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 fairness 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.