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

Citation

O'Reilly, MM and Scheinhardt, W, Stationary distributions for a class of Markov-modulated tandem fluid queues, Stochastic Models pp. 1-28. ISSN 1532-6349 (In Press) [Refereed Article]


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Abstract

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 Laplaceľ 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:tandem fluid model
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:120231
Year Published:In Press
Funding Support:Australian Research Council (LP140100152)
Deposited By:Mathematics and Physics
Deposited On:2017-08-16
Last Modified:2017-08-17
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