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Discrete-time modified number- and time-limited vacation queues

Journal Contribution - Journal Article

A vast amount of literature has appeared on vacation queues. In the well-knownnumber- and time-limited vacation policies, the server goes on vacation if the numberof customers, respectively, work (time slots) served since the previous vacation reachesa specified value, or if the system becomes empty, whichever occurs first. However,in practice, the server does not always go on vacation when the system is empty ifthe number of customers/work to be served has not yet reached the specified amount.Therefore, we study modified number- and time-limited vacation policies, where weaccount for this feature. We complement our recent work on these vacation policies byconsidering a discrete time, instead of a continuous-time, setting. We therefore adopta different analysis approach, which enables us to obtain similar as well as new resultsas compared to our previous work. The results in this paper are valid for a memorylessdistribution, but also for distributions with finite support, and a mixture of geometricdistributions.
ISSN: 1572-9443
Issue: 3-4
Volume: 91
Pages: 297 - 318
Publication year:2019