X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/af016b677c3b80035457ffcfea85a9809f3ee6ce..7ba4d34a63e54829b1a0d1f5fab102747429e8ff:/paper.tex?ds=inline

diff --git a/paper.tex b/paper.tex
index 59c4a67..f1247fe 100644
--- a/paper.tex
+++ b/paper.tex
@@ -77,10 +77,10 @@
 %\itshape{\journalnamelc}\footnotemark[2]}
 
 \author{Charles Emile Ramamonjisoa\affil{1},
-    David Laiymani\affil{1},
-    Arnaud Giersch\affil{1},
-    Lilia Ziane Khodja\affil{2} and
-    RaphaÃ«l Couturier\affil{1}
+  Lilia Ziane Khodja\affil{2},
+  David Laiymani\affil{1},
+  RaphaÃ«l Couturier\affil{1} and
+  Arnaud Giersch\affil{1}
 }
 
 \address{
@@ -244,60 +244,109 @@ magnitude. To our knowledge, there is no study on this problematic.
 
 \section{SimGrid}
 \label{sec:simgrid}
-SimGrid~\cite{SimGrid,casanova+legrand+quinson.2008.simgrid,casanova+giersch+legrand+al.2014.versatile} is a discrete event simulation framework to study the behavior of large-scale distributed computing platforms as Grids, Peer-to-Peer systems, Clouds and High Performance Computation systems. It is widely used to simulate and evaluate heuristics, prototype applications or even assess legacy MPI applications. It is still actively developed by the scientific community and distributed as an open source software.
 
