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

拟议研究的智力价值：近年来，流体建模方法为理解和设计通信网络提供了基础。这种模型在为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的状态的完整、概率描述。基于流体的方法不是列举用户之间的所有可能的相互作用和他们相应的状态转移，而是基于概率极限理论，例如大数定律，允许我们用一组相对简单和确定的具有平均量的差分方程组来描述网络动力学的平均宏观行为。由于流体建模方法为描述大型网络的动态特性提供了直观和可管理的解决方案，因此它被广泛应用于各种重要的网络问题，包括拥塞控制、稳定性分析、基于优化的技术和对等网络。然而，流体建模方法具有根本的局限性；只有当系统根据底层理论的要求进行扩展时，它才是有效的。对于其他类型的标度，基于流体的方法可能会失效，甚至可能错误地预测一阶系统动力学。具体地说，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，从流体建模框架派生的最优策略或算法可能不是真正最优的，可能会导致较差的性能。然而，几乎没有结果来解决这些与基于流体的方法相关的限制，这将网络设计人员的选择限制在实际可选择的非常小的子集上。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确定性优化的基本限制。虽然确定性表示法很方便，而且在某些情况下通常通过概率极限理论变得精确，但如果网络没有按照平均场方法假设的方式进行缩放，它可能会产生次优的设计指导方针，有时甚至是很差的。(2)开发了一个大型网络的随机框架，在该框架中，我们可以计算定义在系统的随机描述上的真实性能度量，同时利用多个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，我们试图为一些重要的网络问题获得新的、有效的设计指南和算法，包括拥塞控制、网络优化和对等网络，这些在传统的基于流体的方法下是无法获得的。广泛影响：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、对等网络的高效使用、无线网络的优化以及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、统计物理和理论生态学，其中流体建模发挥了关键作用。基于从多学科角度进行的彻底调查，这项拟议的研究将有望在成功完成后获得巨大回报。拟议的研究将促进学生之间的多学科合作，以利于他们自己的研究，促进自主聚会，交流思想和更好地沟通，并将激励具有不同背景的研究生/本科生参与这一项目。本项目制定的所有研究成果和方法都将纳入一门新的课程，并在网上提供，以供更广泛的传播。

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.