Mean-field fluctuations at diffusion scale in threshold-based randomized routing for processor sharing systems and applications
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Bibliographic record
Abstract
In this article, we study the fluctuations of the empirical occupation measures of servers around their mean-field limit in a large system of heterogeneous processor sharing servers. It is assumed that there are M different servers grouped by their speeds and that the total number of servers is N. In particular, we study the sensitivity of the fluctuations to arrival rate parameters at the diffusion scale. The job arrival process is assumed to be Poisson with rate N(λ−βN) and the job lengths are assumed to be exponentially distributed with unit mean. On arrival, a finite number of servers from each group are selected and the destination server depends on the server occupancy normalized to their speeds and pre-defined thresholds, referred to as the Join-Below-Threshold scheme. We derive Functional Central Limit Theorems (FCLTs) for the fluctuations that enable us to estimate the error of the mean-field approximations to the empirical measures associated with a system with N servers. We then use these results to show mean response time for finite systems can be approximated by the response time given by the mean-field limit and the error is O(1N) for which the constants can be precisely calculated.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it