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Analysis of a Queueing Model with Contingent Additional Server

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Computer Networks (CN 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 608))

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Abstract

We consider a two-server queueing system with a finite buffer. Customers arrive to the system according to the Markovian arrival process. Normally, only one server is active. The service time of a customer has a phase-type distribution. An additional server is activated only if the queue length exceeds some fixed preassigned threshold. The service time by the additional server also has a phase-type distribution with the same state space. While the underlying Markov chains of service at two servers have non-coinciding states, service in two servers is provided independently. But if it occurs that the underlying Markov chain for one server, say, server 1, needs transition to the state, at which the underlying Markov chain for server 2 is currently staying, service in the server 1 is postponed until the Markov chain for server 2 transits to another state. Dynamics of the system is described by the multi-dimensional Markov chain. The generator of this Markov chain is written down. Expressions for computation of performance measures are derived. Problem of numerical determination of the optimal threshold is solved.

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Acknowledgments

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2014K2A1B8048465) and by Belarusian Republican Foundation of Fundamental Research (Grant No. F15KOR-001).

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Authors and Affiliations

  1. Sangji University, Wonju, Kangwon, 220-702, Korea

    Chesoong Kim

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

    Alexander Dudin

Authors
  1. Chesoong Kim
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  2. Alexander Dudin
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Corresponding author

Correspondence to Chesoong Kim .

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Editors and Affiliations

  1. Silesian University of Technology, Gliwice, Poland

    Piotr Gaj

  2. Silesian University of Technology, Gliwice, Poland

    Andrzej Kwiecień

  3. Silesian University of Technology, Gliwice, Poland

    Piotr Stera

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© 2016 Springer International Publishing Switzerland

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Kim, C., Dudin, A. (2016). Analysis of a Queueing Model with Contingent Additional Server. In: Gaj, P., Kwiecień, A., Stera, P. (eds) Computer Networks. CN 2016. Communications in Computer and Information Science, vol 608. Springer, Cham. https://doi.org/10.1007/978-3-319-39207-3_27

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  • DOI: https://doi.org/10.1007/978-3-319-39207-3_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39206-6

  • Online ISBN: 978-3-319-39207-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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