Joining behavior and vacation strategy in the queue with heterogeneous customers
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it