-\begin{document} \RCE{Titre a confirmer.} \title{Comparative performance
-analysis of simulated grid-enabled numerical iterative algorithms}
+\begin{document}
+\title{Grid-enabled simulation of large-scale linear iterative solvers}
%\itshape{\journalnamelc}\footnotemark[2]}
\author{Charles Emile Ramamonjisoa\affil{1},
Email:~\email{l.zianekhodja@ulg.ac.be}
}
-\begin{abstract} The behavior of multi-core applications is always a challenge
+\begin{abstract} The behavior of multi-core applications is always a challenge
to predict, especially with a new architecture for which no experiment has been
performed. With some applications, it is difficult, if not impossible, to build
accurate performance models. That is why another solution is to use a simulation
bandwidth, latency, number of processors) and to simulate the execution of such
applications. The main contribution of this paper is to show that the use of a
simulation tool (here we have decided to use the SimGrid toolkit) can really
-help developpers to better tune their applications for a given multi-core
+help developers to better tune their applications for a given multi-core
architecture.
-In particular we focus our attention on two parallel iterative algorithms based
-on the Multisplitting algorithm and we compare them to the GMRES algorithm.
-These algorithms are used to solve linear systems. Two different variants of
-the Multisplitting are studied: one using synchronoous iterations and another
-one with asynchronous iterations. For each algorithm we have simulated
+%In particular we focus our attention on two parallel iterative algorithms based
+%on the Multisplitting algorithm and we compare them to the GMRES algorithm.
+%These algorithms are used to solve linear systems. Two different variants of
+%the Multisplitting are studied: one using synchronoous iterations and another
+%one with asynchronous iterations.
+In this paper we focus our attention on the simulation of iterative algorithms to solve sparse linear systems on large clusters. We study the behavior of the widely used GMRES algorithm and two different variants of the Multisplitting algorithms: one using synchronous iterations and another one with asynchronous iterations.
+For each algorithm we have simulated
different architecture parameters to evaluate their influence on the overall
-execution time. The obtain simulated results confirm the real results
-previously obtained on different real multi-core architectures and also confirm
-the efficiency of the asynchronous multisplitting algorithm compared to the
-synchronous GMRES method.
+execution time.
+%The obtain simulated results confirm the real results
+%previously obtained on different real multi-core architectures and also confirm
+%the efficiency of the asynchronous Multisplitting algorithm compared to the
+%synchronous GMRES method.
+The simulations confirm the real results previously obtained on different real multi-core architectures and also confirm the efficiency of the asynchronous Multisplitting algorithm on distant clusters compared to the synchronous GMRES algorithm.
\end{abstract}
allocations policies under varying CPU power, network speeds and loads is very
challenging and labor intensive~\cite{Calheiros:2011:CTM:1951445.1951450}. This
problematic is even more difficult for the asynchronous scheme where a small
-parameter variation of the execution platform can lead to very different numbers
-of iterations to reach the converge and so to very different execution times. In
-this challenging context we think that the use of a simulation tool can greatly
-leverage the possibility of testing various platform scenarios.
-
-The main contribution of this paper is to show that the use of a simulation tool
-(i.e. the SimGrid toolkit~\cite{SimGrid}) in the context of real parallel
-applications (i.e. large linear system solvers) can help developers to better
-tune their application for a given multi-core architecture. To show the validity
-of this approach we first compare the simulated execution of the multisplitting
-algorithm with the GMRES (Generalized Minimal Residual)
-solver~\cite{saad86} in synchronous mode.
-
-\LZK{Pas trop convainquant comme argument pour valider l'approche de simulation. \\On peut dire par exemple: on a pu simuler différents algos itératifs à large échelle (le plus connu GMRES et deux variantes de multisplitting) et la simulation nous a permis (sans avoir le vrai matériel) de déterminer quelle serait la meilleure solution pour une telle configuration de l'archi ou vice versa.\\A revoir...}
-
-The obtained results on different
-simulated multi-core architectures confirm the real results previously obtained
-on non simulated architectures.
-
-\LZK{Il n y a pas dans la partie expé cette comparaison et confirmation des résultats entre la simulation et l'exécution réelle des algos sur les vrais clusters.\\ Sinon on pourrait ajouter dans la partie expé une référence vers le journal supercomput de krylov multi pour confirmer que cette méthode est meilleure que GMRES sur les clusters large échelle.}
-
-We also confirm the efficiency of the
-asynchronous multisplitting algorithm compared to the synchronous GMRES.
