small modifs

[mpi-energy2.git] / Heter_paper.tex

diff --git a/Heter_paper.tex b/Heter_paper.tex
index 88e7fefb305f4507676d09c565160bae31c22930..c29b2a40b302fc1d68f2a707dd36ab2da9534c32 100644 (file)
--- a/Heter_paper.tex
+++ b/Heter_paper.tex
@@ -110,7 +110,7 @@ such as the L-CSC from the GSI Helmholtz Center which
 became the top of the Green500 list in November 2014 \cite{Green500_List}. 
 This heterogeneous platform executes more than 5  GFLOPS per watt while consumed 57.15 kilowatts.
 
 became the top of the Green500 list in November 2014 \cite{Green500_List}. 
 This heterogeneous platform executes more than 5  GFLOPS per watt while consumed 57.15 kilowatts.
 

-Besides hardware improvements, there are many software techniques to lower the energy consumption of these platforms, 
+Besides platform improvements, there are many software and hardware techniques to lower the energy consumption of these platforms, 

 such as scheduling, DVFS, ... DVFS is a widely  used process to reduce the energy consumption of a processor by lowering 
 its frequency \cite{Rizvandi_Some.Observations.on.Optimal.Frequency}. However, it also  reduces the number of FLOPS 
 executed by the processor which might increase  the execution time of the application running over that processor.
 such as scheduling, DVFS, ... DVFS is a widely  used process to reduce the energy consumption of a processor by lowering 
 its frequency \cite{Rizvandi_Some.Observations.on.Optimal.Frequency}. However, it also  reduces the number of FLOPS 
 executed by the processor which might increase  the execution time of the application running over that processor.


@@ -209,7 +209,7 @@ task which have the highest computation time and no slack time.
   
  \begin{figure}[t]
   \centering
   
  \begin{figure}[t]
   \centering

-   \includegraphics[scale=0.5]{fig/commtasks}
+   \includegraphics[scale=0.6]{fig/commtasks}

   \caption{Parallel tasks on a heterogeneous platform}
   \label{fig:heter}
 \end{figure}
   \caption{Parallel tasks on a heterogeneous platform}
   \label{fig:heter}
 \end{figure}


@@ -254,7 +254,7 @@ vector of scaling factors can be predicted using (\ref{eq:perf}).
 \end{equation}
 Where:\\
 \begin{equation}
 \end{equation}
 Where:\\
 \begin{equation}

-\label{eq:perf}
+\label{eq:perf2}

  MinTcm = \min_{i=1,2,\dots,N} (Tcm_i)
 \end{equation}
 where $TcpOld_i$ is the computation time  of processor $i$ during the first 
  MinTcm = \min_{i=1,2,\dots,N} (Tcm_i)
 \end{equation}
 where $TcpOld_i$ is the computation time  of processor $i$ during the first 


@@ -358,7 +358,7 @@ The communication time of a processor $i$ is noted as $Tcm_{i}$ and could contai
 if it is communicating with slower nodes, see figure(\ref{fig:heter}). Therefore, all nodes do 
 not have equal communication times. While the dynamic energy is computed according to the frequency 
 scaling factor and the dynamic power of each node as in (\ref{eq:Edyn}), the static energy is 
 if it is communicating with slower nodes, see figure(\ref{fig:heter}). Therefore, all nodes do 
 not have equal communication times. While the dynamic energy is computed according to the frequency 
 scaling factor and the dynamic power of each node as in (\ref{eq:Edyn}), the static energy is 

-computed as the sum of the execution time of each processor multiplied by its static power. 
+computed as the sum of the execution time of one iteration multiplied by static power of each processor. 

 The overall energy consumption of a message passing  distributed application executed over a 
 heterogeneous platform during one iteration is the summation of all dynamic and static energies 
 for each  processor.  It is computed as follows:
 The overall energy consumption of a message passing  distributed application executed over a 
 heterogeneous platform during one iteration is the summation of all dynamic and static energies 
 for each  processor.  It is computed as follows:


@@ -435,7 +435,7 @@ time simultaneously.  But the main objective is to produce maximum energy
 reduction with minimum execution time reduction.  
   
 This problem can be solved by making the optimization process for energy and 
 reduction with minimum execution time reduction.  
   
 This problem can be solved by making the optimization process for energy and 

-execution time follow the same direction.  Therefore, the equation of the 
+execution time following 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}
 normalized execution time is inverted which gives the normalized performance equation, as follows:
 \begin{multline}
   \label{eq:pnorm_inv}


@@ -480,14 +480,14 @@ 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 algorithm \ref{HSA} is presented. It 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.  
 It uses information gathered during the first iteration such as the computation time and the 
 communication time in one iteration for each node. The algorithm is executed  after the first 
 iteration and returns a vector of optimal frequency scaling factors   that satisfies the objective 
 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.  
 It uses information gathered during the first iteration such as the computation time and the 
 communication time in one iteration for each node. The algorithm is executed  after the first 
 iteration and returns a vector of optimal frequency scaling factors   that satisfies the objective 

-function (\ref{eq:max}). The program apply DVFS operations to change the frequencies of the CPUs 
+function (\ref{eq:max}). The program applies DVFS operations to change the frequencies of the CPUs 

 according to the computed scaling factors.  This algorithm is called just once during the execution 
 of the program. Algorithm~(\ref{dvfs}) shows where and when the proposed scaling algorithm is called 
 in the iterative MPI program.
 according to the computed scaling factors.  This algorithm is called just once during the execution 
 of the program. Algorithm~(\ref{dvfs}) shows where and when the proposed scaling algorithm is called 
 in the iterative MPI program.


