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Controllable Capacity Queue with Synchronous Constant Service Time and Loss

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Queueing Theory and Network Applications (QTNA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10932))

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Abstract

In this paper we analyze a queue, in which the number of active servers can be controlled by means of probabilities specifying the dependency of the number of active servers on the actual number of customers and the number of active servers. We call this queue as controllable capacity queue. The service time is constant and the concurrently served customers are served in syncronized manner. The active number of servers can be incremented, decremented or kept unchanged at the ends of service time according to the given probabilities. The system has no buffer for long-term customer waiting, it is a loss system. Such system could be relevant in modeling Machine-To-Machine communication systems, in which the resources are limited.

We provide explicit form results for the joint and marginal distributions of the number of servers and the number of customers on PGF level. We give the condition of the stability and also provide the expressions of the most important system measures including the mean stationary number of servers, the mean stationary number of customers and the blocking probability.

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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. Kyoto University, Kyoto, Japan

    Yutaka Takahashi

  2. University of Tsukuba, Tsukuba, Japan

    Tuan Phung-Duc

  3. Ghent University, Gent, Belgium

    Sabine Wittevrongel

  4. Konan University, Kobe, Japan

    Wuyi Yue

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Saffer, Z., Grill, K., Yue, W. (2018). Controllable Capacity Queue with Synchronous Constant Service Time and Loss. In: Takahashi, Y., Phung-Duc, T., Wittevrongel, S., Yue, W. (eds) Queueing Theory and Network Applications. QTNA 2018. Lecture Notes in Computer Science(), vol 10932. Springer, Cham. https://doi.org/10.1007/978-3-319-93736-6_4

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  • DOI: https://doi.org/10.1007/978-3-319-93736-6_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93735-9

  • Online ISBN: 978-3-319-93736-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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