Max–min fairness in multi-commodity flows

In this paper, we provide a study of Max–Min Fair (MMF) multi-commodity flows and focus on some of their applications to multi-commodity networks. We first present the theoretical background for the problem of MMF and recall its relations with lexicographic optimization as well as a polynomial approach for achieving leximin maximization. We next describe two applications to telecommunication networks, one on routing and the second on load-balancing. We provide some deeper theoretical analysis of MMF multi-commodity flows, show how to solve the lexicographically minimum load network problem for the link load functions most frequently used in telecommunication networks.