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The Remaining Busy Time in a Retrial System with Unreliable Servers

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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 this paper, we consider a multiserver retrial queuing system with unreliable servers class-dependent retrial rates and N classes of customers following Poisson input processes. We analyze the distribution of the stationary generalized remaining service time which includes all unavailable periods (setup times) occurring during service of the customer. During service of a class-i customer, the interruptions occur according to the i-dependent Poisson process and the following i-dependent random setup time of the server. We consider two following disciplines caused by the service interruptions: preemptive repeat different and preemptive resume. Using coupling method and regenerative approach, we derive the stationary distribution of the generalized remaining service time in an arbitrary server. For each class i, this distribution is expressed as a convolution of the corresponding original service times and setup times, and in general is available in the terms of the Laplace-Stieltjes transform allowing to calculate the moments of the target distribution. Some numerical examples are included as well.

The research is supported by Russian Foundation for Basic Research, projects No. 19-07-00303, 18-07-00156, 18-07-00147.

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Authors and Affiliations

  1. Petrozavodsk State University, Lenin str. 33, Petrozavodsk, 185910, Russia

    Evsey Morozov & Taisia Morozova

  2. Institute of Applied Mathematical Research of the Karelian Research Centre of RAS, Pushkinskaya str. 11, Petrozavodsk, 185910, Russia

    Evsey Morozov

  3. Moscow Center for Fundamental and Applied Mathematics, Moscow State University, Moscow, 119991, Russia

    Evsey Morozov

Authors
  1. Evsey Morozov
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  2. Taisia Morozova
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Correspondence to Evsey Morozov .

Editor information

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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Morozov, E., Morozova, T. (2020). The Remaining Busy Time in a Retrial System with Unreliable Servers. 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_42

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  • DOI: https://doi.org/10.1007/978-3-030-66471-8_42

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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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