Long-range Dependence and Heavy Tails in Communication Networks

近年来，有关现代通信网络流量测量的统计分析和数学建模的研究数量大幅增加。 虽然许多测量的流量轨迹在高频行为方面彼此不同，但它们通常表现出许多统计特征，这些特征往往对现实数据网络随时间推移而经历的不断变化不敏感。 这种鲁棒的特性有时被称为“流量不变量”，并且包括诸如长程依赖和/或重尾的现象。 当随着滞后的增加，手头的业务过程的相关性缓慢地衰减到零时（即，幂律衰减），并导致业务量表现出明显的大于平均值的"突发“和低于平均值的”间歇“。 重尾指的是潜在概率分布的幂律衰减，并抓住了极端可变性和“不稳定性”的概念。 在网络环境中，长期依赖和重尾现象比比皆是，并且在网络层次结构的几乎所有层都可以观察到。 本研究的重点是这些流量不变量：如何检测和测量它们，如何解释它们在现实网络情况下的存在，它们对排队/丢失性能的影响是什么，以及如何识别其他潜在的不变量，特别是在高频域中明显的混沌结构。 在理解网络业务的动态性质中的一个公开问题是当底层业务（例如，分组速率过程）除了表现出强的时间依赖性之外，其本身是非高斯的并且表现出重尾。 这项研究旨在开发物理模型，可以解释的联合存在， 宏观层面的长程相关性和重尾效应。这些模型应该是有用的，在实践中，产生有效的流量生成方法，导致合成的痕迹与现实的功能，并提供新的见解到广泛的网络性能分析领域。另一个问题领域涉及网络流量的性质在微观层面上，我们将建立在最近发现的乘法机制，导致网络流量在精细的时间尺度上表现出多重分形标度特性的存在。 这项研究也集中在网络上，并计划跟踪自相似性，重尾和多重分形在不断变化的互联网中的表现。访问速度的不断增加的可变性（例如，一方面是传统的调制解调器，另一方面是电缆调制解调器、100 Mbps以太网）以及接入技术越来越多的异构性（例如，电话调制解调器、电缆调制解调器、ADSL）将影响当前考虑的工作负载模型的性质以及它们将如何影响缩放（即，自相似性）特性。 该项目涉及P.I.（Murad S. Taqqu）在波士顿大学和Co-P.I.（Walter Willinger）AT T-Labs Research。 欲了解更多详情，请访问网站AREF=”http://math.bu.edu/people/murad“http://math.bu.edu/people/murad/A。

There has been recently a big increase in the number of studies related to the statistical analysis and mathematical modeling of traffic measurements from modern communication networks. While many of the measured traffic traces differ from each other in their high-frequency behavior, they typically exhibit a number of statistical characteristics that tend to be insensitive to the constant changes that real-life data networks experience over time. Such robust characteristics are sometimes called "traffic invariants", and include such phenomena as long-range dependence and/or heavy tails. Long-range dependence occurs when the correlations of the traffic processes at hand decay to zero slowly as the lag increases (i.e., power-law decay) and causes traffic to exhibit pronounced larger-than average ``bursts'' and lower-than-average ``lulls''. Heavy tails refer to the power-law decay of the underlying probability distributions and capture the notions of extreme variability and ``intermittancy''. In the networking context, long-range dependence and heavy tails abound and have been observed at practically all layers in the networking hierarchy. This research focuses on these traffic invariants: how to detect and measure them, how to explain their presence in realistic networking situations, what is their effect on queuing/loss performance, and also how to identify other potential invariants, especially within the apparent chaotic structure in the high-frequency domain. One of the open problems in understanding the dynamic nature of network traffic is when the underlying traffic (e.g., packet rate process), in addition to exhibiting strong temporal dependencies, is itself non-Gaussian and exhibits heavy tails. This research aims to develop physical models that can explain the joint presence of long-range dependence and heavy tails at the macroscopic level. These models should be useful in practice, give rise to efficient traffic generation methods that result in synthetic traces with realistic features, and provide novel insights into the wide area of network performance analysis. Another problem area concerns the nature of network traffic at the microscopic level, where we will build upon the recent discovery of the presence of multiplicative mechanisms that cause network traffic over fine time scales to exhibit multifractal scaling properties. This research also focuses on the Web and plans to track how self-similarity, heavy-tails, and multifractals fare in a constantly changing Internet. How does the ever increasing variability in access speeds (e.g., traditional modems on one hand, cable modems, 100 Mbps Ethernet on the other) and the more and more heterogeneous nature of access technologies (e.g., phone modems, cable modems, ADSL) will affect the nature of currently considered workload models and how they will impact the scaling (i.e., self-similarity) properties of aggregate packet traffic. This project involves the collaborative effort of the P.I. (Murad S. Taqqu) at Boston University and the Co-P.I. (Walter Willinger) at AT&T-Labs Research. For more details please refer to the web site AREF="http://math.bu.edu/people/murad" http://math.bu.edu/people/murad/A.