SERVICE-ADAPTIVE MULTITYPE REPAIRMAN PROBLEMS

The classical ''repairman problem'' (cf. [Feller, An Introduction to Probability Theory and its Applications, Vol. I, 3rd ed., John Wiley, New York, 1967]) is generalized to consider r failure-prone machine types, each type having its own individual failure rate and repair rate. Each failed machine joins its type queue and is repaired by a single server. Several dynamic service priority schemes are considered that approximate first-come first-served, longest-line first, and least-available first situations. A heavy-traffic asymptotic analysis determines approximations to the time-dependent mean and covariance of individual-type queue lengths and shows that the marginal joint distribution of queue lengths is approximately Ornstein-Uhlenbeck. Numerical illustrations of approximation accuracy are provided, as well as suggested applications to computer performance and manufacturing systems analysis.