The threshold policy in theM/G/1 queue with server vacations

Offer Kella

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Advanced Queuing Theory Analysis Optimization and Search Problems Age of Information Optimization

Abstract

This article deals with the M/G/1 queue with server vacations in which the return of the server to service depends on the number of customers present in the system. The main goal is optimization, which is done under the average cost criterion in the multiple- and single-vacation models as well as for the “total cost for one busy cycle” criterion in the multiple-vacation case. Expressions that characterize the optimal number of customers, below which the server should not start a new service period, are exhibited for the various cases. It is found that under the average cost criterion, the expression may be universal in the sense that it may hold for a general class of problems including such that arise in production planning and inventory theory (for the particular cost structure discussed).

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References

1982Poisson Arrivals See Time Averages 1986Queueing systems with vacations ? A survey 1985Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations 1982Introduction to Queueing Theory 1963Queueing Systems with a Removable Service Station 1975Utilization of Idle Time in an M / G /1 Queueing System 1968Optimal Operating Policies for M / G /1 Queuing Systems 1970Queues Served in Cyclic Order: Waiting Times

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