Phase-Type Distributions

Abstract

Both analytical (Chap. 6) and simulation- and experimentation-based (Chap. 17) approaches to resilience assessment rely on models for the various phenomena that may affect the system under study. These models must be both accurate, in that they reflect the phenomenon well, and suitable for the chosen approach. Analytical methods require models that are analytically tractable, while methods for experimentation, such as fault-injection (see Chap. 13), require the efficient generation of random-variates from the models. Phase-type (PH) distributions are a versatile tool for modelling a wide range of real-world phenomena. These distributions can capture many important aspects of measurement data, while retaining analytical tractability and efficient random-variate generation. This chapter provides an introduction to the use of PH distributions in resilience assessment. The chapter starts with a discussion of the mathematical basics. We then describe tools for fitting PH distributions to measurement data, before illustrating application of PH distributions in analysis and in random-variate generation.