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Study on Transient Queueing Delay in a Single-Channel Queueing Model with Setup and Closedown Times

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Information and Software Technologies (ICIST 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 639))

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Abstract

A single-channel queueing model with finite buffer capacity, Poisson arrival stream and generally distributed processing times is considered. After each busy period the service station is being switched off but this operation requires a randomly distributed closedown time. Similarly, after the idle time, the first service in a new busy period is preceded by a random setup time, during which the processing is still suspended and the server achieves full readiness for the service process. A system of integral equations for transient conditional queueing delay distribution is derived, by using the idea of embedded Markov chain and the formula of total probability. The solution of the corresponding system written for Laplace transforms is obtained via the linear algebraic technique. Numerical examples are attached as well.

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Authors and Affiliations

  1. Faculty of Applied Mathematics, Institute of Mathematics, Silesian University of Technology, 23 Kaszubska Street, 44-100, Gliwice, Poland

    Wojciech M. Kempa

  2. Faculty of Mechanical Engineering, Institute of Engineering Processes Automation and Integrated Manufacturing Systems, Silesian University of Technology, 18A Konarskiego Street, 44-100, Gliwice, Poland

    Iwona Paprocka, Krzysztof Kalinowski, Cezary Grabowik & Damian Krenczyk

Authors
  1. Wojciech M. Kempa
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  2. Iwona Paprocka
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  3. Krzysztof Kalinowski
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  4. Cezary Grabowik
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  5. Damian Krenczyk
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Corresponding author

Correspondence to Wojciech M. Kempa .

Editor information

Editors and Affiliations

  1. Kaunas University of Technology , Kaunas, Lithuania

    Giedre Dregvaite

  2. Kaunas University of Technology , Kaunas, Lithuania

    Robertas Damasevicius

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Kempa, W.M., Paprocka, I., Kalinowski, K., Grabowik, C., Krenczyk, D. (2016). Study on Transient Queueing Delay in a Single-Channel Queueing Model with Setup and Closedown Times. In: Dregvaite, G., Damasevicius, R. (eds) Information and Software Technologies. ICIST 2016. Communications in Computer and Information Science, vol 639. Springer, Cham. https://doi.org/10.1007/978-3-319-46254-7_37

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  • DOI: https://doi.org/10.1007/978-3-319-46254-7_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46253-0

  • Online ISBN: 978-3-319-46254-7

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