A correlated M/G/1-type queue with randomized server repair and maintenance modes

We consider a single machine, subject to breakdown, that produces items to inventory, continuously and uniformly. While the machine is working (an ON period), there is a deterministic net ow into the bu er. There are also two di erent types of OFF periods; one is a repair operation initiated after a breakdown, and the other is a preventive maintenance operation. The length of an OFF period depends on the length of the preceding ON period. During OFF periods there is a uniform out ow from the inventory bu er. The bu er content process can then be described as a uid model. The main tool employed in determining its steady-state law exploits an equivalence relationship between the bu er content process and the virtual waiting time process of a special single-server queue in which the interarrival times and the service requirements depend on each other. We present an appropriate cost function and provide an optimization scheme illustrated by some numerical results. c © 2000 Elsevier Science B.V. All rights reserved.