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 meanheld 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-held 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-held 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-held limit when N → ∞. We show that for both the transient and stationary regimes, the limiting process is characterized by an OrnsteinUhlenbeck (OU) process. We also show that the interchange of limits limN→∞limt→∞= limt→∞limN→∞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 hxed-point of the mean-held, is of the order o(N-1/2) and thus establish the accuracy of the mean-held approximation for hnite 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 | 0.013 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| 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".