Journal of Applied Probability
- J. Appl. Probab.
- Volume 49, Number 3 (2012), 710-718.
Fractional Brownian motion with H < 1/2 as a limit of scheduled traffic
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.
J. Appl. Probab., Volume 49, Number 3 (2012), 710-718.
First available in Project Euclid: 6 September 2012
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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
Araman, Victor F.; Glynn, Peter W. Fractional Brownian motion with H < 1/2 as a limit of scheduled traffic. J. Appl. Probab. 49 (2012), no. 3, 710--718. doi:10.1239/jap/1346955328. https://projecteuclid.org/euclid.jap/1346955328