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

journal contribution
posted on 2023-05-19, 09:53 authored by Malgorzata O'ReillyMalgorzata O'Reilly, Scheinhardt, W

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.

Funding

Australian Research Council

History

Publication title

Stochastic Models

Volume

33

Issue

4

Pagination

524-550

ISSN

1532-6349

Department/School

School of Natural Sciences

Publisher

Marcel Dekker Inc

Place of publication

270 Madison Ave, New York, USA, Ny, 10016

Rights statement

Copyright 2017 Taylor & Francis

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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