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

Bruno Sericola 1 Marie-Ange Remiche 2
1 DIONYSOS - Dependability Interoperability and perfOrmance aNalYsiS Of networkS
Inria Rennes – Bretagne Atlantique , IRISA-D2 - RÉSEAUX, TÉLÉCOMMUNICATION ET SERVICES
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.
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https://hal.inria.fr/hal-00713141
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Submitted on : Friday, June 29, 2012 - 2:20:59 PM
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Bruno Sericola, Marie-Ange Remiche. Maximum Level and Hitting Probabilities in Stochastic Fluid Flows Using Matrix Differential Riccati Equations. Methodology and Computing in Applied Probability, Springer Verlag, 2011, 13 (2), ⟨10.1007/s11009-009-9149-z⟩. ⟨hal-00713141⟩

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