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Account of Disasters in Analysis of Queueing Systems Modeled by the Quasi-Birth-and-Death-Process

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1803))

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Abstract

We present a way for the derivation of the generator of a multidimensional continuous-time Markov chain describing the behavior of a queueing model with account of possibility of disaster occurrence under the known generator of the Quasi-Birth-and-Death-Process (QBD) describing behavior of the corresponding queueing model without disasters. The stationary distribution of the Markov chain in the case of the level-independent QBD describing the behavior of a queueing model without disasters is found in the matrix geometric form.

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Authors and Affiliations

  1. Belarusian State University, 4 Nezavisimosti Avenue, 220030, Minsk, Belarus

    Alexander Dudin

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  1. Alexander Dudin
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Correspondence to Alexander Dudin .

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Editors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Tomsk State University, Tomsk, Russia

    Alexander Moiseev

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Dudin, A. (2023). Account of Disasters in Analysis of Queueing Systems Modeled by the Quasi-Birth-and-Death-Process. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2022. Communications in Computer and Information Science, vol 1803. Springer, Cham. https://doi.org/10.1007/978-3-031-32990-6_8

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  • DOI: https://doi.org/10.1007/978-3-031-32990-6_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-32989-0

  • Online ISBN: 978-3-031-32990-6

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