corrections

[mpi-energy2.git] / mpi-energy2-extension / Heter_paper.tex

diff --git a/mpi-energy2-extension/Heter_paper.tex b/mpi-energy2-extension/Heter_paper.tex
index 4b55dd4cd78b3fc0e5923d96b3f0d021c8973aef..9108cb1280e4f0c9757839a22b1761a96d5bc9e5 100644 (file)
--- a/mpi-energy2-extension/Heter_paper.tex
+++ b/mpi-energy2-extension/Heter_paper.tex
@@ -392,16 +392,19 @@ where $N$ is the number of  clusters in the grid, $M_i$ is the number of  nodes
 and $\Tcm[hj]$ is the communication time of processor $j$ in the cluster $h$ during the 
 first  iteration.  The execution time for one iteration is equal to the sum of the maximum computation time for all nodes with the new scaling factors
 and the  communication time of the slowest node without slack time during one iteration.
 and $\Tcm[hj]$ is the communication time of processor $j$ in the cluster $h$ during the 
 first  iteration.  The execution time for one iteration is equal to the sum of the maximum computation time for all nodes with the new scaling factors
 and the  communication time of the slowest node without slack time during one iteration.

- The slowest node $h$ is the node which takes the  maximum execution time to execute an iteration  before scaling down its  frequency.
+The slowest node in cluster $h$ is the node which takes the  maximum execution time to execute an iteration  before scaling down its  frequency.

 It means that only the communication time without any slack time is taken into account.
 Therefore, the execution time of the  application is equal to
 the execution time of one iteration as in Equation (\ref{eq:perf}) multiplied by the
 number of iterations of that application.
 
 It means that only the communication time without any slack time is taken into account.
 Therefore, the execution time of the  application is equal to
 the execution time of one iteration as in Equation (\ref{eq:perf}) multiplied by the
 number of iterations of that application.
 

-This prediction model is developed from the model to predict the execution time
-of message passing distributed applications for homogeneous and heterogeneous clusters
-~\cite{Our_first_paper,pdsec2015}. \textcolor{blue}{where the homogeneous cluster predication model was used one scaling factor denoted as $S$, because all the nodes in the cluster have the same computing powers. Whereas, in heterogeneous cluster prediction model all the nodes have different scales and the scaling factors have denoted as one dimensional vector $(S_1, S_2, \dots, S_N)$. The execution time prediction model for a grid Equation \ref{eq:perf} defines a two dimensional array of scales  
-$(S_{11}, S_{12},\dots, S_{NM_i})$}. This model is used in the method to optimize both the energy consumption and the performance of iterative methods, which is presented in the following sections.
+This model is an adaptation of the one developed in ~\cite{Our_first_paper}  which predicts the execution time
+of message passing  applications with iterations running on homogeneous clusters. 
+In a  homogeneous cluster only one scaling factor denoted as $S$ was used because all the nodes in the cluster have the same computing power.
+In a heterogeneous cluster, each node may have a different scaling factor denoted as  $(S_i)$ where $i$ is the index of the node. In a grid, each node in each cluster may have a scaling factor. The whole set of scaling factors of all the computing nodes in the grid  is denoted by a two dimensional array of scales  
+$(S_{11}, S_{12},\dots, S_{NM_i})$ where $N$ is the number of used clusters and $M_i$ is the number of nodes in cluster $i$.  
+
+The execution time model, Equation \ref{eq:perf}, is used in the algorithm presented in section \ref{sec.optim}. The latter selects the scaling factors that optimize both the energy consumption and the performance of message passing applications with iterations running on grids.

 
 
 \subsection{Energy model for heterogeneous grid platform}
 
 
 \subsection{Energy model for heterogeneous grid platform}


@@ -488,9 +491,9 @@ processor after scaling its frequency is computed as follows:
 
 In the considered heterogeneous grid platform, each node $j$ in cluster $i$ may have
 different dynamic and static powers from the nodes of the other clusters, 
 
 In the considered heterogeneous grid platform, each node $j$ in cluster $i$ may have
 different dynamic and static powers from the nodes of the other clusters, 

