A note on a bulk arrivals quorum queuing system with an unreliable server
Why this work is in the frame
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Bibliographic record
Abstract
This paper considers a service system with bulk service and an unreliable server, generalising the work of Tadj and Choudhury [Applied Mathematics Letters, 22 (2009) 1710–1714]. While Tadj and Choudhury assume single arrivals, we allow arrivals to occur in bulk, which increases the analytical challenge. The first objective is to derive the probability generating function of the number of customers in the system at a service completion epoch and at an arbitrary instant of time as well as the performance characteristics of the system. The second objective is to develop an optimal management policy to obtain the optimal value of the parameter which minimises a suitable cost structure. This model is useful in different real-world operational management problems to minimise the organisation costs while keeping a high customer satisfaction level.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.002 | 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