A single-server M/G/1 queueing system subject to breakdowns - Some reliability and queueing problems

We consider a single-server M/G/1 queueing system. While the server is up and working it is subject to breakdowns according to a Poisson process with rate sigma(> 0); while the server is up but idle it is subject to breakdowns according to a renewal process with distribution Y(t). When the server breaks down, we need to repair the broken server immediately with two repair models as types 1 and 2, corresponding to whether the breakdowns occur in the server's working or idle period. Under some mild conditions on the repair time and service time distributions, we study not only some queueing problems of the system, but also some reliability problems of the server, and obtain some satisfactory results. Copyright (C) 1996 Elsevier Science Ltd.