Maximum Level and Hitting Probabilities in Stochastic Fluid Flows Using Matrix Differential Riccati Equations Bruno Sericola and Marie-ange Remiche

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. Key-words: Fluid Queues, Matrix Differential Riccati Equations, Markov Chains