CDI Type II: Complex Dynamics in the Internet: A Computational Analytic Approach

了解互联网和其他大型网络的动态行为是一个令人望而生畏的问题。传统的方法试图捕捉互联网？S细致入微地描述行为，但随后又与系统作斗争？S的复杂性令人难以置信。在另一个极端，强调大范围而忽略细节的模型更容易处理，但经常忽略实际工程问题所需的功能，特别是当动态行为而不是静态行为是重要关注的时候。这项研究通过分析和计算技术的新融合开发了一种快乐的媒介。对三个重要问题进行了探讨。第一个是关于互联网的整体效率和稳定性；第二个是开发改进传感器网络(可用于监测环境变化的大量小型传感器阵列)功能的方法；第三个重点是通过激励用户以有利于整体的方式行为来提高大型协作计算系统的质量。这项研究的潜在变革性方面在于其计算分析？为广泛的复杂网络创建有效模型的方法。在这一策略中，计算技术与分析技术交织在一起，使用了无方程建模等方法。来自化学工程和来自统计物理的数值重整化。这种方法基本上是跨学科的，有能力统一和扩展适用于动力系统理论、数学物理和理论生物学等不同领域的多尺度分析方法。这里创造的技术的副产品是预期的，并将被研究涉及复杂网络的其他重要问题，包括互联网上的路由、神经网络中的同步以及全球金融网络中的稳定性。

Understanding the dynamical behavior of the Internet and other large networks is a daunting problem. Traditional approaches try to capture the Internet?s detailed behavior at a granular level, but then struggle with the system?s overwhelming complexity. At the other extreme, models that emphasize the large scale while ignoring fine details are more tractable, but frequently neglect features needed for practical engineering issues, especially when dynamical rather than static behaviors are an important concern. This research develops a happy medium through a novel fusion of analytical and computational techniques. Three important problems are explored. The first concerns the overall efficiency and stability of the Internet; the second develops methods for improving the functioning of sensor networks (large arrays of small sensors that can be used to monitor environmental changes); and the third focuses on improving the quality of large cooperative computing systems by providing incentives for users to behave in ways that benefit the whole.The potentially transformative aspect of this research lies in its ?computational-analytic? approach to creating effective models for a wide range of complex networks. In this strategy, computational techniques are interlaced with analytical ones, using such methods as ?equation-free modeling?? from chemical engineering and numerical renormalization from statistical physics. The approach is radically interdisciplinary, with the power to unify and extend multi-scale analytical methods adapted from such diverse fields as dynamical systems theory, mathematical physics and theoretical biology. Spin-offs of the techniques created here are expected and will be investigated for other important problems involving complex networks, including routing on the Internet, synchronization in neural networks, and stability in global financial networks.