\newcommand{\MI}{\mathit{MaxIter}}
-\usepackage{array}
-\usepackage{color, colortbl}
-\newcolumntype{M}[1]{>{\centering\arraybackslash}m{#1}}
-\newcolumntype{Z}[1]{>{\raggedleft}m{#1}}
-
\begin{document}
\title{Simulation of Asynchronous Iterative Numerical Algorithms Using SimGrid}
SimGrid~\cite{casanova+legrand+quinson.2008.simgrid,SimGrid} is a simulation
framework to sudy the behavior of large-scale distributed systems. As its name
says, it emanates from the grid computing community, but is nowadays used to
-study grids, clouds, HPC or peer-to-peer systems.
-%- open source, developped since 1999, one of the major solution in the field
-%
+study grids, clouds, HPC or peer-to-peer systems. The early versions of SimGrid
+date from 1999, but it's still actively developped and distributed as an open
+source software. Today, it's 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. The SMPI interface supports applications written in C or Fortran,
-with little or no modifications.
-%- implements most of MPI-2 \cite{ref} standard [CHECK]
+with little or no modifications. SMPI implements about \np[\%]{80} of the MPI
+2.0 standard~\cite{bedaride:hal-00919507}.
%%% explain simulation
%- simulated processes folded in one real process
%%% validation + refs
-\AG{Décrire SimGrid~\cite{casanova+legrand+quinson.2008.simgrid,SimGrid} (Arnaud)}
-
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Simulation of the multisplitting method}
%Décrire le problème (algo) traité ainsi que le processus d'adaptation à SimGrid.
\centering
\caption{2 clusters, each with 50 nodes}
\label{tab.cluster.2x50}
-
- \tiny
-
-\begin{tabular}{|Z{0.55cm}|Z{0.25cm}|Z{0.25cm}|M{0.25cm}|Z{0.25cm}|M{0.25cm}|M{0.25cm}|M{0.25cm}|M{0.25cm}|M{0.25cm}|M{0.25cm}|M{0.25cm}|M{0.25cm}|M{0.25cm}|}
- \hline
- \bf bw & 5 &5 & 5 & 5 & 5 & 50 & 50 & 50 & 50 & 50 & 10 & 10\\
- \hline
- \bf lat & 0.02 & 0.02 & 0.02 & 0.02 & 0.02 & 0.02 & 0.02 & 0.02 & 0.02 & 0.02 & 0.03 & 0.01\\
- \hline
- \bf power & 1 & 1 & 1 & 1.5 & 1.5 & 1.5 & 1.5 & 1.5 & 1.5 & 1.5 & 1 & 1.5\\ \hline \bf size & 62 & 62 & 62 & 100 & 100 & 110 & 120& 130 & 140 & 150 & 171 & 171\\ \hline
- \bf Prec/Eprec & 10$^{-5}$ & 10$^{-8}$ & 10$^{-9}$ & 10$^{-11}$ & 10$^{-11}$ & 10$^{-11}$ & 10$^{-11}$ & 10$^{-11}$ & 10$^{-11}$ & 10$^{-11}$ & 10$^{-5}$ & 10$^{-5}$\\ \hline
- \bf speedup & 0.396 & 0.392 & 0.396 & 0.391 & 0.393 & 0.395 & 0.398 & 0.388 & 0.393 & 0.394 & 0.63 & 0.778\\ \hline
- \end{tabular}
-\end{table}
+ \renewcommand{\arraystretch}{1.3}
+
+ \begin{tabular}{|>{\bfseries}r|*{12}{c|}}
+ \hline
+ bw
+ & 5 & 5 & 5 & 5 & 5 & 50 \\
+ \hline
+ lat
+ & 0.02 & 0.02 & 0.02 & 0.02 & 0.02 & 0.02 \\
+ \hline
+ power
+ & 1 & 1 & 1 & 1.5 & 1.5 & 1.5 \\
