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A MAP-modulated fluid flow model with multiple vacations

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Abstract

We consider a MAP-modulated fluid flow queueing model with multiple vacations. As soon as the fluid level reaches zero, the server leaves for repeated vacations of random length V until the server finds any fluid in the system. During the vacation period, fluid arrives from outside according to the MAP (Markovian Arrival Process) and the fluid level increases vertically at the arrival instance. We first derive the vector Laplace–Stieltjes transform (LST) of the fluid level at an arbitrary point of time in steady-state and show that the vector LST is decomposed into two parts, one of which the vector LST of the fluid level at an arbitrary point of time during the idle period. Then we present a recursive moments formula and numerical examples.

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Acknowledgements

Authors are thankful to the referees for their valuable comments.

This paper was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (grant number: 2010-0010023).

Soohan Ahn was partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (grant number 20100021831) and also by the University of Seoul 2010 Research Fund.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Canada

    Jung Woo Baek

  2. Department of Systems Management Engineering, Sungkyunkwan University, Suwon, Korea

    Ho Woo Lee

  3. Department of Business Administration, Dongguk University Seoul, Seoul, Korea

    Se Won Lee

  4. Department of Statistics, The University of Seoul, Seoul, Korea

    Soohan Ahn

Authors
  1. Jung Woo Baek
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  2. Ho Woo Lee
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  3. Se Won Lee
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  4. Soohan Ahn
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Corresponding author

Correspondence to Ho Woo Lee.

Additional information

This paper was prepared and submitted when Jung Woo Baek was a postdoc researcher at Research Inst. of Information and Communication, Sungkyunkwan University, Suwon, Korea and Se Won Lee was a BK-21 postdoc researcher at Dept. of Industrial Engineering, Sungkyunkwan University, Suwon, Korea.

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Baek, J.W., Lee, H.W., Lee, S.W. et al. A MAP-modulated fluid flow model with multiple vacations. Ann Oper Res 202, 19–34 (2013). https://doi.org/10.1007/s10479-012-1100-y

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