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ON A GENERIC CLASS OF LÉVY-DRIVEN VACATION MODELS

Published online by Cambridge University Press:  21 December 2009

Onno Boxma ,
Offer Kella  and
Michel Mandjes
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
Offer Kella
Affiliation:
Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel E-mail: offer.kella@huji.ac.il
Michel Mandjes
Affiliation:
Korteweg-de Vries Institute for Mathematics, The University of Amsterdam, Science Park 904, 1098 TV Amsterdam, The Netherlands E-mail: mmandjes@science.uva.nl
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Abstract

This article analyzes a generic class of queuing systems with server vacation. The special feature of the models considered is that the duration of the vacations explicitly depends on the buffer content evolution during the previous active period (i.e., the time elapsed since the previous vacation). During both active periods and vacations, the buffer content evolves as a Lévy process. For two specific classes of models, the Laplace–Stieltjes transform of the buffer content distribution at switching epochs between successive vacations and active periods, and in steady state, is derived.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 1 , January 2010 , pp. 1 - 12
Copyright
Copyright © Cambridge University Press 2009

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