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A Lévy input model with additional state-dependent services

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  • Palmowski, Zbigniew
  • Vlasiou, Maria

Abstract

We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers according to a spectrally positive Lévy process Y(t) which is reflected at 0. When the exponential clock ends, the additional state-dependent service requirement modifies the workload so that the latter is equal to at epoch for some random nonnegative i.i.d. functionals Fi. In particular, we focus on the case when Fi(y)=(Bi-y)+, where {Bi}i=1,2,... are i.i.d. nonnegative random variables. We analyse the steady-state workload distribution for this model.

Suggested Citation

  • Palmowski, Zbigniew & Vlasiou, Maria, 2011. "A Lévy input model with additional state-dependent services," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1546-1564, July.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:7:p:1546-1564
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    References listed on IDEAS

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    1. Maulik, Krishanu & Zwart, Bert, 2006. "Tail asymptotics for exponential functionals of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 156-177, February.
    2. Embrechts, Paul & Goldie, Charles M., 1982. "On convolution tails," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 263-278, September.
    3. Krishanu Maulik & Bert Zwart, 2009. "An extension of the square root law of TCP," Annals of Operations Research, Springer, vol. 170(1), pages 217-232, September.
    4. Bertoin, J. & Doney, R. A., 1994. "Cramer's estimate for Lévy processes," Statistics & Probability Letters, Elsevier, vol. 21(5), pages 363-365, December.
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    Cited by:

    1. Baurdoux, Erik J. & Palmowski, Z & Pistorius, Martijn R, 2017. "On future drawdowns of Lévy processes," LSE Research Online Documents on Economics 84342, London School of Economics and Political Science, LSE Library.
    2. 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.
    3. Baurdoux, E.J. & Palmowski, Z. & Pistorius, M.R., 2017. "On future drawdowns of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2679-2698.

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