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ON A QUEUING MODEL WITH SERVICE INTERRUPTIONS

Published online by Cambridge University Press:  25 September 2008

Onno Boxma ,
Michel Mandjes  and
Offer Kella
Onno Boxma
Affiliation:
EURANDOM and Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands E-mail: boxma@win.tue.nl
Michel Mandjes
Affiliation:
Korteweg-de Vries Institute for Mathematics, The University of Amsterdam, 1018 TV Amsterdam, The Netherlands and CWI, 1090 GB Amsterdam, The Netherlands E-mail: mmandjes@science.uva.nl
Offer Kella
Affiliation:
Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel E-mail: Offer.Kella@huji.ac.il
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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.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 4 , October 2008 , pp. 537 - 555
Copyright
Copyright © Cambridge University Press 2008

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