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Single Server Queues with Batch Poisson Input and Multiple Types of Outgoing Calls

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1109))

Abstract

In this paper, we consider a single server queueing model \(M^{[n]}|GI|GI|1|L\) with Batch Poisson input flow. Upon arrival, an incoming call from the batch occupies the server, if the server is idle. Other calls from the batch join the orbit and try to occupy the server after an exponentially distributed time. If the server is busy all incoming calls from the batch join the orbit and make a delay for an exponentially distributed time then repeat their request for service. The server makes an outgoing call in its idle time. Our contribution is to derive the stationary probability distribution of the number of incoming calls in the system.

The reported study was funded by RFBR according to the research project 18-01-00277.

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Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 36 Lenina Avenue, Tomsk, 634050, Russia

    Anatoly Nazarov, Svetlana Paul & Olga Lizura

  2. Faculty of Engineering Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Tuan Phung-Duc

Authors
  1. Anatoly Nazarov
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  2. Tuan Phung-Duc
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  3. Svetlana Paul
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  4. Olga Lizura
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Corresponding author

Correspondence to Svetlana Paul .

Editor information

Editors and Affiliations

  1. Faculty of Applied Mathematics and Computer Science, Belarusian State University, Minsk, Belarus

    Alexander Dudin

  2. Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk, Russia

    Alexander Moiseev

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Nazarov, A., Phung-Duc, T., Paul, S., Lizura, O. (2019). Single Server Queues with Batch Poisson Input and Multiple Types of Outgoing Calls. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2019. Communications in Computer and Information Science, vol 1109. Springer, Cham. https://doi.org/10.1007/978-3-030-33388-1_15

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  • DOI: https://doi.org/10.1007/978-3-030-33388-1_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33387-4

  • Online ISBN: 978-3-030-33388-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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