-%%%%%%%%%%%%%%%%%%%%%%%%%
-% SimGrid~\cite{SimGrid,casanova+legrand+quinson.2008.simgrid,casanova+giersch+legrand+al.2014.versatile}
-% is a simulation framework to study the behavior of large-scale distributed
-% systems.  As its name suggests, it emanates from the grid computing community,
-% but is nowadays used to study grids, clouds, HPC or peer-to-peer systems.  The
-% early versions of SimGrid date back from 1999, but it is still actively
-% developed and distributed as an open source software.  Today, it is one of the
-% major generic tools in the field of simulation for large-scale distributed
-% systems.
-
-SimGrid provides several programming interfaces: MSG to simulate Concurrent
-Sequential Processes, SimDAG to simulate DAGs of (parallel) tasks, and SMPI to
-run real applications written in MPI~\cite{MPI}.  Apart from the native C
-interface, SimGrid provides bindings for the C++, Java, Lua and Ruby programming
-languages.  SMPI is the interface that has been used for the work described in
-this paper.  The SMPI interface implements about \np[\%]{80} of the MPI 2.0
-standard~\cite{bedaride+degomme+genaud+al.2013.toward}, and supports
-applications written in C or Fortran, with little or no modifications (cf Section IV - paragraph B).
-
-Within SimGrid, the execution of a distributed application is simulated by a
-single process.  The application code is really executed, but some operations,
-like communications, are intercepted, and their running time is computed
-according to the characteristics of the simulated execution platform.  The
-description of this target platform is given as an input for the execution, by
-means of an XML file.  It describes the properties of the platform, such as
-the computing nodes with their computing power, the interconnection links with
-their bandwidth and latency, and the routing strategy.  The scheduling of the
-simulated processes, as well as the simulated running time of the application
-are computed according to these properties.
-
-To compute the durations of the operations in the simulated world, and to take
-into account resource sharing (e.g. bandwidth sharing between competing
-communications), SimGrid uses a fluid model.  This allows users to run relatively fast
-simulations, while still keeping accurate
-results~\cite{bedaride+degomme+genaud+al.2013.toward,
-  velho+schnorr+casanova+al.2013.validity}.  Moreover, depending on the
-simulated application, SimGrid/SMPI allows to skip long lasting computations and
-to only take their duration into account.  When the real computations cannot be
-skipped, but the results are unimportant for the simulation results, it is
-also possible to share dynamically allocated data structures between
-several simulated processes, and thus to reduce the whole memory consumption.
-These two techniques can help to run simulations on a very large scale.
-
-The validity of simulations with SimGrid has been asserted by several studies.
-See, for example, \cite{velho+schnorr+casanova+al.2013.validity} and articles
-referenced therein for the validity of the network models.  Comparisons between
-real execution of MPI applications on the one hand, and their simulation with
-SMPI on the other hand, are presented in~\cite{guermouche+renard.2010.first,
-  clauss+stillwell+genaud+al.2011.single,
-  bedaride+degomme+genaud+al.2013.toward}.  All these works conclude that
-SimGrid is able to simulate pretty accurately the real behavior of the
-applications.
+In the scope of this paper, the Simgrid
+toolkitSimGrid~\cite{SimGrid,casanova+legrand+quinson.2008.simgrid,casanova+giersch+legrand+al.2014.versatile},
+an open source framework actively developped by its community, has been choosen
+to simulate the behavior of the solvers algorithms in different grid
+computational configurations. Simgrid pretends to be non-specialized in opposite
+to some other simulators which stayed to be very specific oriented-application.
+One of the well-known Simgrid advantage is its SMPI (Simulated MPI). SMPI
+purpose is to execute by simulation in a similar way as in real life, an MPI
+distributed application and to get accurate results with the detailed resources
+consumption. Several studies have demonstrated the accuracy of the simulation
+compared with execution on real physical architectures. In addition of SMPI,
+Simgrid provides other API which can be convienent for different distrbuted
+applications: computational grid applications, High Performance Computing (HPC),
+P2P but also clouds applications. In this paper we use the SMPI API. It
+implements about \np[\%]{80} of the MPI 2.0 standard and allows minor
+modifications of the initial code~\cite{bedaride+degomme+genaud+al.2013.toward}
+(see Section~\ref{sec:04.02}).
+
+
+ Provided as an input to the simulator, at least $3$ XML files describe the
+ computational grid resources: number of clusters in the grid, number of
+ processors/cores in each cluster, detailed description of the intra and inter
+ networks and the list of the hosts in each cluster (see the details in Section~\ref{sec:expe}). Simgrid uses a fluid model to simulate the program execution.
+ This gives several simulation modes which produce accurate
+ results~\cite{bedaride+degomme+genaud+al.2013.toward,
+ velho+schnorr+casanova+al.2013.validity}. For instance, the "in vivo" mode
+ really executes the computation but "intercepts" the communications (running
+ time is then evaluated according to the parameters of the simulated platform).
+ It is also possible for SimGrid/SMPI to only keep duration of large
+ computations by skipping them. Moreover the application can be run "in vitro"
+ by sharing some in-memory structures between the simulated processes and
+ thus allowing the use of very large data scale.
+
+
+The choice of Simgrid/SMPI as a simulator tool in this study has been emphasized
+by the results obtained by several studies to validate, in real environments,
+the behavior of different network models simulated in
+Simgrid~\cite{velho+schnorr+casanova+al.2013.validity}. Other studies underline
+the comparison between real MPI executions  and SimGrid/SMPI
+ones\cite{guermouche+renard.2010.first, clauss+stillwell+genaud+al.2011.single,
+bedaride+degomme+genaud+al.2013.toward}. These works show the accuracy of
+SimGrid simulations.
+
+
+
+
+
+
+% SimGrid~\cite{SimGrid,casanova+legrand+quinson.2008.simgrid,casanova+giersch+legrand+al.2014.versatile} is a discrete event simulation framework to study the behavior of large-scale distributed computing platforms as Grids, Peer-to-Peer systems, Clouds and High Performance Computation systems. It is widely used to simulate and evaluate heuristics, prototype applications or even assess legacy MPI applications. It is still actively developed by the scientific community and distributed as an open source software.
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%
+% % SimGrid~\cite{SimGrid,casanova+legrand+quinson.2008.simgrid,casanova+giersch+legrand+al.2014.versatile}
+% % is a simulation framework to study the behavior of large-scale distributed
+% % systems.  As its name suggests, it emanates from the grid computing community,
+% % but is nowadays used to study grids, clouds, HPC or peer-to-peer systems.  The
+% % early versions of SimGrid date back from 1999, but it is still actively
+% % developed and distributed as an open source software.  Today, it is one of the
+% % major generic tools in the field of simulation for large-scale distributed
+% % systems.
+%
+% SimGrid provides several programming interfaces: MSG to simulate Concurrent
+% Sequential Processes, SimDAG to simulate DAGs of (parallel) tasks, and SMPI to
+% run real applications written in MPI~\cite{MPI}.  Apart from the native C
+% interface, SimGrid provides bindings for the C++, Java, Lua and Ruby programming
+% languages.  SMPI is the interface that has been used for the work described in
+% this paper.  The SMPI interface implements about \np[\%]{80} of the MPI 2.0
+% standard~\cite{bedaride+degomme+genaud+al.2013.toward}, and supports
+% applications written in C or Fortran, with little or no modifications (cf Section IV - paragraph B).
+%
+% Within SimGrid, the execution of a distributed application is simulated by a
+% single process.  The application code is really executed, but some operations,
+% like communications, are intercepted, and their running time is computed
+% according to the characteristics of the simulated execution platform.  The
+% description of this target platform is given as an input for the execution, by
+% means of an XML file.  It describes the properties of the platform, such as
+% the computing nodes with their computing power, the interconnection links with
+% their bandwidth and latency, and the routing strategy.  The scheduling of the
+% simulated processes, as well as the simulated running time of the application
+% are computed according to these properties.
+%
+% To compute the durations of the operations in the simulated world, and to take
+% into account resource sharing (e.g. bandwidth sharing between competing
+% communications), SimGrid uses a fluid model.  This allows users to run relatively fast
+% simulations, while still keeping accurate
+% results~\cite{bedaride+degomme+genaud+al.2013.toward,
+%   velho+schnorr+casanova+al.2013.validity}.  Moreover, depending on the
+% simulated application, SimGrid/SMPI allows to skip long lasting computations and
+% to only take their duration into account.  When the real computations cannot be
+% skipped, but the results are unimportant for the simulation results, it is
+% also possible to share dynamically allocated data structures between
+% several simulated processes, and thus to reduce the whole memory consumption.
+% These two techniques can help to run simulations on a very large scale.
+%
+% The validity of simulations with SimGrid has been asserted by several studies.
+% See, for example, \cite{velho+schnorr+casanova+al.2013.validity} and articles
+% referenced therein for the validity of the network models.  Comparisons between
+% real execution of MPI applications on the one hand, and their simulation with
+% SMPI on the other hand, are presented in~\cite{guermouche+renard.2010.first,
+%   clauss+stillwell+genaud+al.2011.single,
+%   bedaride+degomme+genaud+al.2013.toward}.  All these works conclude that
+% SimGrid is able to simulate pretty accurately the real behavior of the
+% applications.
 %%%%%%%%%%%%%%%%%%%%%%%%%
 
