\ref{eq:energy}). 
 The energy model is also significantly dependent  on the execution time model because the static energy is 
@@ -282,13 +282,13 @@ to compute the best scaling factors vector.  The algorithm complexity is $O(F\cd
 of iterations and $N$ is the number of computing nodes. The algorithm needs  from 12 to 20 iterations to select the best 
 vector of frequency scaling factors that gives the results of the sections (\ref{sec.res}) and (\ref{sec.compare}).
 slowest node, it means  only the  communication time without any slack time. 
-Therefore, we can consider the execution time of the iterative application is 
+Therefore, the execution time of the iterative application is 
 equal to the execution time of one iteration as in EQ(\ref{eq:perf}) multiplied 
 by the number of iterations of that application.
 
-This prediction model is developed from our model for predicting the execution time of 
+This prediction model is developed from the model for predicting the execution time of 
 message passing distributed applications for homogeneous architectures~\cite{Our_first_paper}. 
-The execution time prediction model is used in our method for optimizing both 
+The execution time prediction model is used in the method for optimizing both 
 energy consumption and performance of iterative methods, which is presented in the 
 following sections.
 
@@ -330,8 +330,8 @@ voltage with respect to various frequency values in~\cite{Rauber_Analytical.Mode
 process of the frequency can be expressed by the scaling factor $S$ which is the
 ratio between the maximum and the new frequency as in EQ(\ref{eq:s}).
 The CPU governors are power schemes supplied by the operating
-system's kernel to lower a core's frequency. we can calculate the new frequency 
-$F_{new}$ from EQ(\ref{eq:s}) as follow:
+system's kernel to lower a core's frequency. The new frequency 
+$F_{new}$ from EQ(\ref{eq:s}) can be calculated as follows:
 \begin{equation}
   \label{eq:fnew}
    F_\textit{new} = S^{-1} \cdot F_\textit{max}
@@ -357,7 +357,7 @@ and is given by the following equation:
 \end{equation}
 The static power is related to the power leakage of the CPU and is consumed during computation 
 and even when idle. As in~\cite{Rauber_Analytical.Modeling.for.Energy,Zhuo_Energy.efficient.Dynamic.Task.Scheduling}, 
-we assume that the static power of a processor is constant 
+ the static power of a processor is considered as constant 
 during idle and computation periods, and for all its available frequencies. 
 The static energy is the static power multiplied by the execution time of the program. 
 According to the execution time model in EQ(\ref{eq:perf}), the execution time of the program 
@@ -392,8 +392,8 @@ for each  processor.  It is computed as follows:
 Reducing the frequencies of the processors according to the vector of
 scaling factors $(S_1, S_2,\dots, S_N)$ may degrade the performance of the
 application and thus, increase the static energy because the execution time is
-increased~\cite{Kim_Leakage.Current.Moore.Law}. We can measure the overall energy consumption for the iterative 
-application by measuring  the energy consumption for one iteration as in EQ(\ref{eq:energy}) 
+increased~\cite{Kim_Leakage.Current.Moore.Law}. The overall energy consumption for the iterative 
+application can be measured by measuring  the energy consumption for one iteration as in EQ(\ref{eq:energy}) 
 multiplied by the number of iterations of that application.
 
 
@@ -422,8 +422,8 @@ The relation between the energy consumption and the execution time for an applic
 complex and nonlinear, Thus, unlike the relation between the execution time 
 and the scaling factor, the relation of the energy with the frequency scaling
 factors is nonlinear, for more details refer to~\cite{Freeh_Exploring.the.Energy.Time.Tradeoff}.  
-Moreover, they are not measured using the same metric.  To solve this problem, we normalize the
-execution time by computing the ratio between the new execution time (after 
+Moreover, they are not measured using the same metric.  To solve this problem,  the
+execution time is normalized by computing the ratio between the new execution time (after 
 scaling down the frequencies of some processors) and the initial one (with maximum 
 frequency for all nodes,) as follows:
 \begin{multline}
@@ -434,7 +434,7 @@ frequency for all nodes,) as follows:
 \end{multline}
 
 
-In the same way, we normalize the energy by computing the ratio between the consumed energy 
+In the same way, the energy is normalized by computing the ratio between the consumed energy 
 while scaling down the frequency and the consumed energy with maximum frequency for all nodes:
 \begin{multline}
   \label{eq:enorm}
@@ -455,9 +455,9 @@ reduction with minimum execution time reduction.
 
