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%\title{Energy Consumption Optimization of Parallel Applications with
%Iterations using CPU Frequency Scaling} 
\vspace{2cm}

\title{   \textbf{Energy Consumption Optimization of   Parallel Applications with Iterations   using CPU Frequency Scaling} \\ \vspace{0.2cm} \hspace{1.8cm}\textbf{\textcolor{cyan}{\small PhD Dissertation Defense}}}\vspace{-0.5cm}
\author{ \textbf{Ahmed Badri Muslim Fanfakh} \\ \vspace{0.5cm}\small Under the supervision of: \\ \textcolor{cyan}{\small  Raphaël COUTURIER and Jean-Claude CHARR} \\\vspace{0.1cm} \textcolor{blue}{ UBFC - FEMTO-ST - DISC Dept.  - AND Team} \\ ~~~~~~~~~~~~~~~~~~~~~ \textbf{\textcolor{blue}{ 17 October 2016 }}} 

\date{}
\vspace{-3cm}
%  ____  _____ ____  _   _ _____ 
% |  _ \| ____| __ )| | | |_   _|
% | | | |  _| |  _ \| | | | | |  
% | |_| | |___| |_) | |_| | | |  
% |____/|_____|____/ \___/  |_|  
% 
\begin{document}
\setbeamertemplate{background}{\titrefemto}

%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 01    %%
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\begin{frame}[plain]
\vspace{1cm}
\centering
   \titlepage
\end{frame}


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 02    %%
%%%%%%%%%%%%%%%%%%%% 
\setbeamertemplate{background}{\pagefemto}
\begin{frame}{Outline}

\setbeamertemplate{section in toc}[sections numbered] 
\tableofcontents
\end{frame}

%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 03    %%
%%%%%%%%%%%%%%%%%%%% 
\begin{frame}{Definition of parallel computing}
\section{\small {Introduction and Problem definition}}
 \centering
 \includegraphics[width=0.99\textwidth]{para.pdf} 
\end{frame}

 

\begin{frame}{Execution of synchronous parallel tasks}
\vspace{-0.5 cm}
\begin{figure}
  \centering
  \subfloat[Synchronous imbalanced communications]{%
    \includegraphics[scale=0.49]{c1/commtasks}\label{fig:h1}}
  \subfloat[Synchronous imbalanced computations]{%
    \includegraphics[scale=0.49]{c1/compt}\label{fig:h2}}
 % \caption{Parallel tasks on homogeneous platform}
  \label{fig:homo}
\end{figure}

 \end{frame}
 
 
%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 07   %%
%%%%%%%%%%%%%%%%%%%% 


\begin{frame}{\large Synchronous and asynchronous iterative methods }
\vspace{-0.5 cm}
\begin{figure}

\includegraphics[scale=0.42]{syn_tasks.pdf}
\vspace{0.6 cm}
\includegraphics[scale=0.42]{Asyn_tasks.pdf}
\end{figure}

 
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%
%%    SLIDE 03    %%
%%%%%%%%%%%%%%%%%%%% 
\begin{frame}{Approaches to get more computing power}
 
   %\bf \textcolor{blue}{}
     \begin{minipage}{0.5\textwidth} 
      \textcolor{blue}{1)} \small  \bf \textcolor{black}{Increase the frequency of a  processor.\\ (limited due to overheating)}
    \end{minipage}%
    \begin{minipage}{0.6\textwidth} 
    
\begin{figure}[h!]
        
    \includegraphics[width=0.7\textwidth]{fig/freq-years} 
    \end{figure}
    \end{minipage}%
    \vspace{0.2cm}
    \begin{minipage}{0.5\textwidth} 
     \textcolor{blue}{2)} \small \bf \textcolor{black}{Increase the number of computing   
     units.}
     
 \textcolor{black}{The supercomputer Tianhe-2 has more than 3 million cores and consumes around 17.8 megawatts.}  
          
    \end{minipage}%
    \begin{minipage}{0.6\textwidth} 
    \begin{figure}[h!]
     \includegraphics[width=0.7\textwidth]{fig/clusters} 
    \end{figure}
    \end{minipage}%
 \end{frame}
 
 
 
 %%%%%%%%%%%%%%%%%%%
%%    SLIDE 04   %%
%%%%%%%%%%%%%%%%%%%% 
\begin{frame}{Techniques for energy consumption reduction}

     \textcolor{blue}{1)} \bf \textcolor{black}{Switch-off idle nodes method}  
    \vspace{-0.9cm}
    \begin{figure}
     \animategraphics[autopause,controls,scale=0.26,buttonsize=0.2cm]{200}{on-off/a-}{0}{111}
     %\includegraphics[width=0.6\textwidth]{on-off/a-69}
    \end{figure}
 \end{frame}

%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 05    %%
%%%%%%%%%%%%%%%%%%%% 
\begin{frame}{Techniques for energy consumption reduction}
 
  \textcolor{blue}{2)} \bf \textcolor{black}{Dynamic Voltage and Frequency Scaling (DVFS)}
     \vspace{-0.9cm}
    \begin{figure}
    \animategraphics[autopause,controls,scale=0.26,buttonsize=0.2cm]{10}{DVFS-meq/a-}{0}{175}
     %\includegraphics[width=0.6\textwidth]{DVFS-meq/a-109}
    \end{figure}
    \end{frame}
 
