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Bounds on the Optimal Operating Policy for a Class of Single-Server Queues

Daniel P. Heyman and Kneale T. Marshall
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Daniel P. Heyman: Bell Telephone Laboratories, Holmdel, New Jersey
Kneale T. Marshall: Bell Telephone Laboratories, Holmdel, New Jersey

Operations Research, 1968, vol. 16, issue 6, 1138-1146

Abstract: We consider the economic behavior of a single-channel queuing system operating with the following cost structure: a server start-up cost, a server shut-down cost, a cost per unit time when the server is turned off, a cost per unit time when the server is turned on, and a holding cost per unit time spent in the system for each customer. For the undiscounted, infinite-horizon problem, bounds are obtained for the cost rate and optimal policy when the interarrival time distribution is a member of the class of increasing-failure-rate distributions. Some of the bounds hold for all interarrival-time distributions.

Date: 1968
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