CPS: Small: Sensor Network Information Flow Dynamics

本研究的目的是发展数值技术解决偏微分方程（PDE），管理密集的无线网络中的信息流。尽管在这些网络中的信息流的物理现象，如热力学和流体力学的类比，许多物理和协议施加的约束，使信息流PDE独特的和不同的物理现象中观察到的PDE。该方法是开发一种系统的方法，其中一个统一的框架是能够优化的信息流在大量的节点的网络中的目标函数的广泛的类。目标函数根据信息的几何路径的期望属性来定义。这导致了形式根据优化目标而变化的偏微分方程。最后，数值技术将被开发，以解决在网络环境中的偏微分方程，并以分布式的方式。该项目的智力价值是：开发数学工具，在统一的框架下解决大规模无线传感器网络中广泛的设计目标;开创密集无线网络中信息流数值分析的新领域;开发网络问题的设计工具，如传输容量，路由和负载平衡。该研究的更广泛影响是：帮助下一代无线网络的发展;鼓励本科生和代表性不足的群体参与，并将研究成果纳入研究生课程。此外，该研究是跨学科的，汇集了传感器网络，理论物理，偏微分方程和数值优化。

The objective of this research is to develop numerical techniques for solving partial differential equations (PDE) that govern information flow in dense wireless networks. Despite the analogy of information flow in these networks to physical phenomena such as thermodynamics and fluid mechanics, many physical and protocol imposed constraints make information flow PDEs unique and different from the observed PDEs in physical phenomena. The approach is to develop a systematic method where a unified framework is capable of optimizing a broad class of objective functions on the information flow in a network of a massive number of nodes. The objective function is defined depending on desired property of the geometric paths of information. This leads to PDEs whose form varies depending on the optimization objective. Finally, numerical techniques will be developed to solve the PDEs in a network setting and in a distributed manner. The intellectual merits of this project are: developing mathematical tools that address a broad range of design objectives in large scale wireless sensor networks under a unified framework; initiating a new field on numerical analysis of information flow in dense wireless networks; and developing design tools for networking problems such as transport capacity, routing, and load balancing.The broader impacts of this research are: helping the development of next generation wireless networks; encouraging involvement of undergraduate students and underrepresented groups, and incorporating the research results into graduate level courses. Additionally, the research is interdisciplinary, bringing together sensor networking, theoretical physics, partial differential equations, and numerical optimization.