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%%    SLIDE 06   %%
%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 07    %%
%%%%%%%%%%%%%%%%%%%% 
\begin{frame}{Motivations}
\vspace{0.05cm}
\section{\small {Motivations}}
\textcolor{blue}{Why we used the DVFS method:}
\vspace{-0.49cm}
\begin{minipage}{0.5\textwidth} 
    \vspace{-0.49cm} 
      \begin{itemize} 
       \item  \small \textcolor{black}{ The CPU is the component that consumes the  highest amount of energy in a node \textsuperscript{1}. }
  		
 	 \end{itemize}

    \end{minipage}%
    \begin{minipage}{0.5\textwidth}
     \vspace{-0.49cm} 
    \begin{figure}[h!]
     \includegraphics[width=0.85\textwidth]{fig/node-power} 
     
    \end{figure}
    \end{minipage}%
    
  \begin{itemize} \item \small  \textcolor{black}{DVFS reduces the energy consumption while 
   keeping all the nodes working.}
  		\item \small \textcolor{black}{It has a very small overhead compared to switching-off the idle nodes.}  \end{itemize} 
    
\vspace{-0.12cm}

 \begin{block}{\textcolor{white}{Challenge and Objective}}

  	\small	\textcolor{blue}{Challenge:} \textcolor{black}{DVFS is used to reduce the energy consumption, \textcolor{blue}{but} it also degrades the performance of the CPU.}
  		
  		\vspace{0.1cm}
 \small	 \textcolor{blue}{Objective:} \textcolor{black}{Applying the DVFS to minimize the energy consumption while maintaining the performance of the parallel application.}
\end{block}
 
 \tiny \textsuperscript{1} Fan, X., Weber, W., and Barroso, L. A. 2007.  Power provisioning
for a warehouse-sized computer.

    \end{frame}



%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 08    %%
%%%%%%%%%%%%%%%%%%%% 


\begin{frame}{The first contribution}

\section{\small {Energy optimization of a homogeneous platform}}
%\vspace{-3cm}
 % \includegraphics[width=0.6\textwidth]{white.pdf} 

\begin{center}
\bf  \Large \textcolor{blue}{Energy optimization of a parallel application with iterations running over a homogeneous platform}
\end{center}
 \end{frame}



%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 09    %%
%%%%%%%%%%%%%%%%%%%% 
 
\begin{frame}{Objectives}
        
                \begin{itemize}   \small \justifying
                 
                   \item   Studying the effect of the frequency scaling  on the \textbf{energy consumption and performance } of parallel  applications with iterations. \medskip
                   
                   \item   Discovering the \textbf{energy-performance trade-off relation} when changing the frequency of the processor.\medskip
                   \item   Proposing an algorithm for selecting the scaling factor that produces  \textbf {the good trade-off} between the energy consumption and the performance. \medskip
                   \item   Comparing the proposed algorithm to existing methods.
                   
                   
                   %\footnote{\tiny Thomas Rauber and Gudula Rünger. Analytical modeling and simulation of the  
                          %energy consumption \\  \quad ~ ~\quad    of  independent tasks. In Proceedings of the Winter Simulation Conference, 2012.} method that our method best on. 
                \end{itemize}
                 %\let\thefootnote\relax\footnote{}
        
        
\end{frame}




%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 13   %%
%%%%%%%%%%%%%%%%%%%% 
\begin{frame}{Performance evaluation of MPI programs}  

\small The frequency scaling factor is the ratio between the maximum and the new frequency, \textcolor{blue}{$S = \frac{F_{max}}{F_{new}}$}.  
    \vspace{5 mm}
    
        \begin{femtoBlock}{}
              \vspace{-5 mm}
              \begin{block}{\small Execution time prediction model}
                     \centering{ $ \textcolor{red}{T_{new}} = \textcolor{blue}{T_{Max Comp Old} \cdot S + T_{{Min Comm Old}}}$}
          \end{block}   
          \vspace{5 mm}
           \centering{\includegraphics[width=.4\textwidth]{c1/cg_per}
           \quad%
           \includegraphics[width=.4\textwidth]{c1/lu_pre}}
            \vspace{1 mm}
            
           \small The maximum normalized error for CG=0.0073 \textbf{(the smallest)} and LU=0.031 \textbf{(the worst)}.
           \end{femtoBlock}
\end{frame}







  


 
 
 

%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 11   %%
%%%%%%%%%%%%%%%%%%%% 
\begin{frame}{Energy model for a homogeneous platform}    
      The power consumed by a processor is divided into two power metrics: the dynamic (\textcolor{red}{$P_d$}) and  the static   
       (\textcolor{red}{$P_s$}) powers. 
    \begin{equation}
     \label{eq:pd}
     \textcolor{red}{ P_d} = \textcolor{blue}{\alpha \cdot CL \cdot V^2 \cdot F}
   \end{equation}
    \scriptsize \underline{Where}: \\ 
    \scriptsize {\textcolor{blue}{$\alpha$}: switching activity. \hspace{15 mm}  \textcolor{blue}{$CL$}: load capacitance [F].\\     
    \textcolor{blue}{$V$}: the supply voltage [V]. \hspace{8 mm} \textcolor{blue}{$F$}: operational frequency [Hz].}
   \begin{equation}
     \label{eq:ps}
     \small \textcolor{red}{P_s} = \textcolor{blue}{V \cdot N_{trans} \cdot K_{design} \cdot I_{Leak}}
   \end{equation}
    \underline{Where}:\\ 
   	\scriptsize{ \textcolor{blue}{$V$}: the supply voltage [V].  \hspace{19 mm}   \textcolor{blue}{$N_{trans}$}: number of transistors. \\   
   	\textcolor{blue}{$K_{design}$}: design dependent parameter. \hspace{3 mm} \textcolor{blue}{$I_{leak}$}: technology dependent  
   	     parameter [A].} 
   	     
