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Markov-modulated fluid flow model with server maintenance period

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Abstract

We consider a Markov-modulated fluid flow model with server maintenance period. As soon as the fluid level reaches zero, the server begins a maintenance period of a random length. During the maintenance period, fluid arrives from outside depending on the state of the background Markov process and the level increases either vertically or linearly. This model can be applied to various real-world systems such as inventory systems and production systems. We first derive the distribution of the fluid level and the mean performance measures. Then, we present some numerical examples to show the effect of the maintenance time.

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Acknowledgements

Jung Woo Baek was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07043146). Soohan Ahn acknowledge the support by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (Grant numbers NRF-2018R1D1A1A09082881).

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Authors and Affiliations

  1. Department of Industrial Engineering, Chosun University, Gwangju, Korea

    Jung Woo Baek

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

    Ho Woo Lee

  3. Department of Statistics, University of Seoul, Seoul, Korea

    Soohan Ahn

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  1. Jung Woo Baek
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  2. Ho Woo Lee
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  3. Soohan Ahn
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Correspondence to Ho Woo Lee.

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Baek, J.W., Lee, H.W. & Ahn, S. Markov-modulated fluid flow model with server maintenance period. J. Korean Stat. Soc. 49, 395–421 (2020). https://doi.org/10.1007/s42952-019-00020-0

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