The threshold policy in the M/G/1 queue with server vacations

Offer Kella*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

114 Scopus citations


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).

Original languageAmerican English
Pages (from-to)111-123
Number of pages13
JournalNaval Research Logistics
Issue number1
StatePublished - Feb 1989
Externally publishedYes


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