@@ -526,7 +526,7 @@ scaling factors starts the search method from these initial frequencies and take
 toward lower frequencies. The algorithm iterates on all left frequencies, from the higher bound until all 
 nodes reach their minimum frequencies, to compute their overall energy consumption and performance, and select 
 the optimal frequency scaling factors vector. At each iteration the algorithm determines the slowest node 
 toward lower frequencies. The algorithm iterates on all left frequencies, from the higher bound until all 
 nodes reach their minimum frequencies, to compute their overall energy consumption and performance, and select 
 the optimal frequency scaling factors vector. At each iteration the algorithm determines the slowest node 

-according to (\ref{eq:perf}) and keeps its frequency unchanged, while it lowers the frequency of  
+according to the equation (\ref{eq:perf}) and keeps its frequency unchanged, while it lowers the frequency of  

 all other nodes by one gear.
 The new overall energy consumption and execution time are computed according to the new scaling factors. 
 The optimal set of frequency scaling factors is the set that gives the highest distance according to  the objective 
 all other nodes by one gear.
 The new overall energy consumption and execution time are computed according to the new scaling factors. 
 The optimal set of frequency scaling factors is the set that gives the highest distance according to  the objective 


@@ -622,7 +622,7 @@ which results in bigger energy savings.
 The precision of the proposed algorithm mainly depends on the execution time prediction model defined in 
 (\ref{eq:perf}) and the energy model computed by (\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 
 (\ref{eq:perf}) and the energy model computed by (\ref{eq:energy}). 
 The energy model is also significantly dependent  on the execution time model because the static energy is 

-linearly related the execution time and the dynamic energy is related to the computation time. So, all of 
+linearly related to the execution time and the dynamic energy is related to the computation time. So, all of 

 the works presented in this paper is based on the execution time model. To verify this model, the predicted 
 execution time was compared to  the real execution time over SimGrid/SMPI simulator, v3.10~\cite{casanova+giersch+legrand+al.2014.versatile}, 
 for all  the NAS parallel benchmarks NPB v3.3 
 the works presented in this paper is based on the execution time model. To verify this model, the predicted 
 execution time was compared to  the real execution time over SimGrid/SMPI simulator, v3.10~\cite{casanova+giersch+legrand+al.2014.versatile}, 
 for all  the NAS parallel benchmarks NPB v3.3 


@@ -1020,10 +1020,10 @@ results in less energy saving but less performance degradation.
 \begin{figure}
   \centering
   \subfloat[Comparison  of the results on 8 nodes]{%
 \begin{figure}
   \centering
   \subfloat[Comparison  of the results on 8 nodes]{%

-    \includegraphics[width=.30\textwidth]{fig/sen_comp}\label{fig:sen_comp}}%
+    \includegraphics[width=.33\textwidth]{fig/sen_comp}\label{fig:sen_comp}}%

 
   \subfloat[Comparison the selected frequency scaling factors of MG benchmark class C running on 8 nodes]{%
 
   \subfloat[Comparison the selected frequency scaling factors of MG benchmark class C running on 8 nodes]{%

-    \includegraphics[width=.34\textwidth]{fig/three_scenarios}\label{fig:scales_comp}}
+    \includegraphics[width=.33\textwidth]{fig/three_scenarios}\label{fig:scales_comp}}

   \label{fig:comp}
   \caption{The comparison of the three power scenarios}
 \end{figure}  
   \label{fig:comp}
   \caption{The comparison of the three power scenarios}
 \end{figure}  


@@ -1033,49 +1033,45 @@ results in less energy saving but less performance degradation.
 
 \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
-is compared to Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS}. 
+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, $EDP=Enegry*Delay$ using the predicted overall energy consumption and execution time delay for each frequency.
 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, $EDP=Enegry*Delay$ 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 
+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.
 
