Optimal Tradeoff Between Sum-Rate Efficiency and Jain's Fairness Index in Resource Allocation
Bibliographic record
Abstract
The focus of this paper is on studying the tradeoff between the sum efficiency and Jain's fairness index in general resource allocation problems. Such problems are frequently encountered in wireless communication systems with M users. Among the commonly-used methods to approach these problems is the one based on the α-fair policy. Analyzing this policy, it is shown that it does not necessarily achieve the optimal Efficiency-Jain tradeoff (EJT) except for the case of M=2 users. When the number of users M>2, it is shown that the gap between the efficiency achieved by the α-fair policy and that achieved by the optimal EJT policy for the same Jain's index can be unbounded. Finding the optimal EJT corresponds to solving a family of potentially difficult non-convex optimization problems. To alleviate this difficulty, we derive sufficient conditions which are shown to be sharp and naturally satisfied in various radio resource allocation problems. These conditions provide us with a means for identifying cases in which finding the optimal EJT and the rate vectors that achieve it can be reformulated as convex optimization problems. The new formulations are used to devise computationally-efficient resource schedulers that enable the optimal EJT to be achieved for both quasi-static and ergodic time-varying communication scenarios. Analytical findings are confirmed by numerical examples.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".