Skip to main content

Sojourn Times in Dependability Modeling

  • Chapter
  • First Online:
Principles of Performance and Reliability Modeling and Evaluation

Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

  • 1139 Accesses

Abstract

We consider Markovian models of computing or communication systems, subject to failures and, possibly, repairs. The dependability properties of such systems lead to metrics that can all be described in terms of the time that the Markov chain spends in subsets of its state space. Some examples of such metrics are MTTF and MTTR, reliability or availability at a point in time, the mean or the distribution of the interval availability in a fixed time interval, and more generally different performability versions of these measures. This chapter reviews this point of view and its consequences, and discusses some new results related to it.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bobbio A, Trivedi KS (1986) An aggregation technique for the transient analysis of stiff Markov chains. IEEE Trans Comput 35(9)

    Google Scholar 

  2. Choi H, Wang W, Trivedi KS (1998) Analysis of conditional MTTF of fault-tolerant systems. Microelen Reliab 38(3)

    Google Scholar 

  3. Ciardo G, Marie R, Sericola B, Trivedi KS (1990) Performability analysis using semi-Markov reward processes. IEEE Trans Comput 39(10)

    Google Scholar 

  4. Couto da Silva AP, Rubino G (2006) Bounding the mean cumulated reward up to absorption. In: Langville A, Stewart W (eds) Markov anniversary meeting, Boson Books

    Google Scholar 

  5. Csenki A (1994) Dependability for systems with a partitioned state space. Markov and semi-Markov theory and computational implementation. Lecture notes in statistics, 90. Springer

    Google Scholar 

  6. Hawkes AG, Cui L, Du S (2014) Occupancy times for markov and semi-markov models in systems reliability. In: Chapter 16 reliability applied reliability engineering and risk analysis: probabilistic models and statistical inference. Wiley

    Google Scholar 

  7. Mahévas S, Rubino G (2001) Bound computation of dependability and performability measures. IEEE Trans Comput 50(5)

    Google Scholar 

  8. Muppala J, Fricks R, Trivedi KS (2000) Techniques for system dependability evaluation. In: Grassman W (ed) Computational probability. Kluwer Academic Publishers, The Netherlands

    Google Scholar 

  9. Reibman A, Smith RM, Trivedi KS (1989) Markov and markov reward models: a survey of numerical approaches. Eur J Oper Res 40

    Google Scholar 

  10. Rubino G, Sericola B (1989) Sojourn times in Markov processes. J Appl Probab 26

    Google Scholar 

  11. Rubino G, Sericola B (1989) Distribution of operational times in fault-tolerant systems modeled by semi-Markov processes. In: 12th International Conference on Fault-Tolerant Systems and Diagnostics. Prague, Czech Republic, September 1989

    Google Scholar 

  12. Rubino G, Sericola B (1991) A finite characterization of weak lumpable Markov processes. Part I: The discrete time case. Stoch Proces Appl 38

    Google Scholar 

  13. Rubino G, Sericola B (1992) Interval availability analysis using operational periods. Perform Eval 14(3)

    Google Scholar 

  14. Rubino G, Sericola B (1993) Interval availability distribution computation. In: Proceedings of the 23rd IEEE international symposium on fault tolerant computing (FTCS’23), Toulouse, France, June 1993

    Google Scholar 

  15. Rubino G, Sericola B (1993) Sojourn times in semi-Markov reward processes. Application to fault-tolerant systems modelling. Reliab Eng Syst Safety 41

    Google Scholar 

  16. Rubino G, Sericola B (1993) A finite characterization of weak lumpable Markov processes. Part II: The continuous time case. Stoch Process Appl 45

    Google Scholar 

  17. Rubino G, Sericola B (2014) Markov chains and dependability theory. Cambridge University Press

    Google Scholar 

  18. Sericola B (2013) Markov Chains: theory, algorithms and applications. Iste Series, Wiley

    Google Scholar 

  19. de Souza e Silva E, Gail HR (1986) Calculating cumulative operational time distributions of repairable computer systems. IEEE Trans Comput 35(4)

    Google Scholar 

  20. Trivedi KS (2001) Probability and statistics with reliability, queuing, and computer science applications. 2nd edn, Prentice Hall

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gerardo Rubino .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Rubino, G., Sericola, B. (2016). Sojourn Times in Dependability Modeling. In: Fiondella, L., Puliafito, A. (eds) Principles of Performance and Reliability Modeling and Evaluation. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-30599-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-30599-8_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30597-4

  • Online ISBN: 978-3-319-30599-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics