A two-stage bulk-service queueing model with rework, closedown and multiple vacations
Bibliographic record
Abstract
In the manufacturing industry, the quality of products is of great significance in the preservation of the brand image. Quality inspection is defined as a procedure for ensuring the compliance, reliability, uniformity, and standard of a specific product. Through effective inspection, manufacturers are able to detect problems that require correction and prevent errors to ensure quality products for customers. To study such scenarios in queueing systems, we examine a two-stage bulk service single server with batch arrivals, incorporating rework, system closedown, and multiple vacation periods. Once a batch of fabric completes the first stage of regular service, the server proceeds to the second inspection stage for the same batch. If the inspection stage identifies defects, the server returns the batch for rework in the regular service stage with a specific probability. The server initiates regular service for the next batch with a specified probability when inspection yields no defects, and the queue length exceeds $``a"$. Conversely, if the queue length is below $``a"$ and no defects are present, the server may enter a closedown state with a given probability. After closedown, the server can take multiple vacations of random duration. Using the supplementary variable technique, we develop a model to analyze the probability-generating function of the queue size at any given moment. Additionally, we explore performance metrics through numerical examples, provide a cost analysis, and present the findings with graphical representations.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.006 | 0.002 |
| Research integrity | 0.005 | 0.003 |
| Insufficient payload (model declined to judge) | 0.013 | 0.002 |
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".