   	     
\end{frame}


  
%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 12   %%
%%%%%%%%%%%%%%%%%%%% 

\begin{frame}{Energy model for a homogeneous platform}
       \vspace{-0.77cm} 
            \begin{figure}
  \animategraphics[autopause,controls,scale=0.3,buttonsize=0.2cm]{10}{homo-model/a-}{0}{441}
  %\includegraphics[width=0.6\textwidth]{homo-model/a-356}
  \end{figure}  
              
      %  \begin{block}{\small Rauber and Rünger's energy model}
         %$ E = P_{d} \cdot S_1^{-2} \cdot
         %\left( T_1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^2} \right) +
          %  P_{s} \cdot S_1  \cdot T_1 \cdot N$
        %\end{block}     
          % \textcolor{blue}{$S_1$}: the maximum scaling factor.\\ 
          % \textcolor{blue}{$P_{d}$}: the dynamic power.\\
          % \textcolor{blue}{$P_{s}$}: the static power.\\
          % \textcolor{blue}{$T_I$}: the execution time of the slower task.\\ 
          % \textcolor{blue}{$T_i$}: the execution time of task i.\\ 
          % \textcolor{blue}{$N$}:  the number of  nodes.
          
          
       
\end{frame}




 %%%%%%%%%%%%%%%%%%%%
%%    SLIDE 14   %%
%%%%%%%%%%%%%%%%%%%%  
\begin{frame}{Performance and energy reduction trade-off}      
        \begin{femtoBlock}{} \vspace{-15 mm}
               \begin{figure}
     \centering
     \subfloat[\small  Real relation.]{%
     \includegraphics[width=.43\textwidth]{c1/file3}\label{fig:r2}}
     \quad%
     \subfloat[\small Converted relation.]{%
     \includegraphics[width=.43\textwidth]{c1/file}\label{fig:r1}}%
  \label{fig:rel}
 % \caption{The energy and performance relation}
\end{figure}

 Where:~~~ $\textcolor{blue}{Performance} = execution~time^{-1}$

%\vspace{-0.3cm}
      \small 
         \begin{block}{\small Our objective function}
         \centering{$\textbf{\emph {\textcolor{red}{MaxDist}}} = \max_{j=1,2,\dots ,F}             
                    (\overbrace{P_{Norm}(S_j)}^{{\textcolor{blue}{Maximize}}} - 
                     \overbrace{E_{Norm}(S_j)}^{{\textcolor{blue}{Minimize}}} )$}
                                         
        \end{block}                
        \end{femtoBlock}
       
\end{frame}

%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 15   %%
%%%%%%%%%%%%%%%%%%%% 
 %\begin{frame}{Scaling factor selection algorithm}
%\vspace{-0.75cm}
    % \begin{center}
      %\includegraphics[width=.56 \textwidth]{c1/algo-homo}
     %\end{center}
     
%\end{frame}


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 16   %%
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\begin{frame}{Scaling factor selection algorithm}
\vspace{-0.75cm}
     
     \begin{figure}
  \animategraphics[autopause,controls,scale=0.29,buttonsize=0.2cm]{10}{dvfs-homo/a-}{0}{335}
  %\includegraphics[width=0.6\textwidth]{dvfs-homo/a-159}
  \end{figure}
\end{frame}

%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 17   %%
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\begin{frame}{Experiment over SimGrid }
      \begin{femtoBlock}{}      
        \begin{itemize}
         \small
           \item The experiments were executed on the simulator SimGrid/SMPI v3.10.\medskip
           \item The proposed algorithm was applied to the NAS parallel benchmarks.\medskip
           \item Each node in the cluster has 18 frequency values from \textbf{2.5$GHz$} to \textbf{800$MHz$}.\medskip
           \item The proposed algorithm was evaluated over the A, B and C classes of the benchmarks using 4, 8 or 9 and 16 nodes respectively. \medskip
           \item $P_d=20W$,  $P_s=4W$.
                \end{itemize}
        \end{femtoBlock}
\end{frame}


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 18   %%
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\begin{frame}{Experimental results}
  \begin{femtoBlock}{}  
      \centering { 
     \includegraphics[width=.35\textwidth]{c1/ep}
     \includegraphics[width=.35\textwidth]{c1/cg}
     \includegraphics[width=.35\textwidth]{c1/bt}}
     
\hspace{0.5cm}     
     
     \centering {\includegraphics[width=.55\textwidth]{c1/results.pdf}}
 \end{femtoBlock}
\end{frame}


  %%%%%%%%%%%%%%%%%%%%
%%    SLIDE 19   %%
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\begin{frame}{Results comparison}
         \small \textcolor{blue}{Rauber and Rünger's  scaling factor  \textcolor{black}{ \tiny \textsuperscript{2}}}
         
