Generalized α-fair resource allocation in wireless networks

A Jain's Index Perspective on α-Fairness Resource Allocation over Slow Fading Channels

“…It is intuitively accepted that larger α yields resource allocations that are more fair but less efficient [2], [6]. However, this is not always true [7], [8].…”

“…By investigating the α-utility function, [5] showed that the fairness-efficiency reward ratio, i.e., the ratio between the utility function gradient in the direction of more fairness and that in the direction of more efficiency, is nondecreasing with α. In particular, the results in [5] indicate three possible cases: 1) fairness increases with α while efficiency decreases with α (e.g., [2] and [6]), 2) both fairness and efficiency increase with α (e.g., [7]) and 3) both fairness and efficiency decrease with α (e.g., [8]). Nevertheless, there is a little ambiguity to apply the conclusions in [5] to specific resource allocation problems in practical systems.…”

“…Proof: Substituting (5) into (1) and (2), we can get the system efficiency and Jain's index of users' throughput in (6) and (7), respectively.…”

“…Manuscript In the literature, proportional fairness has been extensively considered in single channel Time-Division-MultipleAccess (TDMA) system [9], [10] and Orthogonal-FrequencyDivision-Multiple-Access (OFDMA) system [11], [12]. However, in these systems, it is still unknown how α influences system efficiency and Jain's index under α-fairness resource allocation, where Jain's index is widely utilized to quantify fairness among various fairness measures due to its highly intuitive interpretation 1 [4]- [6], [8]. In this letter, we focus on the tradeoff between system efficiency and Jain's index by maximizing α-utility function in single channel TDMA system, where the conclusions can also be applied to multichannel system, such as OFDMA, with frequency-flat fading.…”

Fair resource allocation with varying time constraints

“…This, as well as other fairness notions can be defined through a set of axioms, see [3]. For a rich literature on concepts of fairness and some interesting applications, the reader is referred to [4], [5], [6], [7], [9], [8] and the references there in. …”