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Asymptotics of palm-stationary buffer content distributions in fluid flow queues

Part of: Computer system organization Operations research and management science Special processes Limit theorems

Published online by Cambridge University Press:  01 July 2016

Tomasz Rolski ,
Sabine Schlegel  and
Volker Schmidt
Tomasz Rolski*
Affiliation:
Wroclaw University
Sabine Schlegel*
Affiliation:
University of Ulm
Volker Schmidt*
Affiliation:
University of Ulm
*
∗ Postal address: Mathematical Institute, Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland.
∗∗ Postal address: Institute of Stochastics, University of Ulm, Helmholtzstraße 18, D-89069 Ulm, Germany.
∗∗ Postal address: Institute of Stochastics, University of Ulm, Helmholtzstraße 18, D-89069 Ulm, Germany.
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Abstract

We study a fluid flow queueing system with m independent sources alternating between periods of silence and activity; m ≥ 2. The distribution function of the activity periods of one source, is supposed to be intermediate regular varying. We show that the distribution of the net increment of the buffer during an aggregate activity period (i.e. when at least one source is active) is asymptotically tail-equivalent to the distribution of the net input during a single activity period with intermediate regular varying distribution function. In this way, we arrive at an asymptotic representation of the Palm-stationary tail-function of the buffer content at the beginning of aggregate activity periods. Our approach is probabilistic and extends recent results of Boxma (1996; 1997) who considered the special case of regular variation.

Keywords

Regular variationsubexponential distributionaggregatingtail asymptoticsrandom walkon-off fluid flow

MSC classification

Primary: 60K25: Queueing theory 60F10: Large deviations 68M20: Performance evaluation; queueing; scheduling 90B15: Network models, stochastic
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 31 , Issue 1 , March 1999 , pp. 235 - 253
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

Supported by KBN grant 2 PO3A 046 08 (1995-97).

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