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Graphs and Stochastic Automata Networks

In: Computations with Markov Chains

Author

Listed:
  • Jean-Michel Fourneau

    (Université de Versailles Saint-Quentin)

  • Franck Quessette

    (Université de Versailles Saint-Quentin)

Abstract

We show how some graph theoretical arguments may be used to reduce the complexity of the computation of the steady-state distribution of Markov chain. We consider the directed graph associated to a Markov chain derived from a Stochastic Automata Network (SAN). The structural properties of the automata are used to establish new various results. First, we establish the complexity of the resolution for Stochastic Automata Networks with a sparse matrix representation of the automata. This results are used to compare simple SAN (i.e. without functions) with methods which generates a sparse representation of Markov chains (i.e. Markovian Petri Nets for instance) on some examples. Then, we show how to apply state reduction techniques on a chain associated to a SAN. We present an algorithm to solve the steady-state equations and we prove its complexity. Finally, we extend our algorithm to allow the semi-parametric analysis of Stochastic Automata Networks.

Suggested Citation

  • Jean-Michel Fourneau & Franck Quessette, 1995. "Graphs and Stochastic Automata Networks," Springer Books, in: William J. Stewart (ed.), Computations with Markov Chains, chapter 14, pages 217-235, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-2241-6_14
    DOI: 10.1007/978-1-4615-2241-6_14
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