Join, balk, or jettison? The effect of flexibility and ranking knowledge in systems with batch arrivals
Bibliographic record
Abstract
Families that visit theme parks like Disneyland are debating on two aspects when they try to determine whether they prefer to join an activity of interest or would rather balk: (1) Is it better to join or balk as a group or allow the flexibility to get separated and jettison some members? and (2) Will it make any difference if they set a ranking among themselves beforehand as to who will be served first, second, etc.? We tackle the effect of flexibility and ranking knowledge and answer the above questions considering a single server Markovian queue with a generic batch size distribution. We consider two levels of flexibility: an inflexible setting, under which a family makes a common decision, and a flexible setting, under which each member makes her own decision. We pair each level with two sublevels with respect to the ranking knowledge: the case where the members set their ranking beforehand, and the case where they do not and assume they will be served according to a random order. We provide a full analytical characterization of the equilibrium and socially optimal strategies, and a comprehensive analysis of the intricate interplay among flexibility, ranking knowledge, and batch size variability, notions that do not exist in single‐ins arrival systems. We offer insights as to under which circumstances entity jettison is preferable. We investigate the corresponding implications of the above on system throughput and social welfare and determine which setting is preferable for the customers and which for the society, depending on the objective and the system dynamics. Further, we highlight key differences between single versus batch‐arrival models and provide high‐level guidelines for managers and policymakers as to how they can influence customer decisions so that they move toward the preferable setting (e.g., by revealing/concealing the ranking, encouraging flexibility, pricing, etc.).
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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 | 0.007 | 0.032 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".