+ \hline
+ size
+ & 62 & 62 & 62 & 100 & 100 & 110 \\
+ \hline
+ Prec/Eprec
+ & \np{E-5} & \np{E-8} & \np{E-9} & \np{E-11} & \np{E-11} & \np{E-11} \\
+ \hline
+ speedup
+ & 0.396 & 0.392 & 0.396 & 0.391 & 0.393 & 0.395 \\
+ \hline
+ \end{tabular}
+
+ \smallskip
+
+ \begin{tabular}{|>{\bfseries}r|*{12}{c|}}
+ \hline
+ bw
+ & 50 & 50 & 50 & 50 & 10 & 10 \\
+ \hline
+ lat
+ & 0.02 & 0.02 & 0.02 & 0.02 & 0.03 & 0.01 \\
+ \hline
+ power
+ & 1.5 & 1.5 & 1.5 & 1.5 & 1 & 1.5 \\
+ \hline
+ size
+ & 120 & 130 & 140 & 150 & 171 & 171 \\
+ \hline
+ Prec/Eprec
+ & \np{E-11} & \np{E-11} & \np{E-11} & \np{E-11} & \np{E-5} & \np{E-5} \\
+ \hline
+ speedup
+ & 0.398 & 0.388 & 0.393 & 0.394 & 0.63 & 0.778 \\
+ \hline
+ \end{tabular}
+\end{table}
Then we have changed the network configuration using three clusters containing
respectively 33, 33 and 34 hosts, or again by on hundred hosts for all the
\centering
\caption{3 clusters, each with 33 nodes}
\label{tab.cluster.3x33}
-
- \tiny
-
-\begin{tabular}{|Z{0.55cm}|Z{0.25cm}|Z{0.25cm}|M{0.25cm}|Z{0.25cm}|M{0.25cm}|M{0.25cm}|}
- \hline
- \bf bw & 10 &5 & 4 & 3 & 2 & 6\\ \hline
- \bf lat & 0.01 & 0.02 & 0.02 & 0.02 & 0.02 & 0.02\\
- \hline
- \bf power & 1 & 1 & 1 & 1 & 1 & 1\\ \hline
- \bf size & 62 & 100 & 100 & 100 & 100 & 171\\ \hline
- \bf Prec/Eprec & 10$^{-5}$ & 10$^{-5}$ & 10$^{-5}$ & 10$^{-5}$ & 10$^{-5}$ & 10$^{-5}$\\ \hline
- \bf speedup & 0.997 & 0.99 & 0.93 & 0.84 & 0.78 & 0.99\\
- \hline
- \end{tabular}
-\end{table}
+ \renewcommand{\arraystretch}{1.3}
+
+ \begin{tabular}{|>{\bfseries}r|*{6}{c|}}
+ \hline
+ bw
+ & 10 & 5 & 4 & 3 & 2 & 6 \\
+ \hline
+ lat
+ & 0.01 & 0.02 & 0.02 & 0.02 & 0.02 & 0.02 \\
+ \hline
+ power
+ & 1 & 1 & 1 & 1 & 1 & 1 \\
+ \hline
+ size
+ & 62 & 100 & 100 & 100 & 100 & 171 \\
+ \hline
+ Prec/Eprec
+ & \np{E-5} & \np{E-5} & \np{E-5} & \np{E-5} & \np{E-5} & \np{E-5} \\
+ \hline
+ speedup
+ & 0.997 & 0.99 & 0.93 & 0.84 & 0.78 & 0.99 \\
+ \hline
+ \end{tabular}
+\end{table}
In a final step, results of an execution attempt to scale up the three clustered
\centering
\caption{3 clusters, each with 66 nodes}
\label{tab.cluster.3x67}
-
- \tiny
-\begin{tabular}{|M{0.55cm}|M{0.25cm}|}
- \hline
- \bf bw & 1\\ \hline
- \bf lat & 0.02\\
- \hline
- \bf power & 1\\
- \hline
- \bf size & 62\\
- \hline
- \bf Prec/Eprec & 10$^{-5}$\\
- \hline
- \bf speedup & 0.9\\
- \hline
+ \renewcommand{\arraystretch}{1.3}
+
+ \begin{tabular}{|>{\bfseries}r|c|}
+ \hline
+ bw & 1 \\
+ \hline
+ lat & 0.02 \\
+ \hline
+ power & 1 \\
+ \hline
+ size & 62 \\
+ \hline
+ Prec/Eprec & \np{E-5} \\
+ \hline
+ speedup & 0.9 \\
+ \hline
\end{tabular}
-\end{table}
+\end{table}
Note that the program was run with the following parameters:
