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Steady state analysis of Markov Regenerative SPN with age memory policy

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Book cover Quantitative Evaluation of Computing and Communication Systems (TOOLS 1995)

Abstract

Non-Markovian Stochastic Petri Nets (SPN) have been developed as a tool to deal with systems characterized by non exponentially distributed timed events. Recently, some effort has been devoted to the study of SPN with generally distributed firing times, whose underlying marking process belongs to the class of Markov Regenerative Processes (MRGP). We refer to this class of models as Markov Regenerative SPN (MRSPN). In this paper, we describe a computationally effective algorithm for the steady state solution of MRSPN with age memory policy and subordinated Continuous Time Markov Chain (CTMC).

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References

  1. M. Ajmone Marsan, G. Balbo, A. Bobbio, G. Chiola, G. Conte, and A. Cumani. The effect of execution policies on the semantics and analysis of stochastic Petri nets. IEEE Transactions on Software Engineering, SE-15:832–846, 1989.

    Article  Google Scholar 

  2. M. Ajmone Marsan and G. Chiola. On Petri nets with deterministic and exponentially distributed firing times. In Lecture Notes in Computer Science, volume 266, pages 132–145. Springer Verlag, 1987.

    Google Scholar 

  3. A. Bobbio and M. Telek. Computational restrictions for SPN with generally distributed transition times. In D. Hammer K. Echtle and D. Powell, editors, First European Dependable Computing Conference (EDCC-1), Lecture Notes in Computer Science, volume 852, pages 131–148, 1994.

    Google Scholar 

  4. A. Bobbio and M. Telek. Markov regenerative SPN with non-overlapping activity cycles. In International Computer Performance and Dependability Symposium — IPDS95, pages 124–133. IEEE CS Press, 1995.

    Google Scholar 

  5. V. Catania, A. Puliafito, M. Scarpa, and L. Vita. Concurrent generalized petri nets. In Proceedings of Numerical Solution of Markov Chains, pages 359–382, Raleigh, NC, 1995.

    Google Scholar 

  6. Hoon Choi, V.G. Kulkarni, and K. Trivedi. Markov regenerative stochastic Petri nets. Performance Evaluation, 20:337–357, 1994.

    Article  Google Scholar 

  7. G. Ciardo, R. German, and C. Lindemann. A characterization of the stochastic process underlying a stochastic Petri net. IEEE Transactions on Software Engineering, 20:506–515, 1994.

    Article  Google Scholar 

  8. E. Cinlar. Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, 1975.

    Google Scholar 

  9. A. Cumani. Esp — A package for the evaluation of stochastic Petri nets with phase-type distributed transition times. In Proceedings International Workshop Timed Petri Nets, pages 144–151, Torino (Italy), 1985. IEEE Computer Society Press no. 674.

    Google Scholar 

  10. R. German. New results for the analysis of deterministic and stochastic Petri nets. In International Computer Performance and Dependability Symposium — IPDS95, pages 114–123. IEEE CS Press, 1995.

    Google Scholar 

  11. R. German and C. Lindemann. Analysis of stochastic Petri nets by the method of supplementary variables. Performance Evaluation, 20:317–335, 1994.

    Article  Google Scholar 

  12. C. Lindemann. An improved numerical algorithm for calculating steady-state solutions of deterministic and stochastic Petri net models. Performance Evaluation, 18:75–95, 1993.

    Article  Google Scholar 

  13. M. Telek and A. Bobbio. Markov regenerative stochastic Petri nets with age type general transitions. In 16-th International Conference Application and Theory of Petri Nets, June 1995.

    Google Scholar 

  14. Miklós Telek. Some advanced reliability modelling techniques. Phd Thesis, Hungarian Academy of Science, 1994.

    Google Scholar 

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Heinz Beilner Falko Bause

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© 1995 Springer-Verlag Berlin Heidelberg

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Telek, M., Bobbio, A., Jereb, L., Puliafito, A., Trivedi, K.S. (1995). Steady state analysis of Markov Regenerative SPN with age memory policy. In: Beilner, H., Bause, F. (eds) Quantitative Evaluation of Computing and Communication Systems. TOOLS 1995. Lecture Notes in Computer Science, vol 977. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024314

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  • DOI: https://doi.org/10.1007/BFb0024314

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60300-9

  • Online ISBN: 978-3-540-44789-4

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