Efficient estimation of overflow probabilities in queues with breakdowns

Kroese, Dirk P. and Nicola, Victor F. (1999) Efficient estimation of overflow probabilities in queues with breakdowns. Performance Evaluation, 36-37 471-484. doi:10.1016/S0166-5316(99)00036-X

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Author Kroese, Dirk P.
Nicola, Victor F.
Title Efficient estimation of overflow probabilities in queues with breakdowns
Journal name Performance Evaluation   Check publisher's open access policy
ISSN 0166-5316
Publication date 1999-08
Sub-type Article (original research)
DOI 10.1016/S0166-5316(99)00036-X
Open Access Status File (Author Post-print)
Volume 36-37
Start page 471
End page 484
Total pages 14
Place of publication Netherlands
Publisher Elsevier BV * North-Holland
Language eng
Abstract Efficient importance sampling methods are proposed for the simulation of a single server queue with server breakdowns. The server is assumed to alternate between the operational and failure states according to a continuous time Markov chain. Both, continuous (fluid flow) and discrete (single arrivals) sources are considered. In the fluid flow model, we consider Markov-modulated fluid sources and a constant output rate when the server is operational. In the discrete arrivals model, we consider Markov-modulated Poisson sources and generally distributed service time when the server is operational. We show how known results on Markov additive processes may be applied to determine the optimal (exponentially tilted) change of measure for both models. The concept of effective bandwidth is used in models with multiple independent sources. Empirical studies demonstrate the effectiveness of the proposed change of measures when used in importance sampling simulations.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Physical Sciences Publications
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Citation counts: TR Web of Science Citation Count  Cited 6 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 8 times in Scopus Article | Citations
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Created: Fri, 01 Jul 2011, 10:27:41 EST by Ms Lynette Adams on behalf of School of Mathematics & Physics