Fairness via priority scheduling

In the context of multi-agent resource allocation problems, fairness is a paradigm shift in the recent past. An efficient scheduler always allocates resources to the `best´ agent. Some of the agents, who are most often in `bad´ conditions, are starved and fair schedulers are defined in this context. In this paper, we are interested in the actual gains obtained by the otherwise starved agents, due to fair schedulers. We propose a new notion of fairness, via a constrained optimization, which directly indicates the gains. In general, this constrained optimization is an infinite dimensional problem and the primary contribution of this paper is to reduce it to a tractable finite dimensional zero finding problem. We indicate iterative algorithm(s) which achieves the notion of fairness defined in this paper. We also compare it with some of the existing notions of fairness.