Service-Adaptive Multitype Repairman Problems
Gaver, Donald P.
Morrison, John A.
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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.