Expected impulse rewards in Markov regenerative stochastic Petri nets

Reinhard German, Aad P.A. Vanmoorsel, Muhammad A. Qureshi, William H. Sanders

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

Abstract

Reward structures provide a versatile tool for the definition of performance and dependability measures in stochastic Petri nets. In this paper we derive formulas for the computation of expected reward measures in Markov regenerative stochastic Petri nets, which allow for transitions with non-exponentially distributed firing times. The reward measures may be composed of rate rewards which are obtained in certain markings and of impulse rewards which are obtained when transitions fire. The main result of the paper is the derivation of formulas for the expected impulse reward of transitions with non-exponentially distributed firing times. The analysis is based on the method of supplementary variables. Numerical examples are given for an M/D/1/K queueing system with service breakdowns.

Original languageEnglish (US)
Title of host publicationApplication and Theory of Petri Nets 1996 - 17th International Conference, Proceedings
EditorsWolfgang Reisig, Jonathan Billington
PublisherSpringer-Verlag
Pages172-191
Number of pages20
ISBN (Print)3540613633, 9783540613633
DOIs
StatePublished - Jan 1 1996
Event17th International Conference on Application and Theory of Petri Nets, 1996 - Osaka, Japan
Duration: Jun 24 1996Jun 28 1996

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1091
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other17th International Conference on Application and Theory of Petri Nets, 1996
CountryJapan
CityOsaka
Period6/24/966/28/96

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Keywords

  • Markov regenerative stochastic petri nets
  • Method of supplementary variables
  • Rate and impulse reward measures

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

German, R., Vanmoorsel, A. P. A., Qureshi, M. A., & Sanders, W. H. (1996). Expected impulse rewards in Markov regenerative stochastic Petri nets. In W. Reisig, & J. Billington (Eds.), Application and Theory of Petri Nets 1996 - 17th International Conference, Proceedings (pp. 172-191). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1091). Springer-Verlag. https://doi.org/10.1007/3-540-61363-3_10