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 $\Psi$ for the SFMs emerge from the QBD calculations in the natural limit.

Item Type:	Refereed Article
Keywords:	stochastic fluid model, quasi-birth-and-death process, Markov chain, uniformization
Research Division:	Mathematical Sciences
Research Group:	Statistics
Research Field:	Stochastic analysis and modelling
Objective Division:	Expanding Knowledge
Objective Group:	Expanding knowledge
Objective Field:	Expanding knowledge in the mathematical sciences
UTAS Author:	O'Reilly, MM (Associate Professor Malgorzata O'Reilly)
ID Code:	87031
Year Published:	2013
Web of Science® Times Cited:	5
Deposited By:	Mathematics and Physics
Deposited On:	2013-11-06
Last Modified:	2015-01-27
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