ON AN EQUIVALENCE BETWEEN LOSS RATES AND CYCLE MAXIMA IN QUEUES AND DAMS-Reference-Cited by-同舟云学术

ON AN EQUIVALENCE BETWEEN LOSS RATES AND CYCLE MAXIMA IN QUEUES AND DAMS

Published:2005-03-23 Issue:2 Volume:19 Page:241-255
ISSN:0269-9648
Container-title:Probability in the Engineering and Informational Sciences
language:en
Short-container-title:Prob. Eng. Inf. Sci.

Author:

Bekker René,Zwart Bert

Abstract

We consider the loss probability of a customer in a single-server queue with finite buffer and partial rejection and show that it can be identified with the tail distribution of the cycle maximum of the associated infinite-buffer queue. This equivalence is shown to hold for the GI/G/1 queue and for dams with state-dependent release rates. To prove this equivalence, we use a duality for stochastically monotone recursions, developed by Asmussen and Sigman (1996). As an application, we obtain several exact and asymptotic results for the loss probability and extend Takács' formula for the cycle maximum in the M/G/1 queue to dams with variable release rate.

Publisher

Cambridge University Press (CUP)

Subject

Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability

Reference23 articles.

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4. Zwart, A.P. (2000).A fluid queue with a finite buffer and subexponential input.Advances in Applied Probability 32:221–243.

5. Bekker, R. (2004).Finite-buffer queues with workload-dependent service and arrivalrates.SPOR Report 2004-01,Eindhoven University of Technology,The Netherlands.

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