Strategic Joining and Optimal Pricing in a Single‐Server Batch Arrival Queue With Different Information of Batch Size
Bibliographic record
Abstract
ABSTRACT This study explores the strategic behavior of customers in a single‐server batch arrival queue, where the batch size is a random variable. Each customer makes a decision to either join or balk under a linear reward‐cost structure. The utility of each customer is contingent on her individual decision and the decisions of her companions. The research considers two scenarios distinguished by the level of information: the batch size observable case, where customers are aware of their batch size information, and the batch size unobservable case, where customers lack information upon arrival. In both cases, a unique Nash equilibrium joining strategy and a socially optimal joining strategy are derived. To bridge the gap between the individual equilibrium joining strategy and the socially optimal strategy, a proposed fee imposed on customers is introduced. By comparing outcomes across both information scenarios, we derive managerial insights regarding optimal information‐disclosure policies. The key insight from our numerical experiments is that regulating the mean and variance of the batch size distribution is key to maximizing overall system throughput and social welfare.
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How this classification was reachedexpand
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 | 0.002 | 0.003 |
| 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 | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".