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On the overflow time of a fluid model

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  • Andreas Löpker

    (Helmut-Schmidt University)

Abstract

We consider a continuous time stochastic fluid model with alternating on- and off-periods. During on-periods the process increases linearly, during off periods there is an additional negative decrease rate, proportional to the content level. While the durations of the on-periods have an exponential distribution we allow for general distributions for the durations of the off-periods. We study the overflow time of the system and its behavior as the overflow level tends to infinity. Such systems can be related to queuing systems which switch between a one-server mode and phases with infinitely many available servers.

Suggested Citation

  • Andreas Löpker, 2016. "On the overflow time of a fluid model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 59-92, August.
    • Handle: RePEc:spr:mathme:v:84:y:2016:i:1:d:10.1007_s00186-016-0534-4
    DOI: 10.1007/s00186-016-0534-4
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    References listed on IDEAS

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    1. J. Michael Harrison & Sidney I. Resnick, 1976. "The Stationary Distribution and First Exit Probabilities of a Storage Process with General Release Rule," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 347-358, November.
    2. Bruno Sericola & Marie-Ange Remiche, 2011. "Maximum Level and Hitting Probabilities in Stochastic Fluid Flows Using Matrix Differential Riccati Equations," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 307-328, June.
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