The efficiency of unidirectionally patrolled machines

This paper solves the problem of determining the efficiency of N (not identical) machines which are unidirectionally patrolled by one operative. Generally the machines will be equally spaced in a circular configuration so that the time to walk from one machine to the next will be a constant. However, the case of unequal spacing is just as easy to handle. It is assumed that breakdowns of machine j occur at random at average rate γ_j in running time, and that the time to repair this machine is a constant, c_j. This situation could arise from a mix of new and old machines or, in a textile context, in a situation where different types of yarn are being processed on different machines.