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Spatially-coherent uniformization of a stochastic fluid model to a Quasi-Birth-and-Death process

Citation

Bean, NG and O'Reilly, MM, Spatially-coherent uniformization of a stochastic fluid model to a Quasi-Birth-and-Death process, Performance Evaluation, 70, (9) pp. 578-592. ISSN 0166-5316 (2013) [Refereed Article]

Copyright Statement

Copyright 2013 Elsevier

DOI: doi:10.1016/j.peva.2013.05.006

Abstract

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, View the MathML source, and matrix View the MathML source for the SFMs emerge from the QBD calculations in the natural limit.

Item Details

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
Author:O'Reilly, MM (Dr Malgorzata O'Reilly)
ID Code:87031
Year Published:2013
Web of Science® Times Cited:2
Deposited By:Mathematics and Physics
Deposited On:2013-11-06
Last Modified:2015-01-27
Downloads:0

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