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Maximum Level and Hitting Probabilities in Stochastic Fluid Flows Using Matrix Differential Riccati Equations

Author

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  • Bruno Sericola

    (INRIA Rennes—Bretagne Atlantique)

  • Marie-Ange Remiche

    (Université Libre de Bruxelles)

Abstract

In this work, we expose a clear methodology to analyze maximum level and hitting probabilities in a Markov driven fluid queue for various initial condition scenarios and in both cases of infinite and finite buffers. Step by step we build up our argument that finally leads to matrix differential Riccati equations for which there exists a unique solution. The power of the methodology resides in the simple probabilistic argument used that permits to obtain analytic solutions of these differential equations. We illustrate our results by a comprehensive fluid model that we exactly solve.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:2:d:10.1007_s11009-009-9149-z
    DOI: 10.1007/s11009-009-9149-z
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    References listed on IDEAS

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    1. V. Ramaswami, 2006. "Passage Times in Fluid Models with Application to Risk Processes," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 497-515, December.
    2. Fabrice Guillemin & Bruno Sericola, 2007. "Stationary Analysis of a Fluid Queue Driven by Some Countable State Space Markov Chain," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 521-540, December.
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    Cited by:

    1. 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.

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