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The threshold policy in the M / G /1 queue with server vacations
Author(s) -
Kella Offer
Publication year - 1989
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198902)36:1<111::aid-nav3220360109>3.0.co;2-3
Subject(s) - computer science , queue , mathematical optimization , service (business) , operations research , average cost , holding cost , expression (computer science) , real time computing , operations management , computer network , microeconomics , mathematics , business , economics , marketing , programming language
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).