Stochastic Systems

On the superposition of heterogeneous traffic at large time scales

Luis López-Oliveros and Sidney I. Resnick

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Abstract

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].

Article information

Source
Stoch. Syst., Volume 1, Number 2 (2011), 209-245.

Dates
First available in Project Euclid: 24 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.ssy/1393252077

Digital Object Identifier
doi:10.1214/10-SSY023

Mathematical Reviews number (MathSciNet)
MR2949540

Zentralblatt MATH identifier
1291.60197

Citation

López-Oliveros, Luis; Resnick, Sidney I. On the superposition of heterogeneous traffic at large time scales. Stoch. Syst. 1 (2011), no. 2, 209--245. doi:10.1214/10-SSY023. https://projecteuclid.org/euclid.ssy/1393252077


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