Long-range Dependence and Heavy Tails in Communication Networks

最近，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大量增加。虽然许多测量的流量轨迹在高频行为上彼此不同，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着时间的推移所经历的不断变化不敏感。这种健壮的特性有时被称为“流量不变量”，包括远程依赖和/或重尾等现象。当手头的流量过程的相关性随着延迟的增加而缓慢地衰减到零（即幂律衰减）并导致流量表现出明显的大于平均水平的“爆发”和低于平均水平的“平静”时，就会发生远程依赖。重尾指的是潜在概率分布的幂律衰减，并捕捉到极端可变性和“间歇性”的概念。在网络环境中，远程依赖和重尾大量存在，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，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中。理解网络流量动态特性的一个开放问题是，底层流量（例如，数据包速率过程）除了表现出强烈的时间依赖性外，本身是非高斯的，并表现出沉重的尾巴。本研究旨在建立能够在宏观水平上解释远程依赖和重尾共同存在的物理模型。这些模型在实践中应该是有用的，产生有效的流量生成方法，产生具有真实特征的合成轨迹，并为广泛的网络性能分析领域提供新颖的见解。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法机制的基础上，这种机制导致网络流量在精细的时间尺度上表现出多重分形尺度特性。这项研究也关注网络，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，一方面是传统调制解调器，另一方面是电缆调制解调器，100mbps以太网）和访问技术的越来越多的异构性质（例如，电话调制解调器，电缆调制解调器，ADSL）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流量的缩放（即自相似性）属性。该项目涉及波士顿大学私家侦探（Murad S. Taqqu）和co -私家侦探的合作努力。（沃尔特·威林格）在美国电话电报公司t实验室研究。详情请参考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.