Consider a set of n machines and a single repair facility to service them. Suppose that when machine i, i = 1, . . . , n, goes down it requires an exponentially distributed amount of work with rate μi to get it back up. The repair facility divides its efforts equally among all down components in the sense that whenever there are k down machines 1  k  n each receives work at a rate of 1/k per unit time. Finally, suppose that each time machine i goes back up it remains up for an exponentially distributed time with rate λi.

The preceding can be analyzed as a continuous-time Markov chain having 2n states where the state at any time corresponds to the set of machines that are down at that time. Thus, for instance, the state will be (i1, i2, . . . , ik) when machines i1, . . . , ik are down and all the others are up. The instantaneous transition rates are as follows:

q(i1,...,ik−1),(i1,...,ik) = λik , q(i1,...,ik),(i1,...,ik−1) = μik/k where i1, . . . , ik are all distinct. This follows since the failure rate of machine ik is always λik and the repair rate of machine ik when there are k failed machines is μik/k.