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Fractional Brownian Motion with H < 1/2 as a Limit of Scheduled Traffic

Part of: Limit theorems Markov processes Stochastic processes Operations research and management science

Published online by Cambridge University Press:  04 February 2016

Victor F. Araman  and
Peter W. Glynn
Victor F. Araman*
Affiliation:
American University of Beirut
Peter W. Glynn*
Affiliation:
Stanford University
*
∗ Postal address: Olayan School of Business, American University of Beirut, Beirut 1107-2020, Lebanon. Email address: va03@aub.edu.lb
∗∗ Postal address: Management Science and Engineering, Stanford University, Stanford, CA 94305-4121, USA. Email address: glynn@stanford.edu
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Abstract

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In this paper we show that fractional Brownian motion with H < ½ can arise as a limit of a simple class of traffic processes that we call ‘scheduled traffic models’. To our knowledge, this paper provides the first simple traffic model leading to fractional Brownnian motion with H < ½. We also discuss some immediate implications of this result for queues fed by scheduled traffic, including a heavy-traffic limit theorem.

Keywords

Fractional Brownian motionscheduled trafficheavy-tailed distributionlimit theorem

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles 60J60: Diffusion processes 60G99: None of the above, but in this section
Secondary: 60G70: Extreme value theory; extremal processes 90B30: Production models
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 3 , September 2012 , pp. 710 - 718
Copyright
© Applied Probability Trust 

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