Single server Markovian queueing system with working vacation, impatient customers and disasters
Bibliographic record
Abstract
This paper examines the single server Markovian queueing system that incorporates working vacations, disasters, and impatient customers. The server initiates a Vacation when no customers are present in the system, during which it continues to serve arriving customers at a reduced rate. Disasters occurs while the main server is either busy or on a working vacation; leading to the removal of all customers from the system and causing the server to break down. When the main server is down, it is sent for repairs, and a substitute server provides service at a reduced rate until the main server is restored. When a customer arrives while the server is busy, undergoing repairs, or on Working Vacation, an impatience timer is activated. Additionally, arriving customers activate an impatience timer if the server is busy, under repair, or on a working vacation. If service is not completed before the timer expires, the customer abandons the system. The paper further presents a cost analysis and numerical illustrations to evaluate system performance.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".