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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.

90B22 Queues and service in operations research
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