AbstractA situation is considered where a machine or a production line, for example an electronic computer or a data-processing system, has alternate "good" and "bad" periods of operation. Two types of model are described which can be used to tackle this kind of situation and these form an approach to the practical problem of scheduling work through such a system. The two aspects considered are the probability of a preassigned schedule of operation being completed within some critical time, and the optimum assignment of the length of the scheduled operations.