Bibliographic record
Abstract
Analytical tools such as Laplace-Stieltjes transforms and z-transforms are commonly used to characterize queueing-theoretic quantities such as busy-period, waiting-time, and queue-size distributions. Many of these transforms, particularly in M/G/1 priority queueing applications, tend to be cumbersome expressions that involve both implicit and recursive functional relationships. Due to these complications, even the task of deriving moments becomes an algebraically intensive exercise. The focus of this paper is to describe a collection of efficient symbolic procedures useful for automating the tedious mathematical computations one encounters in working with these kinds of transforms. Central to this development is the introduction of a set-partition operator that enables moment expressions for delay cycles to be determined quickly and exactly, without having to derive any sort of higher-order derivative or Taylor-series expansion. Making use of this operator eliminates laborious derivations by hand and permits moments of various priority queueing-related quantities to be easily determined. In particular, the procedures are applied to the classical non-preemptive and preemptive resume queues, as well as two advanced variants of these models.
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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 | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".