Self-similarity through high-variability: statistical analysis of ethernet LAN traffic at the source level
Self-similarity through high-variability: statistical analysis of ethernet LAN traffic at the source level
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DOI：
10.1145/217382.217418
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发表时间：
1995-10
影响因子：
3.9
通讯作者：
W. Willinger;M. Taqqu;R. Sherman;D. V. Wilson
中科院分区：
文献类型：
--
作者：
W. Willinger;M. Taqqu;R. Sherman;D. V. Wilson
最近对来自各种工作分组网络的流量测量的许多经验研究已经令人信服地证明，实际网络流量在本质上是自相似的或长程相关的（即，在很宽的时间尺度上突发）-与通常进行的业务建模假设形成鲜明对比。在本文中，我们提供了一个合理的物理解释的发生在高速网络流量的自相似性。我们的解释是基于表现出高可变性的过程的收敛结果（即，我们的关键数学结果表明，许多ON/OFF源（也称为分组列车）的叠加，其ON周期和OFF周期表现出诺亚效应（即，具有高可变性或无限变化）产生具有约瑟夫效应（即，是自相似的或长程相关的）。此外，描述诺亚效应（高变异性）和约瑟夫效应（自相似性）强度的参数之间存在简单的关系。从两个以太网LAN的（涉及几百个活动的源-目的地对）的两组高时间分辨率的流量测量的广泛的统计分析证实，在单个源或源-目的地对的水平上的数据是一致的诺亚效应。我们还讨论了这个简单的物理解释的影响，在现代高速网络流量的存在下，自相似的流量模式（i）简约的流量建模（ii）有效的合成生成的现实的流量模式，（iii）相关的网络性能和协议分析。
A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is self-similar or long-range dependent in nature (i.e., bursty over a wide range of time scales) - in sharp contrast to commonly made traffic modeling assumptions. In this paper, we provide a plausible physical explanation for the occurrence of self-similarity in high-speed network traffic. Our explanation is based on convergence results for processes that exhibit high variability (i.e., infinite variance) and is supported by detailed statistical analyses of real-time traffic measurements from Ethernet LAN's at the level of individual sources.Our key mathematical result states that the superposition of many ON/OFF sources (also known as packet trains) whose ON-periods and OFF-periods exhibit the Noah Effect (i.e., have high variability or infinite variance) produces aggregate network traffic that features the Joseph Effect (i.e., is self-similar or long-range dependent). There is, moreover, a simple relation between the parameters describing the intensities of the Noah Effect (high variability) and the Joseph Effect (self-similarity). An extensive statistical analysis of two sets of high time-resolution traffic measurements from two Ethernet LAN's (involving a few hundred active source-destination pairs) confirms that the data at the level of individual sources or source-destination pairs are consistent with the Noah Effect. We also discuss implications of this simple physical explanation for the presence of self-similar traffic patterns in modern high-speed network traffic for (i) parsimonious traffic modeling (ii) efficient synthetic generation of realistic traffic patterns, and (iii) relevant network performance and protocol analysis.