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 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 | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| 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".