         \vspace{2 mm}
         
           $S_{opt} = \sqrt[3]{\frac{2}{N} \cdot \frac{P_{dyn}}{P_{static}} \cdot
            \left( 1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^3}\right) } $ 
     
        
   \begin{center}
            \includegraphics[width=.55\textwidth]{c1/compare-c.pdf}
   \end{center}
            
                     
\vspace{-2 mm}
         \tiny \textsuperscript{2}  Thomas Rauber and Gudula Rünger. Analytical modeling and simulation of the energy consumption of  independent tasks. In Proceedings of the Winter Simulation Conference, 2012.
\end{frame}


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 20   %%
%%%%%%%%%%%%%%%%%%%% 
%\begin{frame}{The proposed new energy model}
   % \vspace{-0.75cm}     
  %\begin{figure}
 % \animategraphics[autopause,controls,scale=0.28,buttonsize=0.2cm]{10}{homo-model/a-}{0}{356}
  %\includegraphics[width=0.6\textwidth]{homo-model/a-356}
 % \end{figure}
%\end{frame}


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 21   %%
%%%%%%%%%%%%%%%%%%%% 
%\begin{frame}{\large Comparing the new model with Rauber's model }
% \vspace{0.1cm}    
% \centering
    %\includegraphics[width=.45\textwidth]{c1/energy_con}
    
   %\includegraphics[width=.5\textwidth]{c1/compare-scales}
%\end{frame}




   % \begin{frame}{Summary}
     % \begin{femtoBlock}{}    
     % \begin{itemize}
      %\small
       %\item  We have presented a new online scaling factor selection method that  \textcolor{blue}{optimizes simultaneously the energy and performance}.\medskip
       % \item It predicts \textcolor{blue}{ the energy consumption and the performance} of the parallel applications. \medskip
         %\item Our algorithm  \textcolor{blue}{saves more energy} when the communication and the other slacks times are big.     \medskip    
         %\item It gives the  \textcolor{blue}{best trade-off between energy reduction and
               % performance}. \medskip
         %\item  Our method \ \textcolor{blue}{outperforms Rauber and Rünger's method} in terms of  energy-performance ratio.
         %\item The proposed new energy model is  \textcolor{blue}{more accurate} then Rauber energy model.
         %\end{itemize}      
         
        %\end{femtoBlock}
%\end{frame}


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 22    %%
%%%%%%%%%%%%%%%%%%%% 


\begin{frame}{The second contribution}

\section{\small {Energy optimization of a heterogeneous platform}}
\begin{center}


\bf  \Large \textcolor{blue}{Energy optimization of a parallel application with iterations running over a Heterogeneous platform}
\end{center}
 \end{frame}
 


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 23    %%
%%%%%%%%%%%%%%%%%%%% 
 
\begin{frame}{Objectives}
        \begin{femtoBlock}{} \vspace{-12 mm}
                \begin{itemize} \small
                  \item   Proposing  \textcolor{blue}{new energy and performance models} for message passing  applications with iterations running  
                          over a heterogeneous platform (cluster or Grid). \medskip
                   \item  Studying the effect of the scaling factor $S$ on both the \textcolor{blue}{energy consumption  and the performance} of
                          message passing iterative applications.    \medskip                      
                   
                   \item  Computing  the vector of scaling factors ($S_1, S_2, ..., S_n$)  producing \textcolor{blue} {the good trade-off} between
                          the energy consumption and the performance. 
                \end{itemize}
                 
          \vspace{-10 mm}
        \end{femtoBlock}      
\end{frame}


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 24    %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{The execution time model}    
      \vspace{-8 mm}
     \begin{figure}[!t]
       \centering
       \includegraphics[scale=0.5]{c2/commtasks}
       \label{fig:heter}
     \end{figure}     
       \vspace{-12 mm}
       \medskip
       
    \begin{block}{\small The execution time prediction model}
    \begin{equation}
     \label{eq:perf}
     \small\textcolor{red}{ T_{new}} = \textcolor{blue}{\max_{i=1,2,\dots,N} ({TcpOld_i} \cdot S_{i}) + \min_{i=1,2,\dots,N} (Tcm_i)}
    \end{equation}
    \end{block}   
 \small  Where: $ \textcolor{red}{Tcm} = \textcolor{blue}{communication~times + slack~times}$
  
\end{frame}
 
 %%%%%%%%%%%%%%%%%%%%
%%    SLIDE 25    %%
%%%%%%%%%%%%%%%%%%%%
 %\begin{frame}{The energy consumption model} 
   % The overall energy consumption of a message passing synchronous  application executed over
   %  a heterogeneous platform can be computed as  follows:
   % \begin{multline}
    % \label{eq:energy}
   %  \textcolor{red}{E} = \textcolor{blue}{\sum_{i=1}^{N} {(S_i^{-2} \cdot Pd_i \cdot  Tcp_i)}} + {} \\
  %   \textcolor{blue}{\sum_{i=1}^{N} (Ps_i \cdot (\max_{i=1,2,\dots,N} (Tcp_i \cdot S_{i}) + {\min_{i=1,2,\dots,N} (Tcm_i))}}   
   %   \hspace{10 mm}
   % \end{multline}
   % \underline{where}:\\
   % \textcolor{blue}{N} : is the number of nodes.
%\end{frame}
 
