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A make-to-stock mountain-type inventory model. (English) Zbl 1321.90037

Summary: We consider the buffer content of a fluid queue or storage process. The buffer content varies in a way that depends on the state of an underlying three-state Markov process. In state 0 the buffer content increases at a rate \(\alpha(x)\) that is a function of the current buffer level \(x\); in states 1 and 2 it decreases linearly, with different speeds. We study the steady-state buffer content, by using level crossing theory and by exploiting relations between the fluid queue and queues with instantaneous input and/or output.

MSC:

90B22 Queues and service in operations research
90C40 Markov and semi-Markov decision processes

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References:

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