Machine Repair as a Priority Waiting-Line Problem

A paper by Cobham (Cobham, A. 1954. J. Opns. Res. Soc. Am.2 70.) in this Journal, dealing with the assignment of priorities in waiting-line problems, is taken as the basis for treatment of a particular variety of machine-repair problem in which shortest jobs, rather than first arrivals, receive highest priority. Cobham's results for the single channel case are found to be easily applicable to this type of priority assignment. These results take a particularly simple form when the priority-labeling index is allowed to assume continuous, rather than discrete, values. They apply to any case in which a one-channel facility repairs random failures from a very large population of machines.