-
-\LZK{P.S.: Pour tout le papier, le principal objectif n'est pas de faire des comparaisons entre des méthodes itératives!!\\Sinon, les deux algorithmes Krylov multisplitting synchrone et multisplitting asynchrone sont plus efficaces que GMRES sur des clusters à large échelle.\\Et préciser, si c'est vraiment le cas, que le multisplitting asynchrone est plus efficace et adapté aux clusters distants par rapport aux deux autres algos (je n'ai pas encore lu la partie expé)}
-
-In
-this way and with a simple computing architecture (a laptop) SimGrid allows us
+parameter variation of the execution platform and of the application data can
+lead to very different numbers of iterations to reach the converge and so to
+very different execution times. In this challenging context we think that the
+use of a simulation tool can greatly leverage the possibility of testing various
+platform scenarios.
+
+The {\bf main contribution of this paper} is to show that the use of a
+simulation tool (i.e. the SimGrid toolkit~\cite{SimGrid}) in the context of real
+parallel applications (i.e. large linear system solvers) can help developers to
+better tune their application for a given multi-core architecture. To show the
+validity of this approach we first compare the simulated execution of the Krylov
+multisplitting algorithm with the GMRES (Generalized Minimal Residual)
+solver~\cite{saad86} in synchronous mode. The simulation results allow us to
+determine which method to choose given a specified multi-core architecture.
+Moreover the obtained results on different simulated multi-core architectures
+confirm the real results previously obtained on non simulated architectures.
+More precisely the simulated results are in accordance (i.e. with the same order
+of magnitude) with the works presented in~\cite{couturier15}, which show that
+the synchronous multisplitting method is more efficient than GMRES for large
+scale clusters. Simulated results also confirm the efficiency of the
+asynchronous multisplitting algorithm compared to the synchronous GMRES
+especially in case of geographically distant clusters.
+
+In this way and with a simple computing architecture (a laptop) SimGrid allows us
to run a test campaign of a real parallel iterative applications on
different simulated multi-core architectures. To our knowledge, there is no
related work on the large-scale multi-core simulation of a real synchronous and
experimental results are presented in section~\ref{sec:expe} followed by some
concluding remarks and perspectives.
-\LZK{Proposition d'un titre pour le papier: Grid-enabled simulation of large-scale linear iterative solvers.}
-
\section{The asynchronous iteration model and the motivations of our work}
\label{sec:asynchro}
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}
Figure~\ref{fig:02} shows that end users will reduce the execution time
for both algorithms when using a grid architecture like 4x16 or 8x8: the reduction is about $2$. The results depict also that when
the network speed drops down (variation of 12.5\%), the difference between the two Multisplitting algorithms execution times can reach more than 25\%.
-%\RC{c'est pas clair : la différence entre quoi et quoi?}
-%\DL{pas clair}
-%\RCE{Modifie}
+
%\begin{wrapfigure}{l}{100mm}
from $1$ to $19$ GFlops. The outputs depicted in Figure~\ref{fig:06} confirm the
performance gain, around $95\%$ for both of the two methods, after adding more
powerful CPU.
+\ \\
+%\DL{il faut une conclusion sur ces tests : ils confirment les résultats déjà
+%obtenus en grandeur réelle. Donc c'est une aide précieuse pour les dev. Pas
+%besoin de déployer sur une archi réelle}
-\DL{il faut une conclusion sur ces tests : ils confirment les résultats déjà
-obtenus en grandeur réelle. Donc c'est une aide précieuse pour les dev. Pas
-besoin de déployer sur une archi réelle}
+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 multisplitting methods is in accordance with larger real
+executions on large scale supercomputer~\cite{couturier15}.
\subsection{Comparing GMRES in native synchronous mode and the multisplitting algorithm in asynchronous mode}
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
-Figure~\ref{fig:07} are reported the best grid configurations allowing
+Table~\ref{tab:08} are reported the best grid configurations allowing
the multisplitting method 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
\end{tabular}}
-\begin{figure}[!t]
+\begin{table}[!t]
\centering
%\begin{table}
% \caption{Relative gain of the multisplitting algorithm compared with the classical GMRES}
\hline
\end{mytable}
%\end{table}
- \caption{Relative gain of the multisplitting algorithm compared with the classical GMRES
-\AG{C'est un tableau, pas une figure}}
- \label{fig:07}
-\end{figure}
+ \caption{Relative gain of the multisplitting algorithm compared with the classical GMRES}
+ \label{tab:08}
+\end{table}
\section{Conclusion}
\bibliographystyle{wileyj}
\bibliography{biblio}
-\AG{Des warnings bibtex à corriger (%
- \texttt{entry type for "SimGrid" isn't style-file defined},
- \texttt{empty booktitle in Bru95}%
-).}
+
\end{document}
