Perfect sampling of a single-server queue with periodic Poisson arrivals
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Bibliographic record
Abstract
In this paper we present algorithms for the perfect sampling of single-server time-varying queues with periodic Poisson arrivals under the first come first served (FCFS) discipline. The service durations have periodically time-dependent exponential ( $$\mathrm M _t/\mathrm M _t/1$$ ) or homogeneous general ( $$\mathrm M _t/\mathrm G /1$$ ) distributions. Assuming a cycle length of 1, we construct discrete dominating processes at the integer instants $$n \in \{0, \pm 1, \ldots \}$$ . Perfect sampling of the $$\mathrm M _t/\mathrm M _t/1$$ queue is obtained using dominated CFTP (Kendall and Møller 2000) when the system is relatively lightly loaded or with the regenerative method (Sigman 2012) in the general case. For the $$\mathrm M _t/\mathrm G /1$$ queue, perfect sampling is achieved with dominated CFTP.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it