Pricing in Service Systems with Rational Balking and Abandonment of Time‐Sensitive Customers
Bibliographic record
Abstract
The current literature on pricing in service systems with time‐sensitive customers predominately ignores the rational abandonment of customers with mixed‐risk attitude. The goal of this study is to address this gap. We consider an unobservable queueing system with a nonlinear waiting cost function, which is concave up to a certain point and then becomes convex, capturing the mixed‐risk attitude of customers observed in empirical studies. We assume that customers are sensitive with respect to waiting time (delay) and strategic regarding their balking and abandonment decisions. We characterize the optimal pricing policy that maximizes the service provider's revenue. We show that the pricing policies studied in the literature, including the joint service and cancellation (entrance) fee policy, are suboptimal and cannot induce the socially optimal behavior. We demonstrate that while the cancellation fee can regulate a customer's balking strategy, the service fee cannot effectively control a customer's abandonment decision. We then provide conditions under which the joint service and cancellation fee policy is optimal. We finally prove that the service provider should compensate customers for their waiting in order to efficiently control the abandonment of customers. We propose a pricing policy, which includes entrance, service, and wait time (delay) fees, that maximizes the provider's revenue. We derive the optimal fees and show that, under the proposed optimal pricing policy, customers pay service and cancellation fees while they are partially compensated for the time spent waiting for service.
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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 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| 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".