Phantom Harmonic Gradient Estimators for Nonpreemptive Priority Queueing Systems
Bibliographic record
Abstract
This paper presents a new gradient estimator for the steady-state expected sojourn (system) time in a nonpreemptive priority queueing system. The estimator uses the concept of a phantom system, together with the basic ideas in harmonic gradient estimation, to develop a single simulation run estimator, termed the phantom harmonic gradient (PHG) estimator. The estimator is shown to be strongly consistent and strongly consistent in the average sense as the sample size grows. An upper bound for the variance of the PHG estimator is presented. This bound is used to show that under mild conditions, the variance of the PHG estimator tends to zero as both the number of phantom systems and the sample size approach infinity. A variance-reduction technique that simultaneously uses both common and antithetic random numbers is presented. Computational results on several nonpreemptive queueing systems illustrate the effectiveness of the method and show that common and antithetic random numbers can be used simultaneously to reduce the variance of the phantom harmonic gradient estimator.
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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 | 0.006 | 0.030 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".