CAREER: A Stochastic Approach to the Design of Communication Networks: An Alternative to Fluid Modeling

本研究的智力价值：近年来，流体建模方法为理解和设计通信网络提供了基础。这种模型在对大型网络建模时特别有用，因为通常不可能获得网络中所有用户状态的完整概率描述。而不是枚举所有可能的交互之间的用户和他们相应的状态转换，基于流体的方法，依赖于概率极限理论，如大数定律，允许我们描述网络动力学的平均宏观行为在一组相对简单和确定性的差分/微分方程的平均量。由于流体建模方法为描述大型网络的动态提供了直观和可管理的解决方案，因此它已被广泛用于各种重要的网络问题，包括拥塞控制、稳定性分析、基于优化的技术和点对点网络。然而，流体建模方法有基本的局限性；只有当系统按基础理论的要求进行缩放时，它才有效。对于其他类型的标度，基于流体的方法可能会失效，甚至错误地预测一阶系统动力学。具体来说，流体建模可能产生(i)不准确的系统平衡，以及（ii）大型网络的低效设计指南。此外，从流体建模框架导出的最优策略或算法可能不是真正最优的，并可能导致性能不佳。然而，目前几乎没有研究结果能够解决基于流体的方法的这些局限性，这就限制了网络设计人员的选择，使其只局限于实际可选择的很小一部分。考虑到这些问题，本项目将实现以下目标：(1)了解基于流体的方法和大型网络的确定性优化的基本局限性。尽管确定性表示通过概率极限理论在某些情况下很方便并且经常变得精确，但如果网络没有按照平均场方法假设的方式缩放，它可能会产生次优或有时是糟糕的设计指南。(2)为大型网络开发一个随机框架，在这个框架中，我们可以根据系统的随机描述计算真正的性能指标，同时利用许多用户之间的交互所带来的简单性。通过我们的大型网络随机框架，我们寻求获得新的、有效的设计准则和算法，用于许多重要的网络问题，包括拥塞控制、网络优化和点对点网络，这在传统的基于流体的方法下是不可能获得的。更广泛的影响：该项目的研究成果和发现将影响许多重要的网络问题，如拥塞控制、点对点网络的有效使用、无线网络的优化和网络设计的跨层方法。此外，对所提出问题的研究进展也有可能影响其他科学和工程学科，如复杂理论、统计物理学和理论生态学，流体建模在这些学科中发挥了关键作用。本研究将从多学科的角度进行深入的研究，一旦成功完成，将带来巨大的回报。拟议的研究将促进学生之间的多学科合作，有利于他们自己的研究，促进自主聚会，以交流思想和更好的沟通，并将激励具有不同背景的研究生/本科生参与该项目。在这个项目中发展的所有研究成果和方法将纳入一个新的课程，并在网上提供，以便更广泛地传播。

The intellectual merit of the proposed research: In recent years, a fluid modeling approach has provided the basis for the understanding and design of communication networks. Such models are especially useful when modeling large networks, as it is often impossible to obtain a complete, probabilistic description of the states for all the users in the network. Instead of enumerating all possible interactions among users and their corresponding state transitions, the fluid-based approach, resting on probabilistic limit theories such as the law of large numbers, allows us to describe the average macroscopic behavior of network dynamics in terms of a set of relatively simple and deterministic difference/differential equations with averaged quantities. Since the fluid modeling approach offers intuitive and manageable solutions to describing the dynamics of large networks, it has been widely used for a variety of important networking problems including congestion control, stability analysis, optimization-based techniques, and peer-to-peer networks.However, the fluid modeling approach has fundamental limitations; it is valid only when the system is scaled as required by the underlying theory. For other types of scaling, the fluid-basedapproach may break down and incorrectly predict even first-order system dynamics. Specifically, the fluid modeling may produce (i) inaccurate system equilibrium, and (ii) inefficient design guidelines for large networks. Furthermore, optimal policies or algorithms derived from the fluid modeling framework may not be truly optimal and could result in poor performance. However, there have been virtually no results to address these limitations associated with the fluid-based approach, and this confines a network designer's choice to a very small subset of what can actually be chosen. With these concerns in mind, this project will achieve the following goals: (1) To understand the fundamental limitations of the fluid-based approach and of the deterministic optimization for large networks. Although a deterministic representation is convenient and often becomes exact for some cases via probabilistic limit theory, it may produce sub-optimal or sometimes poor design guidelines if the network is not scaled in the way assumed by the mean-field approach. (2) To develop a stochastic framework for large networks in which we can compute true performance metrics defined on the stochastic description of the system, while at the same time exploiting the simplicity caused by the interaction among many users. Through our stochastic framework for large networks, we seek to obtain new, efficient design guidelines and algorithms for a number of important networking problems including congestion control, network optimization, and peer-to-peer networks, which would be impossible to obtain under the traditional fluid-based approach.Broader Impact: The research outcomes and findings from this project will impact many important networking problems such as congestion control, and efficient usage of peer-to-peer networks, optimization of wireless networks, and cross-layer approaches to network design. Further, research progress on the proposed problems also has the potential to impact other science and engineering disciplines such as complex theory, statistical physics, and theoretical ecology, in which fluid modeling has played a key role. Based on a thorough investigation from multidisciplinary perspectives, the proposed research will promise a huge return upon its successful completion. The proposed research will foster multidisciplinary collaborations among students to the benefit of their own research, facilitate autonomous gatherings for interchanging ideas and better communication, and will motivate graduate/undergraduate students with diverse backgrounds participating in this project. All the research findings and methodologies developed in this project will be integrated into a new course and made available on the Web for wider dissemination.