 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 execution times and the energy consumptions for both versions of the NAS benchmarks while running the class C of each benchmark over 8 or 9 heterogeneous nodes. \textcolor{red}{The results show that our algorithm gives better energy savings than Spiliopoulos et al. algorithm, 
-on average it is up to 17\% higher for  energy saving compared to their algorithm. The average of performance degradation percentage using our method is higher on average by 3.82\%.} 
+Both algorithms were applied to the parallel NAS benchmarks to compare their efficiency. Table \ref{table:compare_EDP}  presents the results of comparing the execution times and the energy consumptions for both versions of the NAS benchmarks while running the class C of each benchmark over 8 or 9 heterogeneous nodes. The results show that our algorithm gives better energy savings than Spiliopoulos et al. algorithm, 
+on average it results in 29.76\% energy saving while their algorithm returns just 25.75\%. The average of performance degradation percentage is approximately the same for both algorithms, about 4\%. 
+

 
 For all benchmarks, our algorithm outperforms 
 
 For all benchmarks, our algorithm outperforms 

-Spiliopoulos et al. algorithm in term of energy and performance tradeoff \textcolor{red}{(on average it has up to 21\% of distance)}, see figure (\ref{fig:compare_EDP}) because it maximizes the distance between the energy saving and the performance degradation values while giving the same weight for both metrics. 
+Spiliopoulos et al. algorithm in term of energy and performance tradeoff, see figure (\ref{fig:compare_EDP}), because it maximizes the distance between the energy saving and the performance degradation values while giving the same weight for both metrics. 

 
 
 
 
 
 

-\begin{table}[htb]
-  \caption{Comparing the proposed algorithm}
-  % title of Table
-  \centering
-  \begin{tabular}{|*{4}{l|}}
-    \hline
-    Program       & Energy      & Performance        & Distance\%    \\
-    name          & saving\%    & degradation\%      &              \\
-    \hline
-    CG            &13.31               &22.34                   &10.89       \\
-    \hline 
-    MG            &14.55               &71.39                   &6.29        \\
-   \hline
-    EP            &44.4                    &0.0                         &44.42        \\
-   \hline
-    LU            &-4.79               &-88.58                  &10.12     \\
-    \hline
-    BT                   &16.76                &22.33                   &15.07     \\
-   \hline
-    SP                   &20.52                &-46.64                  &43.37      \\
-   \hline
-    FT            &14.76               &-7.64                   &17.3     \\
-\hline 
-  \end{tabular}
-  \label{table:compare_EDP}
+
+\begin{table}[h]
+ \caption{Comparing the proposed algorithm}
+ \centering
+\begin{tabular}{|l|l|l|l|l|l|l|l|}
+\hline
+\multicolumn{2}{|l|}{\multirow{2}{*}{\begin{tabular}[c]{@{}l@{}}Program \\ name\end{tabular}}} & \multicolumn{2}{l|}{Energy saving \%} & \multicolumn{2}{l|}{Perf.  degradation \%} & \multicolumn{2}{l|}{Distance} \\ \cline{3-8} 
+\multicolumn{2}{|l|}{}                                                                         & EDP             & MaxDist          & EDP            & MaxDist           & EDP          & MaxDist        \\ \hline
+\multicolumn{2}{|l|}{CG}                                                                       & 27.58           & 31.25            & 5.82           & 7.12              & 21.76        & 24.13          \\ \hline
+\multicolumn{2}{|l|}{MG}                                                                       & 29.49           & 33.78            & 3.74           & 6.41              & 25.75        & 27.37          \\ \hline
+\multicolumn{2}{|l|}{LU}                                                                       & 19.55           & 28.33            & 0.0            & 0.01              & 19.55        & 28.22          \\ \hline
+\multicolumn{2}{|l|}{EP}                                                                       & 28.40           & 27.04            & 4.29           & 0.49              & 24.11        & 26.55          \\ \hline
+\multicolumn{2}{|l|}{BT}                                                                       & 27.68           & 32.32            & 6.45           & 7.87              & 21.23        & 24.43          \\ \hline
+\multicolumn{2}{|l|}{SP}                                                                       & 20.52           & 24.73            & 5.21           & 2.78              & 15.31         & 21.95         \\ \hline
+\multicolumn{2}{|l|}{FT}                                                                       & 27.03           & 31.02            & 2.75           & 2.54              & 24.28        & 28.48           \\ \hline
+
+\end{tabular}
+\label{table:compare_EDP}

 \end{table}
 
 
 \end{table}
 
 

+
+
+

 \begin{figure}[t]
   \centering
    \includegraphics[scale=0.5]{fig/compare_EDP.pdf}
 \begin{figure}[t]
   \centering
    \includegraphics[scale=0.5]{fig/compare_EDP.pdf}


@@ -1093,16 +1089,16 @@ platform. To evaluate the proposed method, it  was  applied on the NAS parallel
  outperforms their algorithm in term of energy-time tradeoff.
 
 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 
  outperforms their algorithm in term of energy-time tradeoff.
 
 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 
+where each task does not wait for others tasks to finish their 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}
 
 This work has been partially supported by the Labex
 energy model because the number of iterations is not 
 known in advance and depends on the global convergence of the iterative system.
 
 \section*{Acknowledgment}
 
 This work has been partially supported by the Labex

-ACTION project (contract “ANR-11-LABX-01-01”). As a PhD student,
+ACTION project (contract “ANR-11-LABX-01-01”). As a PhD student, 

 Mr. Ahmed Fanfakh, would like to thank the University of
 Mr. Ahmed Fanfakh, would like to thank the University of

-Babylon (Iraq) for supporting his work.
+Babylon (Iraq) for supporting his work. 

 
 
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@@ -1114,7 +1110,7 @@ Babylon (Iraq) for supporting his work.
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+   

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