On the Use of Kronenecker Operators for the Solution of Generalized Stochastic Petri Nets.

Abstract

We discuss how to describe the Markov chain underlying a generalized stochastic Petri net using Kronecker operators on smaller matrices. We extend previous approaches by allowing both an extensive type of marking-dependent behavior for the transitions and the presence of immediate synchronizations. The derivation of the results is thoroughly formalized, including the use of Kronecker operators in the treatment of the vanishing markings and the computation of impulse-based reward measures. We use our techniques to analyze a model whose solution using conventional methods would fail because of the state-space explosion. In the conclusion, we point out ideas to parallelize our approach.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1996
Accession Number
ADA311983

Entities

People

  • Gianfranco Ciardo
  • Marco Tilgner

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Computations
  • Computer Science
  • Decomposition
  • Elimination
  • Engineering
  • Firing Rate
  • Iterations
  • Markov Chains
  • Numerical Analysis
  • Petri Nets
  • Probability
  • Steady State
  • Stochastic Processes
  • Transitions
  • Trees (Data Structures)

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space