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Queues with Markovian Arrivals, Phase Type Services, Breakdowns, and Repairs

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Distributed Computer and Communication Networks (DCCN 2020)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 12563))

Abstract

In service sectors, the server interruptions occur naturally and are studied using queueing models with interruptions. Such models have been studied extensively in the literature. The server interruptions may occur due to external events such as shocks and negative customers, or due to internal events which are dictated by a timer or a clock which when expired may result in an interruption. In this paper, we analyze models of MAP/PH/1-type with phase type breakdowns and phase type repairs analytically. The breakdowns are modeled using internal clocks. The study of such breakdowns in the context of MAP/PH/c-type models is carried out via simulation. Some illustrative examples are discussed.

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Acknowledgments

The authors deeply appreciate the constructive suggestions of three anonymous reviewers that improved the presentation of the paper.

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Authors and Affiliations

  1. Departments of Industrial and Manufacturing Engineering and Mathematics, Kettering University, Flint, MI, 48504, USA

    Srinivas R. Chakravarthy

  2. Banaras Hindu University, Varanasi, Uttar Pradesh, India

    Rakesh Kumar Meena

  3. Central University of Rajasthan, Ajmer, India

    Alka Choudhary

Authors
  1. Srinivas R. Chakravarthy
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  2. Rakesh Kumar Meena
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  3. Alka Choudhary
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Corresponding author

Correspondence to Srinivas R. Chakravarthy .

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Editors and Affiliations

  1. Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. RUDN University, Moscow, Russia

    Konstantin E. Samouylov

  3. Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Chakravarthy, S.R., Meena, R.K., Choudhary, A. (2020). Queues with Markovian Arrivals, Phase Type Services, Breakdowns, and Repairs. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks. DCCN 2020. Lecture Notes in Computer Science(), vol 12563. Springer, Cham. https://doi.org/10.1007/978-3-030-66471-8_21

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  • DOI: https://doi.org/10.1007/978-3-030-66471-8_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-66470-1

  • Online ISBN: 978-3-030-66471-8

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