Bayesian Dynamic Pricing in Queueing Systems with Unknown Delay Cost Characteristics
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Bibliographic record
Abstract
The revenue management literature for queues typically assumes that providers know the distribution of customer demand attributes. We study an observable M/M/1 queue that serves an unknown proportion of patient and impatient customers. The provider has a Bernoulli prior on this proportion, corresponding to an optimistic or pessimistic scenario. For every queue length, she chooses a low or a high price, or turns customers away. Only the high price is informative. The optimal Bayesian price for a queue state is belief-dependent if the optimal policies for the underlying scenarios disagree at that queue state; in this case the policy has a belief-threshold structure. The optimal Bayesian pricing policy as a function of queue length has a zone (or, nested-threshold) structure. Moreover, the price convergence under the optimal Bayesian policy is sensitive to the system size, i.e., the maximum queue length. We identify two cases: prices converge (1) almost surely to the optimal prices in either scenario or (2) with positive probability to suboptimal prices. Only Case 2 is consistent with the typical incomplete learning outcome observed in the literature.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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