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.
