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Stationary distributions for a class of Markov-modulated tandem fluid queues


O'Reilly, MM and Scheinhardt, W, Stationary distributions for a class of Markov-modulated tandem fluid queues, Stochastic Models, 33, (4) pp. 524-550. ISSN 1532-6349 (2017) [Refereed Article]

Copyright Statement

Copyright 2017 Taylor & Francis

DOI: doi:10.1080/15326349.2017.1349615


We consider a model consisting of two fluid queues driven by the same background continuous-time Markov chain, such that the rates of change of the fluid in the second queue depend on whether the first queue is empty or not: when the first queue is nonempty, the content of the second queue increases, and when the first queue is empty, the content of the second queue decreases.

We analyze the stationary distribution of this tandem model using operator-analytic methods. The various densities (or Laplace–Stieltjes transforms thereof) and probability masses involved in this stationary distribution are expressed in terms of the stationary distribution of some embedded process. To find the latter from the (known) transition kernel, we propose a numerical procedure based on discretization and truncation. For some examples we show the method works well, although its performance is clearly affected by the quality of these approximations, both in terms of accuracy and run time.

Item Details

Item Type:Refereed Article
Keywords:Laplace-Stieltjes transform, limiting distribution, Markov chain, stochastic fluid model, tandem, transient analysis
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:120231
Year Published:2017
Funding Support:Australian Research Council (LP140100152)
Web of Science® Times Cited:2
Deposited By:Mathematics and Physics
Deposited On:2017-08-16
Last Modified:2018-04-27

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