Optimality of threshold policies in single-server queueing systems with server vacations

Optimality of threshold policies in single-server queueing systems with server vacations

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Article ID: iaor19921952
Country: United Kingdom
Volume: 23
Issue: 2
Start Page Number: 388
End Page Number: 405
Publication Date: Jun 1991
Journal: Advances in Applied Probability
Authors: ,
Keywords: vacation models
Abstract:

In this paper the authors consider a class of single-server queueing systems with compound Poisson arrivals, in which, at service completion epochs, the server has the option of taking off for one or several vacations of random length. The cost structure consists of a holding cost rate specified by a general non-decreasing function of the queue size, fixed costs for initiating and terminating service, and a variable operating cost incurred for each unit of time that the system is in operation. The authors show under some weak conditions with respect to the holding cost rate function and the service time, vacation time and arrival batch size distributions that it is either optimal among all feasible (stationary and non-stationary) policies never to take a vacation, or it is optimal to take a vacation when the systems empties out and to resume work when, upon completion of a vacation, the queue size is equal to or in excess of a critical threshold. These optimality results are generalized for several variants of this model.

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