Sponsor: National Science Foundation (NSF)
Title: Partial Differential Equation Models for Large Networks
This project involves continuum models of large networks using partial differential equations (PDEs). The premise is that some global characteristics of very large networks can be captured by continuum models that consider the behavior of the components on the scale of the aggregate rather than of the individual. The project involves an interdisciplinary team of an electrical engineer with notable expertise in networks, a statistician experienced in asymptotic analysis of stochastic processes and statistical modeling, and an applied mathematician with expertise in modeling and numerical simulation involving nonlinear PDEs. Successful completion of this project will result in the ability to analyze the performance of large networks with a computational effort that is not possible using conventional Monte Carlo simulation. Intellectual Merit: This project contains significant intellectual merit for engineering as well as mathematics. From the mathematical point of view, both creating mathematical descriptions of the continuum behavior of large networks and analyzing the resulting differential equations pose real challenges. From the engineering point of view, continuum modeling will require a detailed understanding of network behavior on the smallest scale of a few nodes and identification of global characteristics that can be modeled. Broader Impacts: This project will also have both an immediate positive impact on the current students of the principal investigators and on training future students. The students working on problems originating in the modeling of networks will have an invaluable practical component to their theses. This will significantly widen their career opportunities in industry and interdisciplinary settings. This in turn will provide a powerful recruiting tool for Colorado State University in the future.