Product form for Stochastic Automata Networks

J.M. Fourneau; B. Plateau; W.  Stewart

2nd International ICST Conference on Performance Evaluation Methodologies and Tools

Research Article

Product form for Stochastic Automata Networks

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@INPROCEEDINGS{10.4108/valuetools.2007.1980,
    author={J.M. Fourneau and B. Plateau and W.  Stewart},
    title={Product form for Stochastic Automata Networks},
    proceedings={2nd International ICST Conference on Performance Evaluation Methodologies and Tools},
    proceedings_a={VALUETOOLS},
    year={2010},
    month={5},
    keywords={Continuous Time Markov Chain Product form steady-state distribution Stochastic Automata Networks},
    doi={10.4108/valuetools.2007.1980}
}

J.M. Fourneau
B. Plateau
W. Stewart
Year: 2010
Product form for Stochastic Automata Networks
VALUETOOLS
ICST
DOI: 10.4108/valuetools.2007.1980

J.M. Fourneau¹^,*, B. Plateau²^,*, W. Stewart³^,*

1: PRiSM CNRS UMR 8144 Universite de Versailles Saint-Quentin Versailles, France
2: INRIA project MESCAL Laboratoire Informatique de Grenoble CNRS UMR 5217 Montobonnot, France
3: North Carolina State University, Raleigh North Carolina, USA

*Contact email: jmf@prism.uvsq.fr, Brigitte.Plateau@imag.fr, billy@csc.ncsu.edu

Abstract

We consider Stochastic Automata Networks (SAN) in continuous time and we prove a sufficient condition for the steady-state distribution to have product form. We consider SAN without synchronizations where the transitions of one automaton may depend of the states of the other automata. Even with this restriction, this sufficient condition is quite simple and this theorem generalizes former results on SAN but also on modulated Markovian queues, such as the Boucherie's theory on competing Markov chain, or on reversible queues considered by Kelly. The sufficient condition and the proof are purely algebraic.

Keywords: Continuous Time Markov Chain Product form steady-state distribution Stochastic Automata Networks

Published: 2010-05-16
Modified: 2011-09-14

: http://dx.doi.org/10.4108/valuetools.2007.1980