Multi-Jain Fairness Index of Per-Entity Allocation Features for Fair and Efficient Allocation of Network Resources

Due to its simplicity and its easy comprehension, Jain's fairness index is still among the most popular measures to compare justness of allocations. However, it was already argued in the original paper that while the way of computing the index is well established, it is not immediately clear to which metric to apply the computation. Thereby, metric stands for a specific choice of a system observable. Here we study the extension of Jain's index to multiple metrics at once. We propose a set of per-entity allocation features to represent justness of an allocation, and to derive corresponding vectors of feature-wise taken Jain's fairness indices. The features give a numerical representation of fulfilling common fairness properties like proportionality, envy-freeness and equity of an allocation. Then, maximizing the smallest index gives an efficient procedure for allocation of goods. We study this procedure for the problem of allocating wireless channels in a multi-user setup and compare the influence of the various feature choices on the efficiency of the solution.