A make-to-stock mountain-type inventory model

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 a(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.