Service-Adaptive Multitype Repairman Problems
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Authors
Gaver, Donald P.
Morrison, John A.
Silveira, Rogerio
Subjects
logistics and repair
adaptive control
dynamic priorities
heavy-traffic asymptotics
flexible manufacturing
adaptive control
dynamic priorities
heavy-traffic asymptotics
flexible manufacturing
Advisors
Date of Issue
1993
Date
1993
Publisher
Society for Industrial and Applied Mathematics (SIAM)
Language
Abstract
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.
Type
Article
Description
Series/Report No
Department
Operations Research (OR)
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funder
Format
12 p.
Citation
Gaver, D.P., Morrison, J.A., and Silveira, R., “Service-Adaptive Multi-Type Repairman Problems,” SIAM Journal of Applied Mathematics, Vol. 53, No. 2, April 1993, pp. 459-470.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.