 \section{Two-stage multisplitting methods}
@@ -581,13 +630,21 @@ convergence of the algorithm is (see the output results obtained from
 configurations 2$\times$16 vs. 4$\times$8 and configurations 4$\times$16 vs.
 8$\times$8).
 
-The execution times between both algorithms is significant with different grid architectures. The synchronous Krylov two-stage algorithm presents better performances than the GMRES algorithm, even for a high number of clusters (about $32\%$ more efficient on a grid of 8$\times$8 than GMRES). In addition, we can observe a better sensitivity of the Krylov two-stage algorithm (compared to the GMRES one) when scaling up the number of the processors in the computational grid: the Krylov two-stage algorithm is about $48\%$ and the GMRES algorithm is about $40\%$ better on 64 processors (grid of 8$\times$8) than 32 processors (grid of 2$\times$16).
+The execution times between both algorithms is significant with different grid
+architectures. The synchronous Krylov two-stage algorithm presents better
+performances than the GMRES algorithm, even for a high number of clusters (about
+$32\%$ more efficient on a grid of 8$\times$8 than GMRES). In addition, we can
+observe a better sensitivity of the Krylov two-stage algorithm (compared to the
+GMRES one) when scaling up the number of the processors in the computational
+grid: the Krylov two-stage algorithm is about $48\%$ and the GMRES algorithm is
+about $40\%$ better on $64$ processors (grid of 8$\times$8) than $32$ processors
+(grid of 2$\times$16).
 
 \begin{figure}[ht]
 \begin{center}
 \includegraphics[width=100mm]{cluster_x_nodes_nx_150_and_nx_170.pdf}
 \end{center}
-\caption{Various grid configurations with the matrix sizes 150$^3$ and 170$^3$}
+\caption{Various grid configurations with two matrix sizes: $150^3$ and $170^3$}
 \label{fig:01}
 \end{figure}
 
@@ -605,9 +662,9 @@ efficient for distributed systems with high latency networks.
 \begin{figure}[ht]
 \centering
 \includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}
-\caption{Various grid configurations with networks $N1$ vs. $N2$}
-\LZK{CE, remplacer les ``,'' des dÃ©cimales par un ``.''}
-\RCE{ok}
+\caption{Various grid configurations with two networks parameters: $N1$ vs. $N2$}
+%\LZK{CE, remplacer les ``,'' des dÃ©cimales par un ``.''}
+%\RCE{ok}
 \label{fig:02}
 \end{figure}
 
@@ -622,7 +679,15 @@ Figure~\ref{fig:03} shows the impact of the network latency on the performances
 \end{figure}
 
