Estimating tail probabilities in queues via extremal statistics
Bibliographic record
Abstract
. We study the estimation of tail probabilities in a queue via the maximum value observed over the time interval sampled. Logarithmic consistency and eciency issues for such estimators are considered. In the course of developing these results, we establish new almost sure limit theory, in the context of regenerative processes, for the extreme value maximum and related rst passage times. 1 Introduction Consider a nite-buer queue that is being monitored over time, and suppose that we wish to exert some control over the input process so as to ensure that the proportion of jobs arriving to a full buer is less than some given value. For example, in a communication network, we may wish to implement some form of admission control so as to ensure that the long-run fraction of dropped packets (or cells) at the buers feeding the switches is acceptably low. In such settings, we expect that the admission control policy would need to, either explicitly or implicitly, estimate the fraction of ...
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.028 | 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; both teacher heads agree on what is shown here.
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".