 
%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 26    %%
%%%%%%%%%%%%%%%%%%%%
  \begin{frame}{The energy  model  for heterogeneous cluster}
  \vspace{-0.77cm}
 \begin{figure}
  \animategraphics[autopause,controls,scale=0.3,buttonsize=0.2cm]{10}{heter-model/a-}{0}{350}
  %\includegraphics[width=0.6\textwidth]{heter-model/a-272}
  \end{figure}
 \end{frame}
 
 
 
 
%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 27    %%
%%%%%%%%%%%%%%%%%%%%
%\begin{frame}{The trade-off between energy  and performance}
   % \vspace{-7 mm}
    %\begin{figure}
   %  \centering{ \includegraphics[width=.4\textwidth]{c2/heter}}
   % \end{figure}
   % \vspace{-7 mm}
   % \textcolor{red}{\underline{Step1}}: computing the normalized energy \textcolor{blue}%{$E_{norm} = \frac{E_{reduced}} 
    %{E_{Max}}$}. \\
    % \textcolor{red}{\underline{Step2}}: computing the normalized performance \textcolor{blue}{$P_{norm} = \frac{T_{Max}}{T_{new}}$}.
   
   %  \begin{block}{\small The tradeoff model}
    % \begin{equation}
    %  \label{eq:max}
    %  \textcolor{red}{MaxDist} =
     % \mathop {\max_{i=1,\dots F}}_{j=1,\dots,N}
      % (\overbrace{P_{norm}(S_{ij})}^{\text{\textcolor{blue}{Maximize}}} -
      % \overbrace{E_{norm}(S_{ij})}^{\text{\textcolor{blue}{Minimize}}} )
      %\end{equation}
    % \end{block}  
%\end{frame}
   
 
%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 28    %%
%%%%%%%%%%%%%%%%%%%%
 %\begin{frame}{The scaling algorithm for heter. cluster}

 %\centering
   %\includegraphics[width=.52\textwidth]{algo-heter}
 %\end{frame}
 
 
 %%%%%%%%%%%%%%%%%%%%
%%    SLIDE 29    %%
%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{The scaling algorithm for heter. cluster}
 \vspace{-0.77cm}
 \centering
 
  \begin{figure}
  \animategraphics[autopause,controls,scale=0.3,buttonsize=0.2cm]{10}{dvfs-heter/a-}{0}{836}
 % \includegraphics[width=0.6\textwidth]{dvfs-heter/a-650}
  \end{figure}
\end{frame}




%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 30    %%
%%%%%%%%%%%%%%%%%%%%
%\begin{frame}{Experiments over a heterogeneous cluster  }   
      %  \begin{itemize}
        % \small
          % \item The experiments were executed on the simulator SimGrid/SMPI v3.10.\medskip
          % \item The scaling algorithm was applied to the NAS parallel benchmarks class C.\medskip
          % \item Four types of processors with different computing powers were used.\medskip
          % \item The benchmarks were executed with different number of nodes ranging from 4 to 144 nodes.\medskip
          % \item It was assumed that the total power consumption of the CPU consist of 80\% dynamic power and 20\% static power.
                 % \medskip
         
        %\end{itemize}

%\end{frame}  


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 31    %%
%%%%%%%%%%%%%%%%%%%%
%\begin{frame}{The simulation results}
  % \vspace{-5 mm}
  % \begin{figure}[!t]
   %\centering
    %\includegraphics[width=0.8\textwidth]{c2/energy_saving.pdf}
    
   % \textcolor{blue}{On average, it reduces the energy consumption by \textcolor{red}{29\%} 
     %for the class C of the NAS Benchmarks executed over 8 nodes}
    
  % \end{figure}
%\end{frame} 
 
 
 
%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 32    %%
%%%%%%%%%%%%%%%%%%%%
%\begin{frame}{The simulation results}
 %  \vspace{-5 mm}
  % \begin{figure}[!t]
  % \centering
    
   % \includegraphics[width=.8\textwidth]{c2/perf_degra.pdf}
   
  % \textcolor{blue}{On average, it degrades  by \textcolor{red}{3.8\%} the performance
    % of NAS Benchmarks class C executed over 8 nodes}
  %   \end{figure}
%\end{frame} 
 
 
 





%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 35    %%
%%%%%%%%%%%%%%%%%%%%
%\begin{frame}{Energy optimization of grid platform} 
  % \begin{figure}[!t]
   % \centering
         %    \includegraphics[width=.6\textwidth]{c2/grid5000.pdf}
             
        %   \small  10 sites distributed over France and Luxembourg
        %\end{figure}
%\end{frame} 


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 36    %%
%%%%%%%%%%%%%%%%%%%%
%\begin{frame}{The grid architecture}
%\begin{center}
%\includegraphics[width=.8\textwidth]{c2/init_freq.pdf}
%\end{center}

 %\begin{frame}{Performance, Energy and trade-off models} \small
  %\begin{block}{\small The performance model of grid}
   % \begin{equation}
  %\label{eq:perf}
  %\Tnew = \mathop{\max_{i=1,\dots N}}_{j=1,\dots,M_i}({\TcpOld[ij]} \cdot S_{ij}) 
 % +\mathop{\min_{j=1,\dots,M_h}}  (\Tcm[hj])
%\end{equation}
    %\end{block}   
 
