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On the superposition of heterogeneous traffic at large time scales. (English) Zbl 1291.60197
Summary: 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 [T. Mikosch et al., Ann. Appl. Probab. 12, No. 1, 23–68 (2002; Zbl 1021.60076); I. Kaj and M. S. Taqqu, Prog. Probab. 60, 383–427 (2008; Zbl 1154.60020)] 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 [Mikosch et al., loc. cit.].
MSC:
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
90B20 Traffic problems in operations research
Software:
ismev
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