Capacity Rationing in Multiserver, Nonpreemptive Priority Queues
Why this work is in the frame
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Bibliographic record
Abstract
Problem definition: Many service and manufacturing systems use both capacity rationing (CR) and priority to differentiate among their customers. We model these as a two-class nonpreemptive priority [Formula: see text] queueing model and the practice of CR; an arriving low-priority customer can directly enter service only when the number of idle servers is higher than the CR level, k. For these systems, we separately discuss two important features that are common in practice but ignored in the literature; supply is narrowly matched with demand, and service rates are heterogeneous, reflecting different customer types. Methodology and results: When the service times of both classes are identical, our asymptotic results indicate that for a system with a large number of servers, the nondegenerative CR level does not exceed [Formula: see text]. When the service times of classes differ, we derive exact solutions for different performance measures of interest using queueing and Markov chain decomposition. We numerically demonstrate the impact of system parameters on these performance measures and provide insights on the CR level. Management implications: We show that as predicted by the asymptotic analysis, an [Formula: see text] CR level can significantly reduce the waits of high-priority customers with little effect on low-priority customers’ waiting. We establish that this insight is robust to heterogeneous service times across classes and other system parameters, such as the number of servers and the arrival rates of the classes. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.0106 .
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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 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| 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