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2011 On the superposition of heterogeneous traffic at large time scales
Luis López-Oliveros, Sidney I. Resnick
Stoch. Syst. 1(2): 209-245 (2011). DOI: 10.1214/10-SSY023


Various empirical and theoretical studies indicate that cumulative network traffic is a Gaussian process. However, depending on whether the intensity at which sessions are initiated is large or small relative to the session duration tail, [25] and [15] have shown that traffic at large time scales can be approximated by either fractional Brownian motion (fBm) or stable Lévy motion. We study distributional properties of cumulative traffic that consists of a finite number of independent streams and give an explanation of why Gaussian examples abound in practice but not stable Lévy motion. We offer an explanation of how much vertical aggregation is needed for the Gaussian approximation to hold. Our results are expressed as limit theorems for a sequence of cumulative traffic processes whose session initiation intensities satisfy growth rates similar to those used in [25].


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Luis López-Oliveros. Sidney I. Resnick. "On the superposition of heterogeneous traffic at large time scales." Stoch. Syst. 1 (2) 209 - 245, 2011.


Published: 2011
First available in Project Euclid: 24 February 2014

zbMATH: 1291.60197
MathSciNet: MR2949540
Digital Object Identifier: 10.1214/10-SSY023

Rights: Copyright © 2011 INFORMS Applied Probability Society


Vol.1 • No. 2 • 2011
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