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Exhaustive Vacation Queue with Dependent Arrival and Service Processes

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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

This paper presents a more general class of MAP/MAP/1 exhaustive vacation queue, in which the Markov modulated arrival and service processes are dependent. This model class requires the evaluation of the busy period of quasi birth death process with arbitrary initial level, which is a new analysis element.

The model is analyzed by applying matrix analytic methods for the underlying quasi birth death process. The main result of the paper is the probability-generating function of the number of jobs in the system. Finally, a numerical example provides an insight into the behavior of the model.

The authors thank the support of the OTKA K101150 project.

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Author information

Authors and Affiliations

  1. Budapest University of Technology and Economics, Budapest, Hungary

    Gábor Horváth, Zsolt Saffer & Miklós Telek

  2. MTA-BME Information Systems Research Group, Budapest, Hungary

    Gábor Horváth & Miklós Telek

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

Correspondence to Gábor Horváth .

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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Horváth, G., Saffer, Z., Telek, M. (2016). Exhaustive Vacation Queue with Dependent Arrival and Service Processes. 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_2

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  • DOI: https://doi.org/10.1007/978-3-319-22267-7_2

  • 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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