Interference Calculus

This book develops a mathematical framework for modeling and optimizing interference-coupled multiuser systems. At the core of this framework is the concept of general interference functions, which provides a simple means of characterizing interdependencies between users. The entire analysis builds on the two core axioms scale-invariance and monotonicity. The proposed network calculus has its roots in power control theory and wireless communications. It adds theoretical tools for analyzing the typical behavior of interference-coupled networks. In this way it complements existing game-theoretic approaches. The framework should also be viewed in conjunction with optimization theory. There is a fruitful interplay between the theory of interference functions and convex optimization theory. By jointly exploiting the properties of interference functions, it is possible to design algorithms that outperform general-purpose techniques that only exploit convexity. The title &quote;network calculus&quote; refers to the fact that the theory of interference functions constitutes a generic theoretical framework for the analysis of interference coupled systems. Certain operations within the framework are &quote;closed&quote;, that is, combinations of interference functions are interference functions again. Also, certain properties are preserved under such operations. This, provides a methodology for analyzing different multiuser performance measures that can be expressed as interference functions or combinations of interference functions.