  
   
-Our solution for this problem is to make the optimization process for energy and 
-execution time follow the same direction.  Therefore, we inverse the equation of the 
-normalized execution time which gives the normalized performance equation, as follows:
+This problem can be solved by making the optimization process for energy and 
+execution time follow the same direction.  Therefore, the equation of the 
+normalized execution time is inverted which gives the normalized performance equation, as follows:
 \begin{multline}
   \label{eq:pnorm_inv}
   P_\textit{Norm} = \frac{T_\textit{Old}}{T_\textit{New}}\\
@@ -477,11 +477,11 @@ normalized execution time which gives the normalized performance equation, as fo
   \caption{The energy and performance relation}
 \end{figure}
 
-Then, we can model our objective function as finding the maximum distance
+Then, the objective function can be modeled   as finding the maximum distance
 between the energy curve EQ~(\ref{eq:enorm}) and the  performance
 curve EQ~(\ref{eq:pnorm_inv}) over all available sets of scaling factors.  This
 represents the minimum energy consumption with minimum execution time (maximum 
-performance) at the same time, see figure~(\ref{fig:r1}) or figure~(\ref{fig:r2}). Then our objective
+performance) at the same time, see figure~(\ref{fig:r1}) or figure~(\ref{fig:r2}). Then the objective
 function has the following form:
 \begin{equation}
   \label{eq:max}
@@ -491,8 +491,8 @@ function has the following form:
        \overbrace{E_\textit{Norm}(S_{ij})}^{\text{Minimize}} )
 \end{equation}
 where $N$ is the number of nodes and $F$ is the  number of available frequencies for each nodes. 
-Then we can select the optimal set of scaling factors that satisfies EQ~(\ref{eq:max}).  
-Our objective function can work with any energy model or any power values for each node 
+Then, the optimal set of scaling factors that satisfies EQ~(\ref{eq:max}) can be selected.  
+The objective function can work with any energy model or any power values for each node 
 (static and dynamic powers). However, the most energy reduction gain can be achieved when 
 the energy curve has a convex form as shown in~\cite{Zhuo_Energy.efficient.Dynamic.Task.Scheduling,Rauber_Analytical.Modeling.for.Energy,Hao_Learning.based.DVFS}.
 
@@ -500,7 +500,7 @@ the energy curve has a convex form as shown in~\cite{Zhuo_Energy.efficient.Dynam
 \label{sec.optim}
 
 \subsection{The algorithm details}
-In this section we  propose algorithm~(\ref{HSA}) which selects the frequency scaling factors 
+In this section algorithm~(\ref{HSA}) is presented. It selects the frequency scaling factors 
 vector that gives the best trade-off between minimizing the energy consumption  and maximizing 
 the performance of a message passing synchronous iterative application executed on a heterogeneous 
 platform. It works online during the execution time of the iterative message passing program.  
@@ -516,7 +516,7 @@ The nodes in a heterogeneous platform have different computing powers, thus whil
 passing iterative synchronous applications, fast nodes have to wait for the slower ones to finish their 
 computations before being able to synchronously communicate with them as in figure (\ref{fig:heter}). 
 These periods are called idle or slack times. 
-Our algorithm takes into account this problem and tries to reduce these slack times when selecting the 
+The algorithm takes into account this problem and tries to reduce these slack times when selecting the 
 frequency scaling factors vector. At first, it selects initial frequency scaling factors that increase 
 the execution times of fast nodes and  minimize the  differences between  the  computation times of 
 fast and slow nodes. The value of the initial frequency scaling factor  for each node is inversely 
@@ -638,7 +638,7 @@ which results in bigger energy savings.
 \end{algorithm}
 
 \subsection{The verifications of the proposed algorithm}
-\label{sec.verif}
+\label{sec.verif.algo}
 The precision of the proposed algorithm mainly depends on the execution time prediction model defined in 
 EQ(\ref{eq:perf}) and the energy model computed by EQ(\ref{eq:energy}). 
 The energy model is also significantly dependent  on the execution time model because the static energy is 
@@ -1055,8 +1055,7 @@ results in less energy saving but less performance degradation.
 
 \section{Conclusion}
 \label{sec.concl} 
-In this paper, we have presented a new online selecting frequency scaling factors algorithm
-that selects the best possible vector of frequency scaling factors for a heterogeneous platform. 
+In this paper, a new online frequency selecting algorithm have been presented. It selects the best possible vector of frequency scaling factors for a heterogeneous platform. 
 This vector gives the maximum distance (optimal tradeoff) between the predicted energy and 
 the predicted performance curves. In addition, we developed a new energy model for measuring  
 and predicting the energy of distributed iterative applications running over heterogeneous