Max-min fairness in multicommodity 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 de-scribe 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 lexico-graphically minimum load network problem for the link load functions most frequently used in telecommunication networks. Some computa-tional results illustrate the behavior of the obtained solutions and the required CPU time for a range of random and well-dimensioned networks.