Mathematical Problems (and Some Solutions) in Networking

Modern data networks are complex, highly engineered systems. The "science of the internet" is changing both how mathematics is done and what kind is done. Measuring and understanding networks involve representing, compressing, and analyzing massive data sets. The size and complexity of these data sets call for new statistical tools that "scale", both with respect to time and to topological scales. Deriving an understanding of the network from these measurements couples sophisticated statistical analysis, engineering knowledge, and mathematical model building. I will discuss several projects that address each of these issues.