Approximate mean waiting time in a <i>GI</i> / <i>D</i> /1 queue with autocorrelated times to failures
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Bibliographic record
Abstract
In this paper, we study process completion time and propose an accurate approximation for the mean waiting time in queues with servers experiencing autocorrelated times to failure, which include only busy periods from a repair completion until the next failure. To do this, we employ a three-parameter renewal approximation that represents the stream of autocorrelated times to failure. The approximation gives rise to a renewal interruption process with two-state Hyper-exponential (H2) times to failure. Then we compute the mean waiting time exactly in a queue experiencing H2 times to failure when the job arrival process is Poisson. This model provides an approximation for the mean waiting time of the original queue having an autocorrelated disruption process. We also propose an accurate approximation for queues with renewal job arrival processes when the server interruption process is general.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| 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) | 0.001 | 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 it