-noted as $\Pd[ij]$ and $\Ps[ij]$ respectively.  \textcolor{blue}{Therefore, even if the distributed 
-message passing  application \textcolor{blue}{with iterations} is load balanced, the computation time of each CPU $j$ 
-in cluster $i$ noted $\Tcp[ij]$ may be slightly different due to the delay caused by the scheduler of the operating system}. Therefore, different frequency scaling factors may be
+noted as $\Pd[ij]$ and $\Ps[ij]$ respectively.  Moreover, even if the distributed 
+message passing  application with iterations is load balanced, the computation time of each CPU $j$ in cluster $i$
+ noted $\Tcp[ij]$ may be slightly different due to the delay caused by the scheduler of the operating system. Therefore, different frequency scaling factors may be

 computed in order to decrease the overall energy consumption of the application
 and reduce the slack times.  The communication time of a processor $j$ in cluster $i$ is noted as
 $\Tcm[ij]$ and could contain slack times when communicating with slower nodes,
 computed in order to decrease the overall energy consumption of the application
 and reduce the slack times.  The communication time of a processor $j$ in cluster $i$ is noted as
 $\Tcm[ij]$ and could contain slack times when communicating with slower nodes,


@@ -499,8 +502,8 @@ 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 one iteration multiplied by the static power of each processor. 
 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 one iteration multiplied by the static power of each processor. 

-\textcolor{blue}{ The CPU during the communication times consumes only the static power. While 
-in the computation times, it consumes both the dynamic and the static power refer to \cite{Freeh_Exploring.the.Energy.Time.Tradeoff}.} 
+ The CPU during the communication times consumes only the static power. While 
+in the computation times, it consumes both the dynamic and the static powers, for more information refer to \cite{Freeh_Exploring.the.Energy.Time.Tradeoff}.

 The overall energy consumption of a message passing distributed application executed over a
 heterogeneous grid platform during one iteration is the summation of all dynamic and
 static energies for $M_i$ processors in $N$ clusters.  It is computed as follows:
 The overall energy consumption of a message passing distributed application executed over a
 heterogeneous grid platform during one iteration is the summation of all dynamic and
 static energies for $M_i$ processors in $N$ clusters.  It is computed as follows:


@@ -509,7 +512,7 @@ static energies for $M_i$ processors in $N$ clusters.  It is computed as follows
  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 {} \\
   (\mathop{\max_{i=1,\dots N}}_{j=1,\dots,M_i}({\Tcp[ij]} \cdot S_{ij}) 
  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 {} \\
   (\mathop{\max_{i=1,\dots N}}_{j=1,\dots,M_i}({\Tcp[ij]} \cdot S_{ij}) 

-  +\mathop{\min_{j=1,\dots M_i}} (\Tcm[hj]) ))
+  +\mathop{\min_{j=1,\dots M_h}} (\Tcm[hj]) ))

 \end{multline}
 
 
 \end{multline}
 
 


@@ -517,7 +520,7 @@ Reducing the frequencies of the processors according to the vector of scaling
 factors $(S_{11}, S_{12},\dots, S_{NM_i})$ 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}. The overall energy consumption
 factors $(S_{11}, S_{12},\dots, S_{NM_i})$ 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}. The overall energy consumption

-for the  application \textcolor{blue}{with iterations} can be measured by measuring the energy
+for a synchronous  application with iterations can be measured by measuring the energy

 consumption for one iteration as in (\ref{eq:energy}) multiplied by the number
 of iterations of that application.
 
 consumption for one iteration as in (\ref{eq:energy}) multiplied by the number
 of iterations of that application.
 


@@ -542,7 +545,7 @@ works, \cite{Our_first_paper} and \cite{pdsec2015}, two methods that select the
 frequency scaling factors for a homogeneous and a heterogeneous cluster respectively, were proposed. 
 Both methods selects the frequencies that gives the best trade-off between 
 energy consumption reduction and performance for  message passing
 frequency scaling factors for a homogeneous and a heterogeneous cluster respectively, were proposed. 
 Both methods selects the frequencies that gives the best trade-off between 
 energy consumption reduction and performance for  message passing

- synchronous applications \textcolor{blue}{with iterations}.   In this work we
+ synchronous applications with iterations.   In this work we

 are interested in grids that are composed of heterogeneous clusters. The nodes from distinct clusters may have 
  different characteristics such  as  dynamic power, static power, computation power, 
 frequencies range, network latency and bandwidth. 
 are interested in grids that are composed of heterogeneous clusters. The nodes from distinct clusters may have 
  different characteristics such  as  dynamic power, static power, computation power, 
 frequencies range, network latency and bandwidth. 


@@ -565,13 +568,13 @@ maximum frequency for all nodes) as follows:
 \end{equation}
 %
 where $Tnew$ is computed as in (\ref{eq:perf}) and $Told$ is computed as in (\ref{eq:told}).
 \end{equation}
 %
 where $Tnew$ is computed as in (\ref{eq:perf}) and $Told$ is computed as in (\ref{eq:told}).

