Formal relation of Markov renewal theory and supplementary variables in the analysis of stochastic Petri nets

Reinhard German, M. Telek

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Citations (Scopus)

Abstract

Non-Markovian stochastic Petri nets have been investigated mainly by means of Markov renewal theory and by the method of supplementary variables. Both approaches provide different analytic descriptions of the same system. Numerical algorithms based on these descriptions lead to similar results. Parallel research effort resulted from the fact that an exact relationship of the two was not known. In this paper such a formal relationship is established for Markov regenerative stochastic Petri nets with general preemption policies in both the transient and stationary case. As a by-product, a closed form solution in Laplace domain is derived, which is easier to apply than previously known ones. An example from communications is used for illustrations.

Original languageEnglish
Title of host publicationProceedings - 8th International Workshop on Petri Nets and Performance Models, PNPM 1999
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages64-73
Number of pages10
ISBN (Electronic)0769503314, 9780769503318
DOIs
Publication statusPublished - Jan 1 1999
Event8th International Workshop on Petri Nets and Performance Models, PNPM 1999 - Zaragoza, Spain
Duration: Sep 8 1999Sep 10 1999

Other

Other8th International Workshop on Petri Nets and Performance Models, PNPM 1999
CountrySpain
CityZaragoza
Period9/8/999/10/99

Fingerprint

Supplementary Variable
Renewal Theory
Stochastic Petri Nets
Petri nets
Preemption
Laplace
Closed-form Solution
Numerical Algorithms
Byproducts
Communication
Relationships
Policy

Keywords

  • Laplace Transforms
  • Markov Regenerative Stochastic Petri Nets
  • Transient and Stationary Analysis

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Modelling and Simulation
  • Theoretical Computer Science

Cite this

German, R., & Telek, M. (1999). Formal relation of Markov renewal theory and supplementary variables in the analysis of stochastic Petri nets. In Proceedings - 8th International Workshop on Petri Nets and Performance Models, PNPM 1999 (pp. 64-73). [796537] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/PNPM.1999.796537

Formal relation of Markov renewal theory and supplementary variables in the analysis of stochastic Petri nets. / German, Reinhard; Telek, M.

Proceedings - 8th International Workshop on Petri Nets and Performance Models, PNPM 1999. Institute of Electrical and Electronics Engineers Inc., 1999. p. 64-73 796537.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

German, R & Telek, M 1999, Formal relation of Markov renewal theory and supplementary variables in the analysis of stochastic Petri nets. in Proceedings - 8th International Workshop on Petri Nets and Performance Models, PNPM 1999., 796537, Institute of Electrical and Electronics Engineers Inc., pp. 64-73, 8th International Workshop on Petri Nets and Performance Models, PNPM 1999, Zaragoza, Spain, 9/8/99. https://doi.org/10.1109/PNPM.1999.796537
German R, Telek M. Formal relation of Markov renewal theory and supplementary variables in the analysis of stochastic Petri nets. In Proceedings - 8th International Workshop on Petri Nets and Performance Models, PNPM 1999. Institute of Electrical and Electronics Engineers Inc. 1999. p. 64-73. 796537 https://doi.org/10.1109/PNPM.1999.796537
German, Reinhard ; Telek, M. / Formal relation of Markov renewal theory and supplementary variables in the analysis of stochastic Petri nets. Proceedings - 8th International Workshop on Petri Nets and Performance Models, PNPM 1999. Institute of Electrical and Electronics Engineers Inc., 1999. pp. 64-73
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