 
 %\begin{block}{\small The energy model of grid}\small
  %  \begin{equation}
  %\label{eq:energy}
 %E = \sum_{i=1}^{N} \sum_{i=1}^{M_i} {(S_{ij}^{-2} \cdot \Pd[ij] \cdot  \Tcp[ij])} +  
% \sum_{i=1}^{N} \sum_{j=1}^{M_i} (\Ps[ij] \cdot \Tnew)
%\end{equation}
   % \end{block}  

%\begin{block}{\small The trade-off model of grid}
%\small
    %\begin{equation}
   %\label{eq:max}
  %\MaxDist =
  %\mathop{  \mathop{\max_{i=1,\dots N}}_{j=1,\dots,M_i}}_{k=1,\dots,F_j}
   %   (\overbrace{\Pnorm(S_{ijk})}^{\text{Maximize}} -
    %   \overbrace{\Enorm(S_{ijk})}^{\text{Minimize}} )
%\end{equation}
   % \end{block}  
     
     
 %\end{frame}
  
  
  
%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 37    %%
%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{Experiments over Grid'5000}
 
   \textcolor{blue}{The experiments were conducted using three 
          clusters distributed over one or two sites.}
           \vspace{-7 mm}
          \begin{center}
          \includegraphics[width=.5\textwidth]{c2/grid5000-2.pdf}
          \end{center}          
      \vspace{-10 mm}
  \textcolor{blue}{Grid'5000 power measurement tools were used.} 
        \vspace{-9 mm}
  \begin{center}
          \includegraphics[width=.5\textwidth]{c2/power_consumption.pdf}
          \end{center}
          
      
\end{frame}   




%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 38    %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Experiments over Grid'5000}

   \begin{minipage}{0.4\textwidth}
       %\textcolor{blue}{Execution the NAS class D on 16 nodes saves the energy by  
        %\textcolor{red}{30\%}}
     \small \textcolor{blue}{The average energy saving =  \textcolor{red}{30\%}}
   \end{minipage}  
     \begin{minipage}{0.55\textwidth}
        \begin{figure}[h!]
          \includegraphics[width=0.83 \textwidth]{c2/eng_s.eps}
     \end{figure}
\end{minipage}

         \begin{minipage}{0.4\textwidth}
           %\textcolor{blue}{Execution the NAS class D on 16 nodes degrades the 
                %performance by \textcolor{red}{3.2\%}}
      \small  \textcolor{blue}{The average performance degradation  =  \textcolor{red}{3.2\%}}  
        \end{minipage}
       \begin{minipage}{0.55\textwidth}
         \begin{figure}[h!] 
           \includegraphics[width=.83\textwidth]{c2/per_d.eps}
         \end{figure}  
          \end{minipage}
 \end{frame}



%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 33    %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{The results of the three power scenarios}
   \vspace{-5 mm}
   \begin{figure}[!t]
   \centering
   \includegraphics[width=.45\textwidth]{c2/eng_pow.eps}
   \hspace{0.3cm}
   \includegraphics[width=.45\textwidth]{c2/per_pow.eps}
   \vspace{4 mm}
   \includegraphics[width=.7\textwidth]{c2/three_scenarios.pdf}
   \end{figure}
\end{frame}  







%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 39    %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{One core and Multi-cores per node results}
   %\textcolor{blue}{One core  and Multi-cores per node results:}
   
  \begin{figure}[h!] 
  \includegraphics[width=.48\textwidth]{c2/eng_s_mc.eps}
  \hspace{0.3cm}
  \includegraphics[width=.48\textwidth]{c2/per_d_mc.eps}
  \end{figure} 
  
  \centering \small \textcolor{blue}{Using multi-cores per node scenario decreases the computations to communications ratio}.
\end{frame}


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 34    %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Comparing the objective function to EDP}
     
     EDP is the product between the energy consumption and the delay \tiny\textsuperscript{3}.
    \vspace{-5 mm}
    \begin{figure}[!t]
    \centering
    \includegraphics[width=.6\textwidth]{c2/edp_dist.eps}
    
  
    \end{figure}
    
  \tiny  \textsuperscript{3} Spiliopoulos et al, Green governors: A framework for continuously adaptive dvfs, in International Green Computing Conference and Workshops (IGCC), 2011.
\end{frame} 
%\begin{frame}{Summary}
%\begin{itemize}
     % \small
        % \item  Two scaling algorithm were applies to \textcolor{blue}{heterogeneous %cluster} and \textcolor{blue}{grid}.
        % \item  A new \textcolor{blue}{energy} and \textcolor{blue}{performance} models were proposed.
      %   \item  The experimental results ere conducted over \textcolor{blue}{SimGrid}  simulators and real 
          %test-bed \textcolor{blue}{Grid'5000}.
         
         %\item The algorithm saves the energy by \textcolor{blue}{29\%} and only
        %  degrades the performance by \textcolor{blue}{3.8\%} for simulated  heterogeneous
      %    clusters.
         
         %\item The algorithm saves the energy by \textcolor{blue}{30\%} and only
        % degrades the performance by \textcolor{blue}{3.2\%} for  Grid'5000 results.
         
