Information Theoretic Aspects of Fairness Criteria in Network Resource Allocation Problems

The present paper provides a novel characterization of fairness criteria in network resource allocation problems based on information theory. Specifically, the optimization problems that motivate fairness criteria for multi-dimensional resource are characterized using information divergence measures that were originally used in information theory. The characteristics of the fairness criteria clarified herein are summarized as follows: (i) The proportional fairness criterion can be derived through the minimization of the Kullback-Leibler divergence. (ii) The (p, α)-proportional fairness criterion, which is a generalization of the proportional fairness criterion, can be derived through the minimization of the α-divergence and the power-divergence. In addition, the optimization of the fairness criterion is closely related to the Tsallis entropy maximization principle. (iii) The above relationships can be generalized using Csiszár's f-divergence and Bregman's divergence. The information theoretic approach is then applied to a typical example in a practical network resource allocation problem. This example provides a glimpse into the inherent connection between resource allocation problems and information theory.