Singularly Perturbed Markov Modulated Fluid Queues

We consider a Markov modulated fluid queue for which the environment is nearly completely decomposable. Under the basic assumption that both the nearly completely decomposable Markov modulated fluid model and the unperturbed fluid models are positive recurrent, we show that the stationary density of the level can be expanded as convergent power series of the aggregated stationary densities. We go further in the analysis by assuming that one or more of the unperturbed fluid queues is not necessarily positive recurrent. We provide numerical illustration.