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Phase Type and Matrix Exponential Distributions in Stochastic Modeling

In: Principles of Performance and Reliability Modeling and Evaluation

Author

Listed:
  • Andras Horvath

    (Università degli Studi di Torino)

  • Marco Scarpa

    (Università degli Studi di Messina)

  • Miklos Telek

    (Budapest University of Technology and Economics)

Abstract

Since their introduction, properties of Phase Type (PH) distributions have been analyzed and many interesting theoretical results found. Thanks to these results, PH distributions have been profitably used in many modeling contexts where non-exponentially distributed behavior is present. Matrix Exponential (ME) distributions are distributions whose matrix representation is structurally similar to that of PH distributions but represent a larger class. For this reason, ME distributions can be usefully employed in modeling contexts in place of PH distributions using the same computational techniques and similar algorithms, giving rise to new opportunities. They are able to represent different dynamics, e.g., faster dynamics, or the same dynamics but at lower computational cost. In this chapter, we deal with the characteristics of PH and ME distributions, and their use in stochastic analysis of complex systems. Moreover, the techniques used in the analysis to take advantage of them are revised.

Suggested Citation

  • Andras Horvath & Marco Scarpa & Miklos Telek, 2016. "Phase Type and Matrix Exponential Distributions in Stochastic Modeling," Springer Series in Reliability Engineering, in: Lance Fiondella & Antonio Puliafito (ed.), Principles of Performance and Reliability Modeling and Evaluation, pages 3-25, Springer.
    • Handle: RePEc:spr:ssrchp:978-3-319-30599-8_1
    DOI: 10.1007/978-3-319-30599-8_1
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