A mountain process with state dependent input and output and a correlated dam

We consider a single machine, subject to breakdown, that produces items to inventory. While the machine is working (an ON period) there is a net flow, with general deterministic production rate, into the buffer. As a result, the production rate minus the demand rate generate a certain deterministic increase rate which is state dependent. There are two different types of OFF periods. One is the repair operation initiated after a breakdown; the second is a preventive maintenance operation. The length of an OFF period depends on the preceding ON period. During the OFF periods there is a deterministic outflow (whose release rule is general but state dependent), generated by the demand rate. The buffer content process can then be described as a fluid model called the mountain process. The main tool employed in determining its steady state law exploits an equivalence relationship between the mountain process and a special dam process with general release rule whose jumps are also state dependent. This study is a continuation and generalization of a previous work [Oper. Res. Lett. 26 (2000) 137-147], in which both the production rate and the demand rate are assumed to be constant.