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Analyzing the Effect of Catastrophic Breakdowns with Retrial Queues in a Two-Way Communication System

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1605))

Abstract

A two-way communication system is modeled in this paper. A retrial queueing system with a finite and an infinite sources is used in the model. The system has two sources. The first source is finite, the second source is infinite. Jobs from the first source are the primary jobs (requests). They can be called as first order job, as well. Jobs from the second source are the secondary jobs. They can be called as second order job, as well. In case of an idle server, the second order customers are called for service. This situation is said as a special search for customers.

The non-reliable server is subject to random breakdowns. Two types of breakdowns are considered: the regular breakdown, when the first or second order customer under service is sent back to the orbit or the infinite source, respectively, and the catastrophic breakdown, when all of the requests at the server and in the orbit are sent back to the corresponding sources. The novelty of this paper is to investigate the effect of catastrophic breakdown in a two-way communication environment. The goal is to determine the steady-state probabilities and the system characteristics. The system balance equations are formulated for different cases, but the analytic solution is very difficult. A software tool is used instead. Figures illustrate the effect of the system parameters on the performance measures in scenarios of regular and catastrophic breakdowns.

The research work was supported by the Austro-Hungarian Cooperation Grant No 106öu4, 2020.

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Authors and Affiliations

  1. University of Debrecen, Debrecen, Hungary

    Attila Kuki, Tamás Bérczes & János Sztrik

Authors
  1. Attila Kuki
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  2. Tamás Bérczes
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  3. János Sztrik
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Correspondence to Attila Kuki .

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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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Kuki, A., Bérczes, T., Sztrik, J. (2022). Analyzing the Effect of Catastrophic Breakdowns with Retrial Queues in a Two-Way Communication System. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2021. Communications in Computer and Information Science, vol 1605. Springer, Cham. https://doi.org/10.1007/978-3-031-09331-9_12

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  • DOI: https://doi.org/10.1007/978-3-031-09331-9_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-09330-2

  • Online ISBN: 978-3-031-09331-9

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