A Ρ- and T-invariant characterization of product form and decomposition in stochastic Petri nets

Nikky Kortbeek, Richard J. Boucherie

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Abstract

Structural product form and decomposition results for stochastic Petri nets are surveyed, unifed and extended. The contribution is threefold. First, the literature on structural results for product form over the number of tokens at the places is surveyed and rephrased completely in terms of T-invariants. Second, based on the underlying concept of group-local-balance, the product form results for stochastic Petri nets are demarcated and an intuitive explanation is provided of these results based on T-invariants, only. Third, a decomposition result is provided that is completely formulated in terms of both T-invariants and P-invariants.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages47
Publication statusPublished - Mar 2011

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherUniversity of Twente, Department of Applied Mathematics
No.1939
ISSN (Print)1874-4850

Keywords

  • T-invariant
  • Product form
  • Decomposition
  • P-invariant
  • Stochastic Petri net

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    Kortbeek, N., & Boucherie, R. J. (2011). A Ρ- and T-invariant characterization of product form and decomposition in stochastic Petri nets. (Memorandum / Department of Applied Mathematics; No. 1939). Enschede: University of Twente, Department of Applied Mathematics.