On Occupancy Based Randomized Routing Schemes in Large Systems of Shared Servers.
Bibliographic record
Abstract
Recently there has been a great interest in randomized load balancing schemes for large systems of parallel servers. Various policies such as SQ(d) (shortest queue amongst d randomly sampled), threshold based policies etc have been studied via a mean-field approach. All these policies are special cases of occupancy based routing decisions. In this paper we present a unified mean-field approach that holds for any routing scheme that only depends on the server occupancy in a system with a large numbers of processor sharing servers as an archetype of shared resource systems. The mean-field equations we obtain hold for general job length distributions unlike most recent works that assume exponentially distributed job lengths. We then show that the probability measure of occupancy defined on the set of non-negative integers Z_+ obtained from a fixed-point of the mean-field also satisfies the stationary mean-field equations under the assumption that the job lengths are exponential with the same average length. If the mean-field under exponential case has unique fixed-point, then the fixed point is insensitive to the job length distribution. The approach is via a measure-valued Markov process approach.
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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 | 0.006 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".