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

Published online by Cambridge University Press:  23 March 2005

René Bekker  and
Bert Zwart
René Bekker
Affiliation:
CWI, 1090 GB Amsterdam, The Netherlands, and, Department of Mathematics & Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands, E-mail: [email protected]; [email protected]
Bert Zwart
Affiliation:
CWI, 1090 GB Amsterdam, The Netherlands, and, Department of Mathematics & Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands, E-mail: [email protected]; [email protected]
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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 2 , April 2005 , pp. 241 - 255
Copyright
© 2005 Cambridge University Press

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References

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