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]
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 Type:||Refereed Article|
|Keywords:||Laplace–Stieltjes transform, limiting distribution, Markov chain, stochastic fluid model, tandem, transient analysis|
|Research Division:||Mathematical Sciences|
|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)|
|Funding Support:||Australian Research Council (LP140100152)|
|Deposited By:||Mathematics and Physics|
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