ON MARKOVIAN QUEUES WITH SINGLE WORKING VACATION AND BERNOULLI INTERRUPTIONS
Bibliographic record
Abstract
This paper considers the customers’ equilibrium and socially optimal joining–balking behavior in a single-server Markovian queue with a single working vacation and Bernoulli interruptions. The model is motivated by practical service systems where the service rate can be adjusted according to whether or not the system is empty. Specifically, we focus on a single-server queue in which the server's service rate is reduced from a regular to a lower one when the system becomes empty. This lower rate period is called a working vacation for the server which may represent that part of the service facility is under a maintenance process or works on other non-queueing job, or simply for saving the energy (for a machine server case). In this paper, we assume that the working vacation period is terminated after a random period or with probability p after serving a customer in a non-empty system. Such a system is called a queue with single working vacation and Bernoulli interruptions. Customers are strategic and can make choice of joining or balking based on different levels of system information. We consider four scenarios: fully observable, almost observable, almost unobservable, and fully unobservable queue cases. Under a reward-cost structure, we analyze the customer's equilibrium and social-optimal strategies. In addition, the effects of system parameters on optimal strategies are illustrated by numerical examples.
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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 | 0.006 | 0.014 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".