Stationary distributions for a class of Markov-modulated tandem fluid queues
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 ModelsVolume
33Issue
4Pagination
524-550ISSN
1532-6349Department/School
School of Natural SciencesPublisher
Marcel Dekker IncPlace of publication
270 Madison Ave, New York, USA, Ny, 10016Rights statement
Copyright 2017 Taylor & FrancisRepository Status
- Restricted