An Axiomatic Theory of Fairness in Network Resource Allocation

We present five axioms for fairness measures in resource allocation. A family of fairness measures satisfying the axioms is constructed. Special cases of this family include ¿-fairness, Jain\´s index, and entropy. Properties of fairness measures satisfying the axioms are proven, including Schur-concavity. Among the engineering implications is a generalized Jain\´s index that tunes the resolution of fairness measure, a new understanding of ¿-fair utility functions, and an interpretation of "larger ¿ is more fair". We also construct an alternative set of axioms to capture system efficiency and feasibility constraints.