Structural characterization of decomposition in rate-insensitive stochastic Petri nets

Nikky Kortbeek, Richard J. Boucherie, Erik van Ommeren, Peter G. Taylor

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Abstract

This paper focuses on stochastic Petri nets that have an equilibrium distribution that is a product form over the number of tokens at the places. We formulate a decomposition result for the class of nets that have a product form solution irrespective of the values of the transition rates. These nets where algebraically characterized by Haddad et al. as SII2 nets. By providing an intuitive interpretation of this algebraical characterization, and associating state machines to sets of T-invariants, we obtain a one-to-one correspondence between the marking of the original places and the places of the added state machines. This enables us to show that the subclass of stochastic Petri nets under study can be decomposed into subnets that are identified by sets of its T-invariants.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages19
Publication statusPublished - Sep 2012

Publication series

NameMemorandum
PublisherDepartment of Applied Mathematics, University of Twente
No.1993
ISSN (Print)1874-4850

Keywords

  • Stochastic Petri net
  • T-invariant
  • MSC-68M20
  • MSC-60K25
  • MSC-60J27
  • P-invariant
  • Decomposition
  • Product Form

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  • Cite this

    Kortbeek, N., Boucherie, R. J., van Ommeren, E., & Taylor, P. G. (2012). Structural characterization of decomposition in rate-insensitive stochastic Petri nets. (Memorandum; No. 1993). Enschede: University of Twente, Department of Applied Mathematics.