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Buffer content of a leaky-bucket system with long-range dependent input traffic

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Bárbara González-Arévalo  and
Gennady Samorodnitsky
Bárbara González-Arévalo
Affiliation:
Cornell University
Gennady Samorodnitsky*
Affiliation:
Cornell University
*
∗∗Postal address: School of Operations Research and Industrial Engineering and Department of Statistical Science, Cornell University, Ithaca, NY 14853, USA. Email address: gennady@orie.cornell.edu
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Abstract

The leaky bucket is a flow control mechanism that is designed to reduce the effect of the inevitable variability in the input stream into a node of a communication network. In this paper we study what happens when an input stream with heavy-tailed work sessions arrives to a server protected by such a leaky bucket. Heavy-tailed sessions produce long-range dependence in the input stream. Previous studies of single server fluid queues without flow control suggested that such long-range dependence can have a dramatic effect on the system performance. By concentrating on the expected time till overflow of a large finite buffer we show that leaky-bucket flow control does make the system overflow less often, but long-range dependence still makes its presence felt.

Keywords

Fluid queueflow controlleaky bucketfinite bufferheavy tailslong-range dependencetime until overflow

MSC classification

Primary: 90B15: Network models, stochastic
Secondary: 90B18: Communication networks 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 581 - 601
Copyright
Copyright © Applied Probability Trust 2003 

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Footnotes

∗

Current address: Department of Mathematics, University of Louisiana at Lafayette, PO Box 41010, Lafayette, LA 70504-1010, USA

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