Strategies for a Centralized Single Product Multiclass <i>M/G/</i>1 Make-to-Stock Queue
Bibliographic record
Abstract
Make-to-stock queues are typically investigated in the M/M/1 settings. For centralized single-item systems with backlogs, the multilevel rationing (MR) policy is established as optimal and the strict priority (SP) policy is a practical compromise, balancing cost and ease of implementation. However, the optimal policy is unknown when service time is general, i.e., for M/G/1 queues. Dynamic programming, the tool commonly used to investigate the MR policy in make-to-stock queues, is less practical when service time is general. In this paper we focus on customer composition: the proportion of customers of each class to the total number of customers in the queue. We do so because the number of customers in M/G/1 queues is invariant for any nonidling and nonanticipating policy. To characterize customer composition, we consider a series of two-priority M/G/1 queues where the first service time in each busy period is different from standard service times, i.e., this first service time is exceptional. We characterize the required exceptional first service times and the exact solution of such queues. From our results, we derive the optimal cost and control for the MR and SP policies for M/G/1 make-to-stock queues.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".