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. Some computational results illustrate the behavior of the obtained solutions and the required CPU time for a range of random and well-dimensioned networks.