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Fluid queues with level dependent evolution. (English) Zbl 1176.90117
Summary: A fluid queue is a two-dimensional Markov process, of which the first component, or level, varies linearly according to the second component, the phase, which is the state of a finite state space Markov process evolving in the background.In this paper, we construct various models of fluid queues, with a level dependency component: the behavior of the phase process changes when the level crosses certain thresholds, as well as the rate at which fluid increases or decreases; this adds the possibility of having attractive and repellent states at the threshold levels. We derive expressions for the stationary distribution of such processes.

MSC:
90B22 Queues and service in operations research
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