 \subsubsection{Network bandwidth impacts on performances\\}
-Figure~\ref{fig:04} reports the results obtained for the simulation of a grid of 2$\times$16 processors interconnected by a network of latency $lat=50\mu$s to solve a 3D Poisson problem of size $150^3$. The results of increasing the network bandwidth from 1Gbs to 10Gbs show the performances improvement for both algorithms by reducing the execution times. However, the Krylov two-stage algorithm presents a better performance in the considered bandwidth interval with a gain of $40\%$ compared to only about $24\%$ for the classical GMRES algorithm.
+
+Figure~\ref{fig:04} reports the results obtained for the simulation of a grid of
+$2\times16$ processors interconnected by a network of latency $lat=50\mu$s to
+solve a 3D Poisson problem of size $150^3$. The results of increasing the
+network bandwidth from $1$Gbs to $10$Gbs show the performances improvement for
+both algorithms by reducing the execution times. However, the Krylov two-stage
+algorithm presents a better performance gain in the considered bandwidth
+interval with a gain of $40\%$ compared to only about $24\%$ for the classical
+GMRES algorithm.
 
 \begin{figure}[ht]
 \centering
@@ -632,7 +697,18 @@ Figure~\ref{fig:04} reports the results obtained for the simulation of a grid of
 \end{figure}
 
 \subsubsection{Matrix size impacts on performances\\}
-In these experiments, the matrix size of the 3D Poisson problem is varied from $50^3$ to $190^3$ elements. The simulated computational grid is composed of 4 clusters of 8 processors each interconnected by the network $N2$ (see Table~\ref{tab:01}). Obviously, as shown in Figure~\ref{fig:05}, the execution times for both algorithms increase with increased matrix sizes.  For all problem sizes, GMRES algorithm is always slower than the Krylov two-stage algorithm. Moreover, for this benchmark, it seems that the greater the problem size is, the bigger the ratio between execution times of both algorithms is. We can also observe that for some problem sizes, the convergence (and thus the execution time) of the Krylov two-stage algorithm varies quite a lot. %This is due to the 3D partitioning of the 3D matrix of the Poisson problem.
+
+In these experiments, the matrix size of the 3D Poisson problem is varied from
+$50^3$ to $190^3$ elements. The simulated computational grid is composed of $4$
+clusters of $8$ processors each interconnected by the network $N2$ (see
+Table~\ref{tab:01}). As shown in Figure~\ref{fig:05}, the execution
+times for both algorithms increase with increased matrix sizes.  For all problem
+sizes, the GMRES algorithm is always slower than the Krylov two-stage algorithm.
+Moreover, for this benchmark, it seems that the greater the problem size is, the
+bigger the ratio between execution times of both algorithms is. We can also
+observe that for some problem sizes, the convergence (and thus the execution
+time) of the Krylov two-stage algorithm varies quite a lot.
+%This is due to the 3D partitioning of the 3D matrix of the Poisson problem.
 These findings may help a lot end users to setup the best and the optimal targeted environment for the application deployment when focusing on the problem size scale up.
 
 \begin{figure}[ht]
@@ -643,7 +719,15 @@ These findings may help a lot end users to setup the best and the optimal target
 \end{figure}
 
 \subsubsection{CPU power impacts on performances\\}
-Using the SimGrid simulator flexibility, we have tried to determine the impact of the CPU power of the processors in the different clusters on performances of both algorithms. We have varied the CPU power from $1$GFlops to $19$GFlops. The simulation is conducted in a grid of 2$\times$16 processors interconnected by the network $N2$ (see Table~\ref{tab:01}) to solve a 3D Poisson problem of size $150^3$. The results depicted in Figure~\ref{fig:06} confirm the performance gain, about $95\%$ for both algorithms, after improving the CPU power of processors.
+
+Using the SimGrid simulator flexibility, we have tried to determine the impact
+of the CPU power of the processors in the different clusters on performances of
+both algorithms. We have varied the CPU power from $1$GFlops to $19$GFlops. The
+simulation is conducted on a grid of $2\times16$ processors interconnected by
+the network $N2$ (see Table~\ref{tab:01}) to solve a 3D Poisson problem of size
+$150^3$. The results depicted in Figure~\ref{fig:06} confirm the performance
+gain, about $95\%$ for both algorithms, after improving the CPU power of
+processors.
 
 \begin{figure}[ht]
 \centering
@@ -652,11 +736,12 @@ Using the SimGrid simulator flexibility, we have tried to determine the impact o
 \label{fig:06}
 \end{figure}
 \ \\
+
 To conclude these series of experiments, with  SimGrid we have been able to make
 many simulations  with many parameters  variations. Doing all  these experiments
-with a real platform is most of  the time not possible. Moreover the behavior of
-both GMRES and  Krylov two-stage algorithms is in accordance  with larger real
-executions on large scale supercomputers~\cite{couturier15}.
+with a real platform is most of the time not possible or very costly. Moreover
+the behavior of both GMRES and  Krylov two-stage algorithms is in accordance
+with larger real executions on large scale supercomputers~\cite{couturier15}.
 
