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Construction of Phase Type Distributions by Bernstein Exponentials

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Computer Performance Engineering and Stochastic Modelling (EPEW 2023, ASMTA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14231))

Abstract

Analysis of stochastic models is often hurdled by the complexity of probability density functions associated with generally distributed random variables. Among the approximation techniques that can be employed to reduce computational complexity, Bernstein polynomials (BP) exhibit some properties that make them suitable for the needs of that particular context. However, they also show some drawbacks; notably, their application is limited to bounded supports. We introduce Bernstein exponentials (BE) by transforming BP so as to enable approximation over unbounded intervals. We show that BE form a subclass of acyclic phase type (PH) distributions, thus possessing a well defined stochastic interpretation. The characteristics of this subclass allows for efficient analysis in the context of M/PH/1 queues. In particular, we develop a technique to calculate the queue length distribution in case of BE service time with linear time complexity in the number of phases of the service time distribution. Finally, we experiment BE approximations in distribution fitting and in the analysis M/G/1 queues.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Torino, Turin, Italy

    A. Horváth

  2. Dipartimento Sistemi e Informatica, Università di Firenze, Florence, Italy

    E. Vicario

Authors
  1. A. Horváth
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  2. E. Vicario
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Corresponding author

Correspondence to A. Horváth .

Editor information

Editors and Affiliations

  1. Università degli Studi della Campania, Caserta, Italy

    Mauro Iacono

  2. Università degli Studi di Messina, Messina, Italy

    Marco Scarpa

  3. Università Cattolica del Sacro Cuore, Brescia, Italy

    Enrico Barbierato

  4. Università degli Studi di Messina, Messina, Italy

    Salvatore Serrano

  5. Università del Piemonte Orientale, Alessandria, Italy

    Davide Cerotti

  6. Universita degli Studi di Messina, Messina, Italy

    Francesco Longo

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Horváth, A., Vicario, E. (2023). Construction of Phase Type Distributions by Bernstein Exponentials. In: Iacono, M., Scarpa, M., Barbierato, E., Serrano, S., Cerotti, D., Longo, F. (eds) Computer Performance Engineering and Stochastic Modelling. EPEW ASMTA 2023 2023. Lecture Notes in Computer Science, vol 14231. Springer, Cham. https://doi.org/10.1007/978-3-031-43185-2_14

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  • DOI: https://doi.org/10.1007/978-3-031-43185-2_14

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  • Print ISBN: 978-3-031-43184-5

  • Online ISBN: 978-3-031-43185-2

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