In this paper we study a class of open queueing network where servers suffer breakdowns and are subsequently repaired. The network topology is a pipeline with feedback from the final node to the first. Each node consists of a number of queues each with an unreliable server. There are no losses from the queues in this system, however jobs are routed according to the distribution of operational servers at each node in the pipeline. This model is in general intractable, however an iterative technique is presented which combines a number of earlier results to generate an approximation to steady state measures found by simulation.
Information from pubs.doc.ic.ac.uk/approx-queueing-breakdowns.