 
 \subsection{Comparison between synchronous GMRES and asynchronous two-stage multisplitting algorithms}
@@ -669,23 +754,22 @@ classical GMRES in \textit{synchronous mode}.
 
 The  interest of  using  an asynchronous  algorithm  is that  there  is no  more
 synchronization. With  geographically distant  clusters, this may  be essential.
-In  this case,  each  processor can  compute its  iteration  freely without  any
+In  this case,  each  processor can  compute its  iterations  freely without  any
 synchronization  with   the  other   processors.  Thus,  the   asynchronous  may
 theoretically reduce  the overall execution  time and can improve  the algorithm
 performance.
 
 In this section,  the SimGrid simulator is  used to compare the  behavior of the
-two-stage algorithm in  asynchronous mode  with GMRES  in synchronous  mode.  Several
-benchmarks have  been performed with  various combinations of the  grid resources
-(CPU, Network, matrix size, \ldots). The test  conditions are summarized
-in  Table~\ref{tab:02}. In  order to  compare  the execution  times, Table~\ref{tab:03}
-reports the  relative gain between both  algorithms. It is defined  by the ratio
-between  the   execution  time  of   GMRES  and   the  execution  time   of  the
-multisplitting.
-\LZK{Quelle table repporte les gains relatifs?? SÃ»rement pas Table II !!}
-\RCE{Table III avec la nouvelle numerotation}
-The  ratio  is  greater  than  one  because  the  asynchronous
-multisplitting version is faster than GMRES.
+two-stage  algorithm  in  asynchronous  mode with  GMRES  in  synchronous  mode.
+Several benchmarks  have been  performed with various  combinations of  the grid
+resources  (CPU,  Network,  matrix  size,   \ldots).  The  test  conditions  are
+summarized in Table~\ref{tab:02}.
+
+
+
+%\LZK{Quelle table repporte les gains relatifs?? SÃ»rement pas Table II !!}
+%\RCE{Table III avec la nouvelle numerotation}
+
 
 \begin{table}[htbp]
 \centering
@@ -694,7 +778,7 @@ multisplitting version is faster than GMRES.
  Grid architecture                       & 2$\times$50 totaling 100 processors\\
  Processors Power                        & 1 GFlops to 1.5 GFlops \\
  \multirow{2}{*}{Network inter-clusters} & $bw$=1.25 Gbits, $lat=50\mu$s \\
-                                         & $bw$=5 Mbits, $lat=20ms$s\\
+                                         & $bw$=5 Mbits, $lat=20ms$\\
  Matrix size                             & from $62^3$ to $150^3$\\
  Residual error precision                & $10^{-5}$ to $10^{-9}$\\ \hline \\
  \end{tabular}
@@ -743,15 +827,15 @@ multisplitting version is faster than GMRES.
  \label{tab:03}
 \end{table}
 
-Again,  comprehensive and  extensive tests  have been  conducted with  different
-parameters as  the CPU power, the  network parameters (bandwidth and  latency)
-and with different problem size. The  relative gains greater than $1$  between the
-two algorithms have  been captured after  each step  of the test.   In
-Table~\ref{tab:08}  are  reported the  best  grid  configurations allowing
-the  two-stage multisplitting algorithm to  be more than  $2.5$ times faster  than the
-classical  GMRES.  These  experiments also  show the  relative tolerance  of the
-multisplitting algorithm when using a low speed network as usually observed with
-geographically distant clusters through the internet.
+
+Table~\ref{tab:03} reports  the relative gains  between both algorithms.   It is
+defined by the ratio between the execution  time of GMRES and the execution time
+of the  multisplitting. The ratio is  greater than one because  the asynchronous
+multisplitting  version  is  faster  than   GMRES.  In  average,  the  two-stage
+multisplitting algorithm to  be more than $2.5$ times faster  than the classical
+GMRES.  These experiments also show the relative tolerance of the multisplitting
+algorithm when using a low speed network as usually observed with geographically
+distant clusters through the internet.
 
 
 \section{Conclusion}
