The Machine Repair Problem with Heterogeneous Populations

The classic machine repair with spares (finite source) queueing model assumes all calling units are identical in failure and repair characteristics. This paper develops, for a first-come first-served discipline, a procedure for treating nonhomogeneous populations, specifically, a population with two types of items, each with exponential failure and repair times but with different mean values. Exact solutions are obtained for small population sizes and compared to approximate procedures using the classical theory. The exact model is essentially a two-stage cyclic queue with two classes of customers. Extensions of the model to N stages and M customer classes, priority disciplines, and other disciplines, including blocking, are discussed.