The lower-class waiting time distribution in the delayed accumulating priority queue
Bibliographic record
Abstract
The Accumulating Priority Queue model, in which customers accumulate priority as a linear function of their time in the queue, was first introduced by Kleinrock in 1964 under another name. All publications addressing the APQ since then have assumed that customers start accumulating priority credits upon arrival. The model we present herein, called the Delayed Accumulating Priority Queue, entails an initial delay prior to priority accumulation for low-priority customers. The waiting time distribution for the lower class of customers in such an APQ is determined, and the impact of the initial delay upon that distribution is assessed. The equivalence to another model, the Affine Accumulating Priority Queue, is established. A motivation for our work is the potential for very long waiting times for low-acuity patients in health care systems operating at very high utilization. We test cases in an idealized setting motivated by access targets which differ by a factor of two (as occurs in the Canadian Triage and Acuity Scale (CTAS)). This work also considers the problem of finding the minimal lower-class priority accumulation rate which allows for the lower-class customers to meet their access target, as a function of the duration of the initial delay involved.
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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 | 0.004 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".