Section V : Experimental results

[hpcc2014.git] / hpcc.tex

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% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}


\begin{document}
%
% paper title
% can use linebreaks \\ within to get better formatting as desired
\title{Simulation of Asynchronous Iterative Numerical Algorithms Using SimGrid}


% author names and affiliations
% use a multiple column layout for up to three different
% affiliations
\author{\IEEEauthorblockN{Raphaël Couturier and Arnaud Giersch and David Laiymani and Charles-Emile Ramamonjisoa}
\IEEEauthorblockA{Femto-ST Institute - DISC Department\\
Université de Franche-Comté\\
Belfort\\
Email: raphael.couturier@univ-fcomte.fr}
%\and
%\IEEEauthorblockN{Arnaud Giersch}
%\IEEEauthorblockA{Twentieth Century Fox\\
%Springfield, USA\\
%Email: homer@thesimpsons.com}
%\and
%\IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
%\IEEEauthorblockA{Starfleet Academy\\
%San Francisco, California 96678-2391\\
%Telephone: (800) 555--1212\\
%Fax: (888) 555--1212
}



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\begin{abstract}
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The abstract goes here.
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\section{Introduction}

Présenter un bref état de l'art sur la simulation d'algos parallèles. Présenter rapidement les algos itératifs asynchrones et leurs avantages. Parler de leurs inconvénients en particulier la difficulté de déploiement à grande échelle donc il serait bien de simuler. Dire qu'à notre connaissance il n'existe pas de simulation de ce type d'algo.
Présenter les travaux et les résultats obtenus. Annoncer le plan.
 
\section{The asynchronous iteration model}

Décrire le modèle asynchrone. Je m'en charge (DL)

\section{SimGrid}

Décrire SimGrid (Arnaud)

\section{Simulation of the multi-splitting method}

Décrire le problème (algo) traité ainsi que le processus d'adaptation à SimGrid.

\section{Experimental results}
{\raggedright
When the ``real'' application runs in the simulation environment and produces
the expected results, varying the input parameters and the program arguments
allows us to compare outputs from the code execution. We have noticed from this
study that the results depend on the following parameters: (1) at the network
level, we found that the most critical values are the bandwidth (bw) and the
network latency (lat). (2) Hosts power (GFlops) can also influence on the
results. And finally, (3) when submitting job batches for execution, the
arguments values passed to the program like the maximum number of iterations or
the ``external'' precision are critical to ensure not only the convergence of the
algorithm but also to get the main objective of the experimentation of the
simulation in having an execution time in asynchronous less than in synchronous
mode, in others words, in having a ``speedup'' less than 1 (Speedup = Execution
time in synchronous mode / Execution time in asynchronous mode).
}

{\raggedright
A priori, obtaining a speedup less than 1 would be difficult in a local area
network configuration where the synchronous mode will take advantage on the rapid
exchange of information on such high-speed links. Thus, the methodology adopted
was to launch the application on clustered network. In this last configuration,
degrading the inter-cluster network performance will "penalize" the synchronous
mode allowing to get a speedup lower than 1. This action simulates the case of
clusters linked with long distance network like Internet.
}

{\raggedright
As a first step, the algorithm was run on a network consisting of two clusters
containing fifty hosts each, totaling one hundred hosts. Various combinations of
the above factors have providing the results shown in Table 1 with a matrix size
ranging from Nx = Ny = Nz = 62 to 171 elements or from 62$^{3}$ = 238328 to
171$^{3}$ = 5,211,000 entries.
}

{\raggedright
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
clusters. In the same way as above, a judicious choice of key parameters has
permitted to get the results in Table 2 which shows the speedups less than 1 with
a matrix size from 62 to 100 elements.
}

{\raggedright
In a final step, results of an execution attempt to scale up the three clustered
configuration but increasing by two hundreds hosts has been recorded in Table 3.
}

{\raggedright
Note that the program was run with the following parameters:
}

%{\raggedright
\textbullet{} \textbf {SMPI parameters:}
%}

\begin{itemize}
        \item HOSTFILE : Hosts file description.
        \item PLATFORM: file description of the platform architecture : clusters (CPU power,
... ) , intra cluster network description, inter cluster network (bandwidth bw ,
lat latency , ... ).
\end{itemize}


%{\raggedright
\textbullet{} \textbf {Arguments of the program:}
%}

\begin{itemize}
        \item Description of the cluster architecture;
        \item Maximum number of internal and external iterations;
        \item Internal and external precisions;
        \item Matrix size NX , NY and NZ;
        \item Matrix diagonal value = 6.0;
        \item Execution Mode: synchronous or asynchronous.
\end{itemize}

\textbf{Table 1}

\textit{{\scriptsize 2 clusters X 50 nodes}}
\includegraphics[width=209pt]{img-1.eps}

\textbf{Table 2}

\textit{{\scriptsize 3 clusters X 33 n\oe{}uds}}
\includegraphics[width=209pt]{img-1.eps}
\textbf{Table 3}

\textit{{\scriptsize 3 clusters X 67 noeuds}}
\includegraphics[width=128pt]{img-2.eps}

{\raggedright
\textbf{Interpretations and comments}
}

{\raggedright
After analyzing the outputs, generally, for the configuration with two or three
clusters including one hundred hosts (Tables 1 and 2), some combinations of the
used parameters affecting the results have given a speedup less than 1, showing
the effectiveness of the asynchronous performance compared to the synchronous
mode.
}

{\raggedright
In the case of a two clusters configuration, Table 1 shows that with a
deterioration of inter cluster network set with 5 Mbits/s of bandwidth, a latency
in order of a hundredth of a millisecond and a system power of one GFlops, an
efficiency of about 40\% in asynchronous mode is obtained for a matrix size of 62
elements . It is noticed that the result remains stable even if we vary the
external precision from E -05 to E-09. By increasing the problem size up to 100
elements, it was necessary to increase the CPU power of 50 \% to 1.5 GFlops for a
convergence of the algorithm with the same order of asynchronous mode efficiency.
Maintaining such a system power but this time, increasing network throughput
inter cluster up to 50 Mbits /s, the result of efficiency of about 40\% is
obtained with high external  precision of E-11 for a matrix size from 110 to 150
side elements .
}

{\raggedright
For the 3 clusters architecture including a total of 100 hosts, Table 2 shows
that it was difficult to have a combination which gives an efficiency of
asynchronous below 80 \%. Indeed, for a matrix size of 62 elements, equality
between the performance of the two modes (synchronous and asynchronous) is
achieved with an inter cluster of 10 Mbits/s and a latency of E- 01 ms. To
challenge an efficiency by 78\% with a matrix size of 100 points, it was
necessary to degrade the inter cluster network bandwidth from 5 to 2 Mbit/s.
}

{\raggedright
A last attempt was made for a configuration of three clusters but more power
with 200 nodes in total. The convergence with a speedup of 90 \% was obtained
with a bandwidth of 1 Mbits/s as shown in Table 3.
}

\section{Conclusion}


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The authors would like to thank...





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