Macroscopic Analysis of Wireless Sensor Network Routing Problems
The discussion of the applicability and validity of geographic models inevitably leads to the concept of massively-dense networks. Thus, we formally define massively-dense networks, and derive the upper bound of analysis errors obtained from applying geographic models to nonmassively- dense networks. We also present theorems stating that, in addition to routing paths, routing vector fields provide an equivalent alternative approach to formulate routing problems. As an example, we use routing vector fields to analyze and formulate the trajectories used in packet forwarding for load balancing. In summary, we present a formal and consistent theoretical framework for the analysis of routing problems, and believe it can serve as a basis for algorithm development.
Keywords: massively-dense sensor network, geographic model, routing problem, routing vector field, load balancing, partial differential equation