In this talk we examine some of the challenges and opportunities that arise in the mathematical modeling of a dense wireless sensor network. Specifically, we consider the problem of using mathematical program to construct fluid-flow based models of such networks.
These models have been used successfully for the estimation of network lifetime and route optimization, to name a few. However, challenges arise in applying this method to a dense network where locations of individual sensors are not precisely known; instead the deployment is simply given by a certain distribution. In this case both the computational complexity and the lack of a priori knowledge prevent us from using the standard mathematical program. By observing the dense nature of the network, we present a modeling method that views a specific network deployment as an instance (sample path) from an underlying distribution, circumventing the above difficulty.
Numerical studies show that this method produces accurate results, compared to averaging over results from random instances of deployment, with significantly less computation. More importantly, this method motivates the study of stability and robustness of the underlying math program, which has interesting implications on its solution.