Joining behavior and vacation strategy in the queue with heterogeneous customers
Bibliographic record
Abstract
This paper analyzes equilibrium decisions in queues with server vacations and heterogeneous customers, who differ in their reward and holding costs. Customers make decisions to join the queue or balk based on different information settings. Using differential equations applied to a Markov chain model, we explore the joining strategies of these customers under two observable and two unobservable cases, focusing on how factors such as information, reward-cost ratios (reflecting customer heterogeneity), arrival rates (potential market sources), and vacation rates (representing the firm’s responses) influence their decisions. Interestingly, we find that customers may sometimes prefer to join during server vacations rather than when the server is active, due to shorter waiting times. The paper highlights the importance of optimizing the vacation rate to influence customer choices and maximize the service firm’s revenue. The optimal vacation rate can be determined under the fully unobservable information setting, and it is not monotonic with respect to market sources, showing how heterogeneous customers may choose to join or balk based on varying conditions.
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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 | 0.004 | 0.012 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".