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A fluid cluster Poisson input process can look like a fractional Brownian motion even in the slow growth aggregation regime

Part of: Operations research and management science Limit theorems

Published online by Cambridge University Press:  01 July 2016

Vicky Fasen  and
Gennady Samorodnitsky
Vicky Fasen*
Affiliation:
Technische Universität München
Gennady Samorodnitsky*
Affiliation:
Cornell University
*
∗ Postal address: Center for Mathematical Sciences, Technische Universität München, D-85747 Garching, Germany. Email address: [email protected]
∗∗ Postal address: School of Operations Research and Information Engineering, Cornell University, 206 Rhodes Hall, Ithaca, NY 14853, USA. Email address: [email protected]
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Abstract

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We show that, contrary to common wisdom, the cumulative input process in a fluid queue with cluster Poisson arrivals can converge, in the slow growth regime, to a fractional Brownian motion, and not to a Lévy stable motion. This emphasizes the lack of robustness of Lévy stable motions as ‘birds-eye’ descriptions of the traffic in communication networks.

Keywords

Cluster Poisson processfluid queuefractional Brownian motioninput modelslow growth regimescaling limitworkload process

MSC classification

Primary: 90B22: Queues and service
Secondary: 60F17: Functional limit theorems; invariance principles
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 41 , Issue 2 , June 2009 , pp. 393 - 427
Copyright
Copyright © Applied Probability Trust 2009 

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