Fluctuations Around the Mean-Field for a Large Scale Erlang Loss System Under the SQ(d) Load Balancing.
Bibliographic record
Abstract
In this paper, we study the fluctuations of the transient and stationary empirical distributions around the mean-field for a large scale multi-server Erlang Loss system that has N servers. Jobs arrive according to a Poisson process with rate Nλ and each incoming job is dispatched by a central job dispatcher to the server with the minimum occupancy among d randomly chosen servers with ties broken uniformly at random. Previous works have studied the mean-field limit of this model and characterized the asymptotic behavior of the system when N↦∞. In this paper, we focus on quantifying the resulting error when we approximate the transient and stationary behavior of the system when N is large by the mean-field of the system. We obtain functional central limit theorems (FCLTs) by studying the limit of a suitably scaled fluctuation process of the stochastic empirical process of the model with index N around the mean-field limit when N↦∞. We show that for both the transient and stationary regimes, the limiting process is characterized by an Ornstein-Uhlenbeck (OU) process. We also show that the interchange of limits lim_N↦∞ lim_t↦∞=lim_t↦∞ lim_N↦∞ is valid under the CLT scaling. Finally, we exploit the FCLT to show that the gap between the exact average blocking probability of a job in the system with the number of servers N and the limiting average blocking probability which is a function of the fixed-point of the mean-field, is of the order o(N^-1/2) and thus establish the accuracy of the mean-field approximation for finite N.
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How this classification was reachedexpand
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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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 teacher head, 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".