互联网流量的缩放：14年零3天的纵向研究，多尺度分析和随机预测
Scaling in Internet Traffic: a 14 year and 3 day longitudinal study, with multiscale analyses and random projections
摘要：
在90年代中期，它表明，从互联网流量的聚合时间序列的统计数据偏离了传统的短程依赖模型，而不是渐近自相似性的特点。在这一开创性的贡献之后，多年来，许多研究调查了互联网流量缩放的存在和形式。这方面的贡献的目的首先是提出一种方法，结合多尺度分析（小波和小波领导人）和随机投影（或草图），允许一个精确的，高效的和强大的缩放特性，这是能够看到通过非平稳异常。第二，我们应用的方法，以跨越一个非常长的时期的数据集：14年，从MAWI流量档案，从而允许深入的纵向分析的形式，性质和互联网流量的扩展的演变，以及网络机制产生它们。我们还研究了一个单独的3天长的跟踪，以获得补充洞察日内行为。我们发现，bisscaling（两个范围内的独立标度现象）制度系统地观察到：在大尺度上的长程依赖性，和多分形的精细尺度上的标度。我们精确地量化实际的缩放范围，验证高精度的预期之间的关系的长范围相关的参数和重尾参数的流量大小分布，并与精细尺度多重分形缩放典型的IP数据包到达间隔和往返时间分布。
英文摘要：
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.
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