Max-min fairness and its applications to routing and load-balancing in communication networks: a tutorial

This tutorial is devoted to the notion of max-min fairness (MMF), associated optimization problems, and their applications to multi-commodity flow networks.We first introduce a theoretical background for a generic MMF optimization problem and discuss its relation to lexicographic optimization. We next present resolution algorithms for convex MMF optimization, and analyze their properties. In the second half of the tutorial we discuss its applications to communication networks, in particular to routing and load-balancing. We state several properties with respect to each of the studied problems and analyze the behavior of the algorithms.