Scaling in Internet Traffic: A 14 Year and 3 Day Longitudinal Study, With Multiscale Analyses and Random Projections

Abstract

Abstract-In the mid-90's, it was shown that the statistics of aggregated time series from Internet traffic departed from those of traditional short range dependent models, and were instead characterized by asymptotic self-similarity. Following this seminal contribution, over the years, many studies have investigated the existence and form of scaling in Internet traffic. This contribution aims first at presenting a methodology, combining multiscale analysis (wavelet and wavelet leaders) and random projections (or sketches), permitting a precise, efficient and robust characterization of scaling which is capable of seeing through non-stationary anomalies. Second, we apply the methodology to a data set spanning an unusually long period: 14 years, from the MAWI traffic archive, thereby allowing an in-depth longitudinal analysis of the form, nature and evolutions of scaling in Internet traffic, as well as network mechanisms producing them. We also study a separate 3-day long trace to obtain complementary insight into intra-day behavior. We find that a biscaling (two ranges of independent scaling phenomena) regime is systematically observed: long-range dependence over the large scales, and multifractal-like scaling over the fine scales. We quantify the actual scaling ranges precisely, verify to high accuracy the expected relationship between the long range dependent parameter and the heavy tail parameter of the flow size distribution, and relate fine scale multifractal scaling to typical IP packet inter-arrival and to round-trip time distributions.

Wavelet eigenvalue regression for n-variate operator fractional Brownian motion

“…It was soon recognized that the latter phenomenon, referred to as asymptotic selfsimilarity or long range dependence (LRD; Beran (1994)), had strong implications for network management due to its dramatic impact on queuing performance (see Norros (1994), Boxma and Dumas (1997), Boxma and Cohen (2000)). This lead to substantial research efforts in the last 20 years (see Willinger et al (1996), Willinger et al (2002) and Fontugne et al (2017) for reviews and references therein for details). Self-similarity in Internet traffic has been widely investigated, but it remains controversial and a number of issues are still open.…”

Hypersparse Neural Network Analysis of Large-Scale Internet Traffic

“…WIDE operates an internet testbed for both commercial traffic and for conducting research experiments. These data have enabled quantitative analysis of Internet traffic spanning years illustrating trends such as, the emergence of residential usage, peer-to-peer networks, probe scanning, and botnets [23]- [25]. The Tokyo datasets are publicly available packet traces provided by the WIDE project (a.k.a.…”

Assessing Cross-Dependencies Using Bivariate Multifractal Analysis

“…The scale-free concept postulates that a large continuum of scales, rather than a small set of specific scales, all contribute to temporal dynamics. It has permitted significant contributions and successful analyses of numerous real-world applications very different in nature (cf., e.g., [4][5][6][7][8][9][10][11]). However and surprisingly, despite the fact that in many recent applications several time series are collected that need to be analyzed jointly, multifractal analysis remained univariate in essence, that is, even when several time series are jointly available, their analysis is conducted independently on each single one (see a contrario a few notable exceptions in, e.g., [12,13]).…”