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Equilibrium Analysis of the M/M/1 Queues with Setup Times Under N-Policy

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Queueing Theory and Network Applications (QTNA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10591))

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Abstract

Chen et al. (2015) studied the equilibrium threshold balking strategies for the fully observable and fully unobservable single-server queues with threshold policy and setup times. The server shuts down whenever the system becomes empty, and is only resumed when the number of customers reaches to a given threshold. Customers decide whether to join or to balk the system based on their observations of the queue length and status of the server at arrival instants. This paper aims to study the partially observable case and the unobservable case. The stationary probability distribution, the mean queue length and the social welfare are derived. The equilibrium strategies for the customers and the system performance under these strategies are analyzed.

This work is supported by the National Natural Science Foundation of China (Grant Nos. 71571014 and 71390334).

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Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and constructive suggestions that help to improve the presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China

    Yaqian Hao, Jinting Wang, Mingyu Yang & Ruoyu Wang

Authors
  1. Yaqian Hao
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  2. Jinting Wang
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  3. Mingyu Yang
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  4. Ruoyu Wang
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Corresponding author

Correspondence to Jinting Wang .

Editor information

Editors and Affiliations

  1. Konan University, Kobe, Japan

    Wuyi Yue

  2. Yanshan University, Qinhuangdao, China

    Quan-Lin Li

  3. Yanshan University, Qinhuangdao, China

    Shunfu Jin

  4. Yanshan University, Qinhuangdao, China

    Zhanyou Ma

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Hao, Y., Wang, J., Yang, M., Wang, R. (2017). Equilibrium Analysis of the M/M/1 Queues with Setup Times Under N-Policy. In: Yue, W., Li, QL., Jin, S., Ma, Z. (eds) Queueing Theory and Network Applications. QTNA 2017. Lecture Notes in Computer Science(), vol 10591. Springer, Cham. https://doi.org/10.1007/978-3-319-68520-5_1

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  • DOI: https://doi.org/10.1007/978-3-319-68520-5_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68519-9

  • Online ISBN: 978-3-319-68520-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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