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\begin{document}
\title{\bf Investigating Multicasting Traffic in Multistage
    Interconnection Networks with  MOSEL}
\author{B\'{e}la Alm\'{a}si, University of Debrecen, Debrecen, Hungary\\
     {\tt almasi\mbox{@}inf.unideb.hu} \\
Dietmar Tutsch, Technical University of Berlin, Berlin, Germany\\
    {\tt dietmart\mbox{@}cs.tu-berlin.de }
}
\date{January 9, 2004.}
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\footnotetext[1]{Research is  partially supported by
the Hungarian Scientific
Research Fund OTKA T0-34280/2000 and FKFP grant 0191/2001.}

\centerline{\bf Abstract}

Multistage interconnection networks (Banyan networks) are frequently
used
for performance evaluation of communication systems (e.g. Ethernet and
ATM 
switches). There exist several
studies (see  \cite{Theimer}\ and
\cite{Mun}) describing the performance of networks in which
packets (or frames) are unicasted (i.e. one switching element (SE)
sends the packet to one and only one other SE). A model for MINs
in case of packet multicasting (i.e. the SE may send the packet to
one or more SE) was introduced in \cite{DT95}.

In this paper a timed Petri net model is used to analyze
the packet traffic in multistage interconnection networks in the case
of unicasting and multicasting too. 
We consider a Banyan network with 2x2-switches and the two cases of
complete
and partial broadcasting within the switching elements.

We study how effectively the universal modeling
environment of MOSEL (see \cite{GB01}) can be applied for the mentioned
systems to produce analytical performance measures. 
Finally some graphically represented numerical results illustrate the 
problem in question.

%\small
\begin{thebibliography}{30}

\bibitem[1]{Theimer}
{\bf T. H. Theimer, E. P. Rathgeb and M. N. Huber}
Performance ana\-lysis of buffered banyan networks,
\emph{IEEE Transactions on Communications,} Vol. 39, No. 2,
(1994).

\bibitem[2]{Mun}
{\bf Y. Mun and H. Y. Youn}
Performance analysis of finite buffered  multistage interconnection
networks
\emph{IEEE Transactions on Computers,}  Vol. 43, No. 2,
(1994).

\bibitem[3]{DT95}
{\bf D, Tutsch and W. Wilhelmi} Leistunganalyse bei Multicasting
in gepufferten mehrstufigen Verbindungsnetzweken (in German)
\emph{Technical Report 1995-02,} Technical University Berlin, Berlin,
(1999).

\bibitem[4]{GB01}
{\bf K. Begain, G. Bolch, H. Herold,}
Practical Performance Modeling,
Kluwer, (2001).

\end{thebibliography}

\end{document}
