Merge branch 'master' of ssh://info.iut-bm.univ-fcomte.fr/mpi-energy2

[mpi-energy2.git] / Heter_paper.tex

diff --git a/Heter_paper.tex b/Heter_paper.tex
index ec89460ab3efd41c376e64e28ca4ea17a8365b86..a88d174d6305b84e2fe52db18396ad4d28197e6d 100644 (file)
--- 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. 
 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}
 
 \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
 
 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
 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}
 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 
 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. 
 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.
 
 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}. 
 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.
 
 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
 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}
 \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}, 
 \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 
 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
 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.
 
 
 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}.  
 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}
 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}
 
 
 \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}
 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}}\\
 \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}
 
   \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 
 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}
 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. 
        \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}.
 
 (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}
 \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.  
 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. 
 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 
 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 


@@ -613,7 +613,7 @@ which results in bigger energy savings.
     \EndWhile
     \State  Return $Sopt_1,Sopt_2,\dots,Sopt_N$
   \end{algorithmic}
     \EndWhile
     \State  Return $Sopt_1,Sopt_2,\dots,Sopt_N$
   \end{algorithmic}

-  \caption{Heterogeneous scaling algorithm}
+  \caption{frequency scaling factors selection algorithm}

   \label{HSA}
 \end{algorithm}
 
   \label{HSA}
 \end{algorithm}
 


@@ -638,7 +638,7 @@ which results in bigger energy savings.
 \end{algorithm}
 
 \subsection{The verifications of the proposed algorithm}
 \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 
 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 


@@ -1055,19 +1055,14 @@ results in less energy saving but less performance degradation.
 
 \section{Conclusion}
 \label{sec.concl} 
 
 \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. 
-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  
+In this paper, a new online frequency selecting algorithm have been presented. It selects the best possible vector of frequency scaling factors that gives the maximum distance (optimal tradeoff) between the predicted energy and 
+the predicted performance curves for a heterogeneous platform. This algorithm uses a new energy model for measuring  

 and predicting the energy of distributed iterative applications running over heterogeneous 
 and predicting the energy of distributed iterative applications running over heterogeneous 

-cluster. The proposed method evaluated on Simgrid/SMPI  simulator to built a heterogeneous 
-platform to executes NAS parallel benchmarks. The results of the experiments showed the ability of
-the proposed algorithm to changes its behaviour to selects different scaling factors  when 
-the number of computing nodes and both of the static and the dynamic powers are changed. 
-
-In the future, we plan to improve this method to apply on asynchronous  iterative applications 
-where each task does not wait the others tasks to finish there works. This leads us to develop a new 
-energy model to an asynchronous iterative applications, where the number of iterations is not 
+platform. To evaluate the proposed method, it  was  applied on the NAS parallel benchmarks and executed over a heterogeneous platform simulated by  Simgrid. The results of the experiments showed that the algorithm reduces up to 35\% the energy consumption of a message passing iterative method while limiting the degradation of the performance. The algorithm also  selects different scaling factors   according to the percentage of the computing and communication times, and according to the values of  the static and  dynamic powers of the CPUs. 
+
+In the near future, this method will be applied to real heterogeneous platforms to evaluate its performance in a real study case. It would also be interesting to evaluate its scalability over large scale heterogeneous platform and measure the energy consumption reduction it can produce. Afterward, We would like  to develop a similar method that is adapted to asynchronous  iterative applications 
+where each task does not wait for others tasks to finish there works. The development of such method might require a new 
+energy model because the number of iterations is not 

 known in advance and depends on the global convergence of the iterative system.
 
 \section*{Acknowledgment}
 known in advance and depends on the global convergence of the iterative system.
 
 \section*{Acknowledgment}