Advertisement

A Component-Based Solution Method for Non-ergodic Markov Regenerative Processes

  • Elvio Gilberto Amparore
  • Susanna Donatelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6342)

Abstract

This paper presents a new technique for the steady state solution of non-ergodic Markov Regenerative Processes (MRP), based on a structural decomposition of the MRP. Each component may either be a CTMC or a (smaller) MRP. Classical steady state solution methods of MRP are based either on the computation of the embedded Markov chain (EMC) defined over regenerative states, leading to high complexity in time and space (since the EMC is usually dense), or on an iterative scheme that does not require the construction of the EMC.

The technique presented is particularly suited for MRPs that exhibit a semi-sequential structure. In this paper we present the new algorithm, its asymptotic complexity, and its performance in comparison with classical MRP techniques. Results are very encouraging, even when the MRP only loosely exhibits the required semi-sequential structure.

Keywords

Numerical solutions Markov regenerative process 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Amparore, E., Donatelli, S.: DSPN-Tool: a new DSPN and GSPN solver for GreatSPN. In: Tool Demo Presentation Accepted at QEST 2010, Williamsburg, USA, September 15-18. IEEE-CS Press, Los Alamitos (2010)Google Scholar
  2. 2.
    Amparore, E., Donatelli, S.: MC4CSLTA: an efficient model checking tool for CSLTA. In: Tool Demo Presentation Accepted at QEST 2010, Williamsburg, USA, September 15-18, IEEE-CS Press, Los Alamitos (2010)Google Scholar
  3. 3.
    Amparore, E., Donatelli, S.: Revisiting the Iterative Solution of Markov Regenerative Processes. In: NSMC-2010, Williamsburg, USA (submitted 2010)Google Scholar
  4. 4.
    Choi, H., Kulkarni, V.G., Trivedi, K.S.: Markov regenerative stochastic petri nets. Perform. Eval. 20(1-3), 337–357 (1994)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Ciardo, G., Lindemann, C.: Analysis of Deterministic and Stochastic Petri Nets. In: Performance Evaluation, pp. 160–169. IEEE Computer Society, Los Alamitos (1993)Google Scholar
  6. 6.
    Cormen, T.H., Stein, C., Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms. McGraw-Hill Higher Education, New York (2001)zbMATHGoogle Scholar
  7. 7.
    Donatelli, S., Haddad, S., Sproston, J.: Model checking timed and stochastic properties with CSLTA. IEEE Trans. Softw. Eng. 35(2), 224–240 (2009)CrossRefGoogle Scholar
  8. 8.
    German, R.: Performance Analysis of Communication Systems with Non-Markovian Stochastic Petri Nets. John Wiley & Sons, Inc., New York (2000)zbMATHGoogle Scholar
  9. 9.
    German, R.: Iterative analysis of Markov regenerative models. Perform. Eval. 44, 51–72 (2001), http://portal.acm.org/citation.cfm?id=371601.371606 CrossRefzbMATHGoogle Scholar
  10. 10.
    Lindemann, C.: Performance Modelling with Deterministic and Stochostic Petri Nets. John Wiley & Sons, Inc., New York (1998)zbMATHGoogle Scholar
  11. 11.
    Ajmone Marsan, M., Chiola, G.: On Petri nets with deterministic and exponentially distributed firing times. In: Rozenberg, G. (ed.) APN 1987. LNCS, vol. 266, pp. 132–145. Springer, Heidelberg (1987)CrossRefGoogle Scholar
  12. 12.
    Mura, I., Bondavalli, A., Zang, X., Trivedi, K.S.: Dependability modeling and evaluation of phased mission systems: a dspn approach. In: IEEE DCCA-7 - 7th IFIP Int. Conference on Dependable Computing for Critical Applications, pp. 299–318. IEEE Computer Society Press, Los Alamitos (1999)Google Scholar
  13. 13.
    Stewart, W.J.: Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton (1994)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Elvio Gilberto Amparore
    • 1
  • Susanna Donatelli
    • 1
  1. 1.Dipartimento di InformaticaUniversità di TorinoItaly

Personalised recommendations