Journal of Applied Probability

Fractional Brownian motion with H < 1/2 as a limit of scheduled traffic

Victor F. Araman and Peter W. Glynn

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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.

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J. Appl. Probab., Volume 49, Number 3 (2012), 710-718.

First available in Project Euclid: 6 September 2012

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Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles 60J60: Diffusion processes [See also 58J65] 60G99: None of the above, but in this section
Secondary: 60G70: Extreme value theory; extremal processes 90B30: Production models

Fractional Brownian motion scheduled traffic heavy-tailed distribution limit theorem


Araman, Victor F.; Glynn, Peter W. Fractional Brownian motion with H &lt; 1/2 as a limit of scheduled traffic. J. Appl. Probab. 49 (2012), no. 3, 710--718. doi:10.1239/jap/1346955328.

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