Computing Bounds for the Performance Indices of Quasi-Lumpable Stochastic Well-Formed Nets

Giuliana Fraoceschinis, Richard R. Muntz

Research output: Contribution to journalArticlepeer-review

Abstract

Structural symmetries in stochastic well-formed colored Petrinets (SWN's) lead to behavioral symmetries that can be exploited by using the symbolic reachability graph (SRG) construction algorithm. The SRG allows one to compute an aggregated reachability graph (RG) and a “lumped” continuous time Markov chain (CTMC) that contain all the information needed to study the qualitative properties and the performance of the modeled system, respectively. Some models exhibit qualitative behavioral symmetries that are not completely reflected at the CTMC level. We call them quasi-lumpable SWN models. In these cases, exact performance indices can be obtained by avoiding the aggregation of those markings that are qualitatively, but not quantitatively, equivalent. An alternative approach consists of aggregating all the qualitatively equivalent states and computing approximated performance indices. In this paper, a technique is proposed to compute bounds on the performance of SWN models of this kind, using the results we have presented elsewhere. The technique is based on the Courtois and Semal bounded aggregation method.

Original languageEnglish
Pages (from-to)516-525
Number of pages10
JournalIEEE Transactions on Software Engineering
Volume20
Issue number7
DOIs
Publication statusPublished - Jul 1994
Externally publishedYes

Keywords

  • High-level Petri nets
  • Markov chains
  • bounds
  • lumpability
  • model symmetry
  • performance evaluation
  • symbolic reachability graph

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