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Fluid queues with level dependent evolution

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  • Silva Soares, Ana da
  • Latouche, Guy

Abstract

A fluid queue is a two-dimensional Markov process, of which the first component, or level, varies linearly according to the second component, the phase, which is the state of a finite state space Markov process evolving in the background. In this paper, we construct various models of fluid queues, with a level dependency component: the behavior of the phase process changes when the level crosses certain thresholds, as well as the rate at which fluid increases or decreases; this adds the possibility of having attractive and repellent states at the threshold levels. We derive expressions for the stationary distribution of such processes.

Suggested Citation

  • Silva Soares, Ana da & Latouche, Guy, 2009. "Fluid queues with level dependent evolution," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1041-1048, August.
    • Handle: RePEc:eee:ejores:v:196:y:2009:i:3:p:1041-1048
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    Citations

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    Cited by:

    1. Samuelson, Aviva & Haigh, Andrew & O'Reilly, Małgorzata M. & Bean, Nigel G., 2017. "Stochastic model for maintenance in continuously deteriorating systems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1169-1179.
    2. Mehmet Akif Yazici & Nail Akar, 2017. "The finite/infinite horizon ruin problem with multi-threshold premiums: a Markov fluid queue approach," Annals of Operations Research, Springer, vol. 252(1), pages 85-99, May.
    3. Gábor Horváth & Miklós Telek, 2017. "Matrix-analytic solution of infinite, finite and level-dependent second-order fluid models," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 325-343, December.
    4. Van Houdt, Benny, 2012. "Analysis of the adaptive MMAP[K]/PH[K]/1 queue: A multi-type queue with adaptive arrivals and general impatience," European Journal of Operational Research, Elsevier, vol. 220(3), pages 695-704.
    5. O. Boxma & A. Löpker & D. Perry, 2016. "On a make-to-stock production/mountain modeln with hysteretic control," Annals of Operations Research, Springer, vol. 241(1), pages 53-82, June.
    6. Nail Akar & Omer Gursoy & Gabor Horvath & Miklos Telek, 2021. "Transient and First Passage Time Distributions of First- and Second-order Multi-regime Markov Fluid Queues via ME-fication," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1257-1283, December.
    7. Yutaka Sakuma & Onno Boxma & Tuan Phung-Duc, 2021. "An M/PH/1 queue with workload-dependent processing speed and vacations," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 373-405, August.
    8. Salah Al-Deen Almousa & Gábor Horváth & Miklós Telek, 2022. "Transient analysis of piecewise homogeneous Markov fluid models," Annals of Operations Research, Springer, vol. 310(2), pages 333-353, March.
    9. D’Auria, Bernardo & Adan, Ivo J.B.F. & Bekker, René & Kulkarni, Vidyadhar, 2022. "An M/M/c queue with queueing-time dependent service rates," European Journal of Operational Research, Elsevier, vol. 299(2), pages 566-579.
    10. Carmen, Raïsa & Van Nieuwenhuyse, Inneke & Van Houdt, Benny, 2018. "Inpatient boarding in emergency departments: Impact on patient delays and system capacity," European Journal of Operational Research, Elsevier, vol. 271(3), pages 953-967.
    11. O’Reilly, Małgorzata M., 2014. "Multi-stage stochastic fluid models for congestion control," European Journal of Operational Research, Elsevier, vol. 238(2), pages 514-526.

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