Abstract
In the last twenty years the field of Markovmodulated fluid queues has received considerable attention. In these models a fluid reservoir receives and/or releases fluid at rates which depend on the actual state of a background Markov chain. In the first chapter of this thesis we give a short introduction on how the stationary distribution for such a model is usually found, as well as a literature overview on Markovmodulated and related uid queues. The rest of the thesis is concerned with finding stationary distributions for some types of fluid models that have received little or no attention until now. The two main contributions are the following.
1. We focus on models in which the state space of the regulating Markov process is infinitely large, either denumerable or not. Regarding the first type, we mainly look into regulating processes that are of birthdeath type. We present procedures to find the stationary distribution, using the theory of orthogonal polynomials. In the nondenumerable case, we look into simple systems of fluid queues, in which one fluid queue regulates the behaviour of another (one example being a fluid tandem queue).
2. We look into models in which the state of the fluid reservoir in quences the behaviour of the regulating process, so that the latter does not constitute a Markov process. We call suchlike systems feedback fluid queues, to emphasize the twoway dependence between fluid reservoir and regulating process.
1. We focus on models in which the state space of the regulating Markov process is infinitely large, either denumerable or not. Regarding the first type, we mainly look into regulating processes that are of birthdeath type. We present procedures to find the stationary distribution, using the theory of orthogonal polynomials. In the nondenumerable case, we look into simple systems of fluid queues, in which one fluid queue regulates the behaviour of another (one example being a fluid tandem queue).
2. We look into models in which the state of the fluid reservoir in quences the behaviour of the regulating process, so that the latter does not constitute a Markov process. We call suchlike systems feedback fluid queues, to emphasize the twoway dependence between fluid reservoir and regulating process.
Original language  English 

Awarding Institution 

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Award date  4 Dec 1998 
Place of Publication  Enschede 
Publisher  
Print ISBNs  9036512484 
Publication status  Published  4 Dec 1998 