-\textcolor{blue}{
+

 \begin{equation}
   \label{eq:told}
    \Told = \mathop{\max_{i=1,\dots N}}_{j=1,\dots,M_i}({\TcpOld[ij]} ) 
   +\mathop{\min_{j=1,\dots,M_h}}  (\Tcm[hj])    
 \end{equation}
 \begin{equation}
   \label{eq:told}
    \Told = \mathop{\max_{i=1,\dots N}}_{j=1,\dots,M_i}({\TcpOld[ij]} ) 
   +\mathop{\min_{j=1,\dots,M_h}}  (\Tcm[hj])    
 \end{equation}

-}
+

 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:
 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:


@@ -593,13 +596,13 @@ computed as in (\ref{eq:eorginal}).
 While the main goal is to optimize the energy and execution time at the same
 time, the normalized energy and execution time curves do not evolve (increase/decrease) in the same way. 
 According to (\ref{eq:pnorm}) and (\ref{eq:enorm}), the
 While the main goal is to optimize the energy and execution time at the same
 time, the normalized energy and execution time curves do not evolve (increase/decrease) in the same way. 
 According to (\ref{eq:pnorm}) and (\ref{eq:enorm}), the

-vector of frequency scaling factors $S_1,S_2,\dots,S_N$ reduces both the energy
+vector of frequency scaling factors $S_{11},S_{12},\dots,S_{NM_i}$ reduces both the energy

 and the execution time,  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
 execution time follow the same evolution according to the vector of scaling factors
 and the execution time,  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
 execution time follow the same evolution according to the vector of scaling factors

-$(S_{11}, S_{12},\dots, S_{NM})$. Therefore, the equation of the
+$(S_{11}, S_{12},\dots, S_{NM_i})$. Therefore, the equation of the

 normalized execution time is inverted which gives the normalized performance
 equation, as follows:
 \begin{equation}
 normalized execution time is inverted which gives the normalized performance
 equation, as follows:
 \begin{equation}


@@ -709,11 +712,11 @@ in~\cite{Zhuo_Energy.efficient.Dynamic.Task.Scheduling,Rauber_Analytical.Modelin
 
 
 In this section, the scaling factors selection algorithm for  grids, Algorithm~\ref{HSA}, 
 
 
 In this section, the scaling factors selection algorithm for  grids, Algorithm~\ref{HSA}, 

-is presented. It selects the vector of the frequency
+is presented. It selects the vector of  frequency

 scaling factors  that gives the best trade-off between minimizing the
 energy consumption and maximizing the performance of a message passing
 scaling factors  that gives the best trade-off between minimizing the
 energy consumption and maximizing the performance of a message passing

-synchronous  application \textcolor{blue}{with iterations} executed on a  grid. It works
-online during the execution time of the  message passing program \textcolor{blue}{with iterations}.  It
+synchronous  application with iterations executed on a  grid. It works
+online during the execution time of the  application.  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
 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


@@ -721,7 +724,7 @@ scaling factors that satisfies the objective 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
 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  MPI program \textcolor{blue}{with iterations}.
+scaling algorithm is called in the application.

 
 \begin{figure}[!t]
   \centering
 
 \begin{figure}[!t]
   \centering


@@ -851,9 +854,7 @@ selected clusters and are presented in Table~\ref{table:grid5000}.
 
 
 The energy model and the scaling factors selection algorithm were applied to the NAS parallel benchmarks v3.3 \cite{NAS.Parallel.Benchmarks} and evaluated over Grid'5000.
 
 
 The energy model and the scaling factors selection algorithm were applied to the NAS parallel benchmarks v3.3 \cite{NAS.Parallel.Benchmarks} and evaluated over Grid'5000.

-The benchmark suite contains seven applications: CG, MG, EP, LU, BT, SP and FT. \textcolor{blue}{These benchmarks are message passing  applications with iterations compute
-the same block of operations several times, starting from the initial solution until reaching
-the acceptable approximation of the exact solution.}
+The benchmark suite contains seven applications: CG, MG, EP, LU, BT, SP and FT. These benchmarks are considered as message passing  applications with iterations because the same block of operations is executed many times.

  These applications have different computations and communications ratios and strategies which make them good testbed applications to evaluate the proposed algorithm and energy model.
 The benchmarks have seven different classes, S, W, A, B, C, D and E, that represent the size of the problem that the method solves. In the next sections, the  class D was used for all the benchmarks in all the experiments. 
 
