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Fluid Polling System with Markov Modulated Load and Gated Discipline

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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 provide an analysis for fluid polling models with Markov modulated load and gated discipline. The fluid arrival to the stations is modulated by a common continuous-time Markov chain. The fluid is removed at the stations during the service period by a station dependent constant rate.

We build partly on the methods used previously in the analysis of fluid vacation models with gated discipline. We establish steady-state relationships on Laplace transform level regarding the joint distribution of the fluid levels at the stations and the state of the modulating Markov chain among different characteristic epochs including start and end of the service at each station. We derive the steady-state vector Laplace transform of the fluid levels at the stations at arbitrary epoch and its mean.

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Acknowledgment

This work is supported by the OTKA K-123914 project and by the ÚNKP-17-4-III New National Excellence Program of the Ministry of Human Capacities.

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Authors and Affiliations

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

    Zsolt Saffer

  2. MTA-BME Information Systems Research Group, Budapest University of Technology and Economics, Magyar Tudósok Körútja 2, Budapest, 1117, Hungary

    Miklós Telek

  3. Department of Networked Systems and Services, Budapest University of Technology and Economics, Magyar Tudósok Körútja 2, Budapest, 1117, Hungary

    Gábor Horváth

Authors
  1. Zsolt Saffer
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  2. Miklós Telek
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  3. Gábor Horváth
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Corresponding author

Correspondence to Gábor Horváth .

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., Telek, M., Horváth, G. (2018). Fluid Polling System with Markov Modulated Load and Gated Discipline. 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_6

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  • DOI: https://doi.org/10.1007/978-3-319-93736-6_6

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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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