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M/M/1/1 Retrial Queues with Setup Time

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Queueing Theory and Network Applications (QTNA 2015)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 383))

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Abstract

This paper considers single server retrial queues with setup time. In the basic model, if the server completes a service and there are no customers in the orbit, the server is turned off immediately. Arriving customers that see the server occupied join the orbit and repeat their attempt after some random time. The new feature of our models is that an arriving customer that sees the server off waits at the server and the server is turned on. The server needs some setup time to be active so as to serve the waiting customer. If the server completes a service and the orbit is not empty, it stays idle waiting for either a new customer or a customer from the orbit. For this model, we obtain explicit expressions for the generating functions of the joint queue length. We then consider an extended model where the server stays idle for a while before being turned off for which explicit solution is also obtained.

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Authors and Affiliations

  1. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, Japan

    Tuan Phung-Duc

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  1. Tuan Phung-Duc
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Correspondence to Tuan Phung-Duc .

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Editors and Affiliations

  1. Department of Networked Systems and Services, Budapest University of Technology and Economics, Budapest, Hungary

    Tien van Do

  2. Department of Systems Science, Kyoto University Graduate School of Informatics, Kyoto, Japan

    Yutaka Takahashi

  3. Faculty of Science and Engineering, Department of Information Science and Systems Engineering, Konan University, Kobe, Japan

    Wuyi Yue

  4. Faculty of Information Technology, VNU University of Engineering and Technology, Hanoi, Vietnam

    Viet-Ha Nguyen

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Phung-Duc, T. (2016). M/M/1/1 Retrial Queues with Setup Time. In: van Do, T., Takahashi, Y., Yue, W., Nguyen, VH. (eds) Queueing Theory and Network Applications. QTNA 2015. Advances in Intelligent Systems and Computing, vol 383. Springer, Cham. https://doi.org/10.1007/978-3-319-22267-7_9

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  • DOI: https://doi.org/10.1007/978-3-319-22267-7_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22266-0

  • Online ISBN: 978-3-319-22267-7

  • eBook Packages: EngineeringEngineering (R0)

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