Phase Type and Matrix Exponential Distributions in Stochastic Modeling

Andras Horvath (), Marco Scarpa () and Miklos Telek ()
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Andras Horvath: Università degli Studi di Torino
Marco Scarpa: Università degli Studi di Messina
Miklos Telek: Budapest University of Technology and Economics

A chapter in Principles of Performance and Reliability Modeling and Evaluation, 2016, pp 3-25 from Springer

Abstract: 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.

Keywords: ME Distributions; Matrix Exponential (ME); Multi-valued Decision Diagrams (MDD); Vector-matrix Pair; Reachability Graph (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-30599-8_1

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