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Analysis of an M/M/1 Retrial Queue with Speed Scaling

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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

Recently, queues with speed scaling have received considerable attention due to their applicability to data centers, enabling a better balance between performance and energy consumption. This paper proposes a new model where blocked customers must leave the service area and retry after a random time, with retrial rate either varying proportionally to the number of retrying customers (linear retrial rate) or non-varying (constant retrial rate). For both, we study the case without and with setup time. In all four cases, we obtain an exact solution for the stationary queue length distribution. This document presents the resulting expressions as well as their derivation.

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Author information

Authors and Affiliations

  1. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama, Tokyo, 152-8552, Japan

    Tuan Phung-Duc

  2. Department of Telecommunications and Information Processing, Ghent University, St.-Pietersnieuwstraat 41, 9000, Gent, Belgium

    Wouter Rogiest

Authors
  1. Tuan Phung-Duc
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  2. Wouter Rogiest
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Corresponding author

Correspondence to Wouter Rogiest .

Editor information

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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© 2016 Springer International Publishing Switzerland

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Phung-Duc, T., Rogiest, W. (2016). Analysis of an M/M/1 Retrial Queue with Speed Scaling. 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_11

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  • DOI: https://doi.org/10.1007/978-3-319-22267-7_11

  • 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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