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On the optimal assignment of servers and a repairman

Published online by Cambridge University Press:  14 July 2016

C. Derman ,
G. J. Lieberman  and
S. M. Ross
C. Derman*
Affiliation:
Columbia University
G. J. Lieberman*
Affiliation:
Stanford University
S. M. Ross*
Affiliation:
University of California, Berkeley
*
∗Postal address: Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, U.S.A.
∗∗Postal address: Department of Operations Research, Stanford University, Stanford, CA 94305, U.S.A.
∗∗∗Postal address: Operations Research Center, University of California, Berkeley, CA 94720, U.S.A.
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Abstract

We consider an N-server queue with arbitrary arrivals and service times which are random but with differing rates for different servers. Customers arriving when all servers are occupied do not enter the system. We show that the policy of always assigning an arrival to that free server whose service rate is largest (smallest) stochastically minimises (maximises) the number in the system. We then show that in a particular component-repair context with exponential repair times the policy of repairing failed components with the smallest failure rate stochastically maximises the number of working components.

Keywords

ASSIGNMENTQUEUEING SYSTEMN SERVERSEXPONENTIAL SERVICESREPAIRMAN
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 577 - 581
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

This research has been partially supported by the Office of Naval Research under Contract N00014–77–C–0299 and the Air Force Office of Scientific Research (AFSC), USAF, under Grant AFOSR–77–3213 with the University of California; and by the Office of Naval Research under Contract N00014–67–A–0112–0052 with Stanford University and N00014–67–A–108–0003 with Columbia University.

References

Seth, K. (1977) Optimal service policies, just after idle periods, in two-server heterogeneous queueing systems. Operat. Res. 25, 356–361.Google Scholar
Smith, D. R. (1978) Optimal repair of the series system. Operat. Res. 26, 653–663.CrossRefGoogle Scholar