       %  \item  The proposed method \textcolor{blue}{outperforms the EDP method} in terms of  energy-performance ratio.
     %    \end{itemize}   
%\end{frame}


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 40    %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{The third contribution}
\section{\small {Energy optimization of asynchronous applications}}
\begin{center}
\bf  \Large \textcolor{blue}{Energy optimization of asynchronous iterative message passing  applications}
\end{center}
 \end{frame}



%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 41   %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Problem definition}\vspace{0.8 mm}
\textcolor{blue}{The execution of a synchronous parallel iterative application over a grid }
\vspace{-8 mm}
\begin{figure}
 \animategraphics[autopause,controls,scale=0.26,buttonsize=0.2cm]{10}{syn/a-}{0}{647}
 %\includegraphics[width=0.6\textwidth]{syn/a-503}
  \end{figure}
\end{frame}



%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 42   %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Problem definition}\vspace{0.8 mm}
\textcolor{blue}{The execution of an asynchronous parallel iterative application over a grid }
\vspace{-8 mm}
\begin{figure}
 \animategraphics[autopause,controls,scale=0.26,buttonsize=0.2cm]{10}{asyn/a-}{0}{556}
 %\includegraphics[width=0.6\textwidth]{asyn/a-440}
  \end{figure}
\end{frame}



%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 43   %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Solution}\vspace{0.8mm}
\textcolor{blue}{Using asynchronous communications with DVFS }
\vspace{-8 mm}
\begin{figure}
  \animategraphics[autopause,controls,scale=0.26,buttonsize=0.2cm]{10}{asyn+dvfs/a-}{0}{344}
  %\includegraphics[width=0.6\textwidth]{asyn+dvfs/a-314}
  \end{figure}
\end{frame}




%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 44   %%
%%%%%%%%%%%%%%%%%%%%
%\begin{frame}{The performance models}

%\begin{block}{\small The performance model of Asynch. Applications}\small
%\begin{equation}
  %\label{eq:asyn_time}
 %\Tnew =  \frac{\sum_{i=1}^{N} \sum_{j=1}^{M_i}({\TcpOld[ij]} \cdot S_{ij})} {N  \cdot M_i }
%\end{equation}
%\end{block}


%\begin{block}{\small The performance model of Hybrid Applications}\small
%\begin{equation}
  %\label{eq:asyn_perf}
  %\Tnew =  \frac{\sum_{i=1}^{N} (\max_{j=1,\dots, M_i} ({\TcpOld[ij]} \cdot S_{ij}) +  
   %\min_{j=1,\dots,M_i} ({\Ltcm[ij]}))}{N}
%\end{equation}
%\end{block}


%\end{frame}



%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 45   %%
%%%%%%%%%%%%%%%%%%%%
%\begin{frame}{The energy consumption models}

%\begin{block}{\small The energy model of Asynch. Applications}\small
%\begin{equation}
  %\label{eq:asyn_energy1}
% E = \sum_{i=1}^{N} \sum_{j=1}^{M_i} {(S_{ij}^{-2} \cdot  \Tcp[ij] \cdot (\Pd[ij]+\Ps[ij]) )} 
%\end{equation} 
%\end{block}


%\begin{block}{\small The energy model of Hybrid Applications}\small
%\begin{multline}
  %\label{eq:asyn_energy}
 %E = \sum_{i=1}^{N} \sum_{j=1}^{M_i} {(S_{ij}^{-2} \cdot \Pd[ij] \cdot  \Tcp[ij])} +  \sum_{i=1}^{N} \sum_{j=1}^{M_i} (\Ps[ij] \cdot \\
% ( \mathop{\max_{j=1,\dots,M_i}} ({\Tcp[ij]} \cdot S_{ij}) + \mathop{\min_{j=1,\dots,M_i}} ({\Ltcm[ij]}))) 
%\end{multline}
%\end{block}
%\end{frame}



%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 44   %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{The performance and the energy models }

\centering
\includegraphics[width=0.9\textwidth]{syn-vs-asyn.pdf}
\end{frame}





%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 46   %%
%%%%%%%%%%%%%%%%%%%%
%\begin{frame}{The scaling algorithm for Asynch.  applications}
%\vspace{-0.1 mm}
%\centering
%\includegraphics[width=0.55\textwidth]{algo-hybrid.pdf}
%\end{frame}



%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 47   %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{The experiments}
   \vspace{-5 mm}
   \begin{figure}[!t]
   \begin{itemize}
      \small
        \item The architecture of the grid:
   \end{itemize}
    \includegraphics[width=0.5\textwidth]{c3/hybrid-model.pdf} 
   \end{figure}
   \begin{itemize}
      \small
        \item Applying the proposed algorithm to the asynchronous iterative message passing multi-splitting method.
        \item Evaluating the application over the simulator and Grid'5000.
   \end{itemize}
\end{frame} 



%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 48   %%
%%%%%%%%%%%%%%%%%%%%
%\begin{frame}{The simulation results}
%\centering \small \textcolor{blue}{The best scenario in terms of energy and performance  is %the Async. MS with Sync. DVFS}

%\centering
   % \includegraphics[scale=0.42]{c3/energy_saving.eps}

 %\centering  The average energy saving  = \textcolor{red}{22\%}
%\end{frame} 



%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 49   %%
%%%%%%%%%%%%%%%%%%%%
%\begin{frame}{The simulation results}
%\centering
   
