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M/M/1 Queue with Controllable Service Rate

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Queueing Theory and Network Applications (QTNA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11688))

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Abstract

In this paper we consider an M/M/1 queue, in which the customer service rate is allowed to be increased and decreased by a fixed value at each customer service completion. These changes in service rate are controlled by probabilities depending on the actual number of customers and the actual service rate. The dependency on the number of customers follows a specific power form, while the dependency on actual service rate is general and independent of the dependency on the number of customers.

We describe how to compute the partial stationary distribution of the service rate values when the system is empty. Based on it we provide a computational procedure for computing the stationary probability vectors of the number of customers in the system. We derive also the vector probability generating function and the vector mean of the stationary number of customers.

We establish a methodology which utilizes the specific structure of the model. This methodology inherits some element from the stationary analysis of the standard QBD model and provides a first order, forward algorithm for computing the stationary probability vectors of the number of customers in the system.

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Author information

Authors and Affiliations

  1. Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria

    Zsolt Saffer & Karl Grill

  2. Department of Intelligence and Informatics, Konan University, Kobe, 658-8501, Japan

    Wuyi Yue

Authors
  1. Zsolt Saffer
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  2. Karl Grill
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  3. Wuyi Yue
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Corresponding author

Correspondence to Zsolt Saffer .

Editor information

Editors and Affiliations

  1. University of Tsukuba, Tsukuba, Japan

    Tuan Phung-Duc

  2. Nara Institute of Science and Technology, Nara, Japan

    Shoji Kasahara

  3. Ghent University, Ghent, Belgium

    Sabine Wittevrongel

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Saffer, Z., Grill, K., Yue, W. (2019). M/M/1 Queue with Controllable Service Rate. In: Phung-Duc, T., Kasahara, S., Wittevrongel, S. (eds) Queueing Theory and Network Applications. QTNA 2019. Lecture Notes in Computer Science(), vol 11688. Springer, Cham. https://doi.org/10.1007/978-3-030-27181-7_7

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  • DOI: https://doi.org/10.1007/978-3-030-27181-7_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-27180-0

  • Online ISBN: 978-3-030-27181-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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