On a queuing model with service interruptions

Onno Boxma*, Michel Mandjes, Offer Kella

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

Single-server queues in which the server takes vacations arise naturally as models for a wide range of computer, communication, and production systems. In almost all studies on vacation models, the vacation lengths are assumed to be independent of the arrival, service, workload, and queue length processes. In the present study, we allow the length of a vacation to depend on the length of the previous active period (viz. the period since the previous vacation). Under rather general assumptions regarding the offered work during active periods and vacations, we determine the steady-state workload distribution, both for single and multiple vacations. We conclude by discussing several special cases, including polling models, and relate our findings to results obtained earlier.

Original languageAmerican English
Pages (from-to)537-555
Number of pages19
JournalProbability in the Engineering and Informational Sciences
Volume22
Issue number4
DOIs
StatePublished - Oct 2008

Bibliographical note

Funding Information:
The authors are grateful to the referee for several interesting questions and useful suggestions. Part of this work was done while the third author visited EURANDOM and CWI as a Stieltjes visiting professor. The third author is also supported by grant 964/06 from the Israel Science Foundation and the Vigevani Chair in Statistics. The research of the first and second author was done within the framework of the BRICKS project and the European Network of Excellence Euro-NGI.

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