Long-range Dependence and Heavy Tails in Communication Networks

最近，与来自现代通信网络的业务量测量的统计分析和数学建模相关的研究的数量大幅增加。虽然许多测量的流量轨迹在其高频行为上彼此不同，但它们通常显示出一些统计特征，这些特征往往对现实生活中的数据网络随着时间的推移而经历的持续变化不敏感。这种稳健的特征有时被称为“流量不变量”，并且包括诸如长距离依赖和/或重尾等现象。当交通过程的相关性随着滞后的增加而缓慢地衰减到零(即，幂规律衰减)时，就会发生长期相关性，并导致交通表现出明显大于平均的“突发”和低于平均的“平静”。重尾指的是基本概率分布的幂规律衰减，并捕捉到极端变异性和“间歇性”的概念。在网络环境中，长期依赖和重尾现象比比皆是，几乎在网络层次的所有层面都可以观察到。本文主要研究了这些流量不变量：如何检测和测量它们，如何解释它们在现实网络环境中的存在，它们对排队/丢失性能的影响，以及如何识别其他潜在的不变量，特别是在高频域的明显混沌结构中。理解网络流量的动态性质的一个悬而未决的问题是，除了表现出强烈的时间依赖性之外，基础流量(例如，分组速率过程)本身是非高斯的并且表现出重尾。这项研究旨在建立物理模型，在宏观层面上解释长期依赖和重尾的共同存在。这些模型应该在实践中有用，产生有效的流量生成方法，产生具有真实特征的合成轨迹，并为网络性能分析的广泛领域提供新的见解。另一个问题领域涉及微观层面的网络流量的性质，我们将建立在最近发现的乘性机制的基础上，该机制使精细时间尺度上的网络流量呈现多重分形标度特性。这项研究还聚焦于网络，并计划跟踪自相似性、重尾和多重分形图在不断变化的互联网中的表现。接入速度(例如，一方面是传统调制解调器、另一方面是电缆调制解调器、100 Mbps以太网)的不断增加的可变性以及接入技术(例如，电话调制解调器、电缆调制解调器、ADSL)的越来越多的异构性将如何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聚合分组业务的缩放(即，自相似性)属性。这个项目涉及波士顿大学的P.I.(Murad S.Taqquu)和AT&amp；T-Labs Research的合作P.I.(Walter Willinger)的合作努力。有关更多详细信息，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.