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Phase-Type Distributions

  • Philipp Reinecke
  • Levente Bodrog
  • Alexandra Danilkina
Chapter

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.

Keywords

Continuous Time Markov Chain Discrete Time Markov Chain Markov Arrival Process Uniform Random Variate Erlang Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Philipp Reinecke
    • 1
  • Levente Bodrog
    • 2
  • Alexandra Danilkina
    • 1
  1. 1.Institute of Computer ScienceFree University BerlinBerlin Germany
  2. 2.Department of TelecommunicationsBudapest University of Technology and EconomicsBudapest  Hungary

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