Introduction to Probability Models, Ninth Edition
Introduction to Probability Models, Ninth Edition
Hitting probabilities and hitting times for stochastic fluid flows: The bounded model
Probability in the Engineering and Informational Sciences
A stochastic fluid model for an ad hoc mobile network
Queueing Systems: Theory and Applications
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We derive a uniformization of a stochastic fluid model (SFM) to a Quasi-Birth-and-Death process (QBD) that is spatially-coherent since the continuous level in the SFM has a natural correspondence to the discrete level in the QBD. As a consequence of this, the QBD can be used as a direct approximation of the original SFM, in those situations where a discrete state space is an advantage. We treat the unbounded as well as the bounded cases and illustrate the theory with a numerical example. The key fluid generator, Q, and matrix @J for the SFMs emerge from the QBD calculations in the natural limit.