On the optimality of max-min fairness in resource allocation

In this work a basic Resource Allocation (RA) problem is considered, where a fixed capacity must be shared among a set of users. The RA task can be formulated as an optimization problem, with a set of simple constraints and an objective function to be minimized. A fundamental relation between the RA optimization problem and the notion of max-min fairness is established. A sufficient condition on the objective function that ensures the optimal solution is max-min fair is provided. Notably, some important objective functions like Least Squares and Maximum Entropy fall in this case. Finally, an application of max-min fairness for overload protection in 3G networks is considered.