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A MAP-modulated fluid flow model with multiple vacations

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  • Jung Baek
  • Ho Lee
  • Se Lee
  • Soohan Ahn

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. Copyright Springer Science+Business Media, LLC 2013

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  • Jung Baek & Ho Lee & Se Lee & Soohan Ahn, 2013. "A MAP-modulated fluid flow model with multiple vacations," Annals of Operations Research, Springer, vol. 202(1), pages 19-34, January.
    • Handle: RePEc:spr:annopr:v:202:y:2013:i:1:p:19-34:10.1007/s10479-012-1100-y
    DOI: 10.1007/s10479-012-1100-y
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    References listed on IDEAS

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    1. Hyo-Seong Lee & Mandyam M. Srinivasan, 1989. "Control Policies for the M X /G/1 Queueing System," Management Science, INFORMS, vol. 35(6), pages 708-721, June.
    2. Yonatan Levy & Uri Yechiali, 1975. "Utilization of Idle Time in an M/G/1 Queueing System," Management Science, INFORMS, vol. 22(2), pages 202-211, October.
    3. Jung Baek & Ho Lee & Se Lee & Soohan Ahn, 2008. "A factorization property for BMAP/G/1 vacation queues under variable service speed," Annals of Operations Research, Springer, vol. 160(1), pages 19-29, April.
    4. Yeralan, Sencer & Franck, Wallace E. & Quasem, Mohammad A., 1986. "A continuous materials flow production line model with station breakdown," European Journal of Operational Research, Elsevier, vol. 27(3), pages 289-300, December.
    5. Daniel P. Heyman, 1977. "The T-Policy for the M/G/1 Queue," Management Science, INFORMS, vol. 23(7), pages 775-778, March.
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    Cited by:

    1. Xindan Li & Dan Tang & Yongjin Wang & Xuewei Yang, 2014. "Optimal processing rate and buffer size of a jump-diffusion processing system," Annals of Operations Research, Springer, vol. 217(1), pages 319-335, June.
    2. Wojciech M. Kempa, 2016. "Transient workload distribution in the $$M/G/1$$ M / G / 1 finite-buffer queue with single and multiple vacations," Annals of Operations Research, Springer, vol. 239(2), pages 381-400, April.

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