We consider multi-stage stochastic fluid models (SFMs), driven by applications in telecommunications and manufacturing in which control of the behavior of the system during congestion may be required. In a two-stage SFM, the process starts from Stage 1 in level 0, and moves to Stage 2 when reaching threshold b₂ from below. Stage 1 starts again when reaching threshold b₁ < b₂ from above. While in a particular stage, the process evolves according to a traditional SFM with a unique set of phases, generator and fluid rates. We first consider a two-stage SFM with general, real fluid change rates. Next, we analyze a twostage SFM with an upper boundary B > b₂. Finally, we discuss a generalization to multi-stage SFMs. We use matrix-analytic methods and derive efficient methodology for the analysis of this class of models.

Item Type:	Refereed Article
Keywords:	stochastic fluid model, Markov chain, laplace-stieltjes transform, matrix-analytic methods, congestion control
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:	91733
Year Published:	2014
Funding Support:	Australian Research Council (DP1111663)
Web of Science® Times Cited:	4
Deposited By:	Mathematics and Physics
Deposited On:	2014-05-28
Last Modified:	2017-10-30
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