  These applications have different computations and communications ratios and strategies which make them good testbed applications to evaluate the proposed algorithm and energy model.
 The benchmarks have seven different classes, S, W, A, B, C, D and E, that represent the size of the problem that the method solves. In the next sections, the  class D was used for all the benchmarks in all the experiments. 
 


@@ -894,9 +895,7 @@ The benchmarks have seven different classes, S, W, A, B, C, D and E, that repres
 \subsection{The experimental results of the scaling algorithm}
 \label{sec.res}
 In this section, the results of the application of the scaling factors selection algorithm \ref{HSA} 
 \subsection{The experimental results of the scaling algorithm}
 \label{sec.res}
 In this section, the results of the application of the scaling factors selection algorithm \ref{HSA} 

-to the NAS parallel benchmarks are presented. \textcolor{blue}{Each experiment of this section and next sections has been executed many times and the results presented in the figures are the average values of many execution.}
-
-As mentioned previously, the experiments 
+to the NAS parallel benchmarks are presented. Each experiment  has been executed many times and the results presented in the figures are the average values of many executions. As mentioned previously, the experiments 

 were conducted over two sites of Grid'5000,  Lyon and Nancy sites. 
 Two scenarios were considered while selecting the clusters from these two sites :
 \begin{itemize}
 were conducted over two sites of Grid'5000,  Lyon and Nancy sites. 
 Two scenarios were considered while selecting the clusters from these two sites :
 \begin{itemize}


@@ -961,7 +960,7 @@ The overall energy consumption of all the benchmarks solving the class D instanc
 using the proposed frequency selection algorithm is measured 
 using the equation of the reduced energy consumption, Equation~\ref{eq:energy}. This model uses the measured dynamic power showed in Table~\ref{table:grid5000}
 and the static 
 using the proposed frequency selection algorithm is measured 
 using the equation of the reduced energy consumption, Equation~\ref{eq:energy}. This model uses the measured dynamic power showed in Table~\ref{table:grid5000}
 and the static 

-power is assumed to be equal to 20\% of the dynamic power \textcolor{blue}{as in \cite{Rauber_Analytical.Modeling.for.Energy}}. The execution
+power is assumed to be equal to 20\% of the dynamic power as in \cite{Rauber_Analytical.Modeling.for.Energy}. The execution

 time is measured for all the benchmarks over these different scenarios.  
 
 The energy consumptions  and the execution times for all the benchmarks are 
 time is measured for all the benchmarks over these different scenarios.  
 
 The energy consumptions  and the execution times for all the benchmarks are 


@@ -1034,7 +1033,7 @@ nodes when the communications occur in high speed network does not decrease the
 communication ratio. 
 
 The performance degradation percentage of the EP benchmark after applying the scaling factors selection algorithm is the highest in comparison to 
 communication ratio. 
 
 The performance degradation percentage of the EP benchmark after applying the scaling factors selection algorithm is the highest in comparison to 

-the other benchmarks. Indeed, in the EP benchmark, there are no communication and slack times and its 
+the other benchmarks. Indeed, in the EP benchmark, there are no communication and no slack times and its 

 performance degradation percentage only depends on the frequencies values selected by the algorithm for the computing nodes.
 The rest of the benchmarks showed different performance degradation percentages which decrease
 when the communication times increase and vice versa.
 performance degradation percentage only depends on the frequencies values selected by the algorithm for the computing nodes.
 The rest of the benchmarks showed different performance degradation percentages which decrease
 when the communication times increase and vice versa.


@@ -1099,7 +1098,7 @@ Scenario name                          & Cluster name & Nodes per cluster &
 
 The execution times for most of  the NAS  benchmarks are higher over the multi-core per node scenario 
 than over the single core per node  scenario. Indeed,  
 
 The execution times for most of  the NAS  benchmarks are higher over the multi-core per node scenario 
 than over the single core per node  scenario. Indeed,  

- the communication times  are higher in the one site multi-core scenario than in the latter scenario because all the cores of a node  share  the same node network link which can be  saturated when running communication bound applications. Moreover, the cores of a node share the memory bus which can be also saturated and become a bottleneck.    
+ the communication times  are higher in the  multi-core scenario than in the latter scenario because all the cores of a node  share  the same node network link which can be  saturated when running communication bound applications. Moreover, the cores of a node share the memory bus which can be also saturated and become a bottleneck.    

 Moreover, the energy consumptions of the NAS benchmarks are lower over the 
  one core scenario  than over the multi-core scenario because 
 the first scenario had less execution time than the latter which results in less static energy being consumed.
 Moreover, the energy consumptions of the NAS benchmarks are lower over the 
  one core scenario  than over the multi-core scenario because 
 the first scenario had less execution time than the latter which results in less static energy being consumed.


