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Fitting Phase-Type Distributions and Markovian Arrival Processes: Algorithms and Tools

In: Principles of Performance and Reliability Modeling and Evaluation

Author

Listed:
  • Hiroyuki Okamura

    (Graduate School of Engineering, Hiroshima University)

  • Tadashi Dohi

    (Graduate School of Engineering, Hiroshima University)

Abstract

This chapter provides a comprehensive survey of PH (phase-type) distribution and MAP (Markovian arrival process) fitting. The PH distribution and MAP are widely used in analytical model-based performance evaluation because they can approximate non-Markovian models with arbitrary accuracy as Markovian models. Among a number of past research results on PH/MAP fitting, we present the mathematical definition of the PH distribution and MAP, and summarize the most recent state-of-the-art results on the fitting methods. We also offer an overview of the software tools for PH/MAP fitting.

Suggested Citation

  • Hiroyuki Okamura & Tadashi Dohi, 2016. "Fitting Phase-Type Distributions and Markovian Arrival Processes: Algorithms and Tools," Springer Series in Reliability Engineering, in: Lance Fiondella & Antonio Puliafito (ed.), Principles of Performance and Reliability Modeling and Evaluation, pages 49-75, Springer.
    • Handle: RePEc:spr:ssrchp:978-3-319-30599-8_3
    DOI: 10.1007/978-3-319-30599-8_3
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    Citations

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    Cited by:

    1. Junjun Zheng & Hiroyuki Okamura & Tadashi Dohi, 2021. "Availability Analysis of Software Systems with Rejuvenation and Checkpointing," Mathematics, MDPI, vol. 9(8), pages 1-15, April.
    2. Sun, Tianqi & Vatn, Jørn, 2024. "A phase-type maintenance model considering condition-based inspections and maintenance delays," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    3. Ramírez-Cobo, Pepa & Carrizosa, Emilio & Lillo, Rosa E., 2021. "Analysis of an aggregate loss model in a Markov renewal regime," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    4. Eric C. K. Cheung & Oscar Peralta & Jae-Kyung Woo, 2021. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Papers 2201.11122, arXiv.org.
    5. Cheung, Eric C.K. & Peralta, Oscar & Woo, Jae-Kyung, 2022. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 364-389.

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