   %  \includegraphics[scale=0.42]{c3/perf_degra.eps}
     
%\centering    The average speed-up  = \textcolor{red}{5.72\%}
%\end{frame} 



%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 50   %%
%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{The Grid'5000 results}
   \vspace{-10 mm}
   \begin{figure}[!t]
   \centering
   \hspace{-8 mm}
    \includegraphics[width=0.53\textwidth]{c3/energy-s-compare.eps}                    
    \includegraphics[width=0.53\textwidth]{c3/perf-deg-compare.eps}
   \end{figure}
    \vspace{-5 mm}
     \centering \footnotesize
     
     %\small \textcolor{blue}{The best scenario in terms of energy and performance  is the Async. MS with Sync. DVFS}
     
The average energy saving = \textcolor{red}{26.93\%}, the average speed-up =  \textcolor{red}{21.48\%}
\end{frame} 


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 51   %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{The comparison results}
 \centering
    \includegraphics[width=.5\textwidth]{c3/compare.eps}
    
    \includegraphics[width=.5\textwidth]{c3/compare_scales.eps}
\end{frame} 




%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 52  %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Conclusions}
\section{Conclusions and Perspectives}
\begin{itemize}

\small  \barrow  Three \textcolor{blue}{ new energy consumption and performance} models were proposed for synchronous or asynchronous parallel applications with iterations running over 
\textcolor{blue}{homogeneous and  heterogeneous clusters or grids}.  
      


\small \barrow \textcolor{blue}{A new objective function} to optimize both the energy consumption and the performance was proposed.

\small \barrow \textcolor{blue}{New online frequency selecting algorithms} for clusters and grids were developed.

\small \barrow The proposed algorithms were applied to the \textcolor{blue}{NAS parallel benchmarks} and \textcolor{blue}{the
Multi-splitting} method.

\small \barrow The proposed algorithms were evaluated over the \textcolor{blue}{SimGrid simulator} and over  the \textcolor{blue}{Grid'5000 testbed}.

\small  \barrow All the proposed methods were compared to either \textcolor{blue}{Rauber and Rünger's  method} or to the \textcolor{blue}{EDP objective function}.


\end{itemize}
\end{frame}



%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 53   %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Publications}

\begin{block}{\small Journal Articles }\scriptsize
\begin{enumerate}[$\lbrack$1$\rbrack$]

\item Ahmed Fanfakh, Jean-Claude Charr, Raphaël Couturier,  Arnaud Giersch. Optimizing the energy consumption of message passing applications with iterations executed over grids. \textit{Journal of Computational 
      Science}, 2016.

\item Ahmed Fanfakh, Jean-Claude Charr, Raphaël Couturier,  Arnaud Giersch. Energy Consumption Reduction for     
      Asynchronous Message Passing Applications.  \textit{Journal of Supercomputing}, 2016, (Accepted with minor revisions)
 
\end{enumerate}
\end{block}


\begin{block}{\small Conference Articles }\scriptsize

\begin{enumerate}[$\lbrack$1$\rbrack$]

\item Jean-Claude Charr, Raphaël Couturier, Ahmed Fanfakh, Arnaud Giersch. Dynamic Frequency Scaling for
      Energy Consumption Reduction in Distributed MPI Programs. \textit{ISPA 2014}, pp.
      225-230. IEEE Computer Society, Milan, Italy (2014).

\item Jean-Claude Charr, Raphaël Couturier, Ahmed Fanfakh, Arnaud Giersch. Energy Consumption Reduction
      with DVFS for Message Passing Iterative Applications on Heterogeneous Architectures.
      \textit{The $16^{th}$ PDSEC}. pp. 922-931. IEEE Computer Society, INDIA (2015).

\item Ahmed Fanfakh, Jean-Claude Charr, Raphaël Couturier,  Arnaud Giersch. CPUs Energy Consumption
      Reduction for Asynchronous Parallel Methods Running over Grids. \textit{The $19^{th}$ CSE conference}. IEEE Computer Society, 
      Paris (2016).  

\end{enumerate}

\end{block}
\end{frame}


%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 54   %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Perspectives}

\begin{itemize}

\small  \barrow The proposed algorithms should  take into consideration the
\textcolor{blue}{variability between some iterations}.

\small  \barrow The proposed algorithms should be applied to \textcolor{blue}{other message passing methods with iterations} in order to see how they adapt to the characteristics of these methods.

\small \barrow The proposed algorithms for heterogeneous platforms should be applied to heterogeneous platforms composed of \textcolor{blue}{CPUs and GPUs}.

\small \barrow Comparing the results returned by the energy models to the values given by  \textcolor{blue}{real instruments that measure the energy consumptions} of CPUs during the execution time.
\small \barrow  Considering the power consumed by the other devices in the node such as 
\textcolor{blue}{the memory and the hard drive}  in the energy consumption model.

\end{itemize}

\end{frame}

%%%%%%%%%%%%%%%%%%%%
%%    SLIDE 55  %%
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Fin} \vspace{-10 mm}

            \centering \Large \textcolor{blue}{Thank you for your attention}
            
            \vspace{2cm}
            \centering \textcolor{blue}{ {\Large Questions?}}
        
\end{frame}
\end{document}
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