@@ -1243,9 +1242,9 @@ This paper presents a new online frequencies selection algorithm.
  The algorithm selects the best vector of 
 frequencies that maximizes  the trade-off distance 
 between the predicted energy consumption and the predicted execution time of the distributed 
  The algorithm selects the best vector of 
 frequencies that maximizes  the trade-off distance 
 between the predicted energy consumption and the predicted execution time of the distributed 

- applications \textcolor{blue}{with iterations} running over a heterogeneous grid. A new energy model 
+ applications with iterations running over a heterogeneous grid. A new energy model 

 is used by the proposed algorithm to predict the energy consumption 
 is used by the proposed algorithm to predict the energy consumption 

-of the distributed  message passing application \textcolor{blue}{with iterations} running over a grid architecture.
+of the application.

 To evaluate the proposed method on a real heterogeneous grid platform, it was applied on the  
 NAS parallel benchmarks   and the  class D instance was executed over the  Grid'5000 testbed platform. 
 The experiments executed on 16 nodes, distributed over three clusters, showed that the algorithm   on average reduces by 30\% the energy consumption
 To evaluate the proposed method on a real heterogeneous grid platform, it was applied on the  
 NAS parallel benchmarks   and the  class D instance was executed over the  Grid'5000 testbed platform. 
 The experiments executed on 16 nodes, distributed over three clusters, showed that the algorithm   on average reduces by 30\% the energy consumption


@@ -1256,19 +1255,19 @@ Finally, the proposed algorithm was compared to another method that uses
 the well known energy and delay product as an objective function. The comparison results showed 
 that the proposed algorithm outperforms the latter by selecting a vector of frequencies that gives a better trade-off  between energy consumption reduction and performance. 
 
 the well known energy and delay product as an objective function. The comparison results showed 
 that the proposed algorithm outperforms the latter by selecting a vector of frequencies that gives a better trade-off  between energy consumption reduction and performance. 
 

-In the near future, \textcolor{blue}{we will adapt the proposed algorithm to take the variability between some iterations in two steps. In the first step,  the algorithm selects the best frequencies at the end of the first iterations and apply them to the system. In the second step, after some iterations (e.g. 5 iterations) the algorithm recomputes the frequencies depending on the average of the communication and computation times  for all  previous iterations. It will change the frequency of each node if the new frequency is different from the old one. Otherwise, it keeps the old frequency.} 
-Also, we would like to develop a similar method that is adapted to
-asynchronous  applications \textcolor{blue}{with iterations} where iterations are not synchronized and communications are overlapped with computations. 
+In the near future, we will adapt the proposed algorithm to take into consideration the variability between some iterations.  For example, the proposed algorithm can be executed twice: after the first iteration the frequencies are scaled down according to the execution times measured in the first iteration, then after a fixed number of iterations, the frequencies are adjusted according to the execution times measured during the fixed number of iterations. If the  computing power of the system is constantly changing, it would be interesting to implement a mechanism that detects this change and adjusts the frequencies according to the variability of the system. We would like also to develop a similar method that is adapted to
+asynchronous  applications with iterations where iterations are not synchronized and communications are overlapped with computations. 

 The development of such a method might require a new energy model because the
 number of iterations is not known in advance and depends on
 The development of such a 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.
+the global convergence of the iterative system. Finally, it would be interesting to evaluate the scalability of the proposed algorithm by running it on large platforms composed of many thousands of cores. The scalability of the algorithm can be improved by distributing it  in a hierarchical manner where a leader is chosen for each cluster or a group of nodes  to compute their scaled frequencies and by using asynchronous messages to exchange the the data measured at the first iteration. 

 
 
 
 \section*{Acknowledgment}
 
 This work  has been  partially supported by  the Labex ACTION  project (contract
 
 
 
 \section*{Acknowledgment}
 
 This work  has been  partially supported by  the Labex ACTION  project (contract

-``ANR-11-LABX-01-01'').  Computations  have been performed  on the Grid'5000 platform. As  a  PhD student,
+``ANR-11-LABX-01-01'').  Computations  have been performed  on the Grid'5000
+platform and on the mésocentre of Franche-Comté. As  a  PhD student,

 Mr. Ahmed  Fanfakh, would  like to  thank the University  of Babylon  (Iraq) for
 supporting his work.
 
 Mr. Ahmed  Fanfakh, would  like to  thank the University  of Babylon  (Iraq) for
 supporting his work.