Congestion-Based Repair Policy for a Failure-Prone Service System With Strategic Customers
Bibliographic record
Abstract
This study examines the decision-making interaction between a service provider adopting a congestion-based repair policy and strategic customers in a failure-prone M/M/1 queueing system. The server’s lifetime is exponentially distributed, and a repair starts immediately upon the server’s breakdown. The repair rate is adjustable: the service provider employs a high repair rate (with a high cost) if the number of waiting customers reaches a threshold; otherwise, a low repair rate (with a low cost) is adopted. We model the interaction as a two-stage Stackelberg game: the provider (leader) sets the price, repair threshold, and information policy before customers (followers) decide whether to join. Using backward induction, we characterize the resulting Stackelberg equilibrium. Under fully unobservable and almost unobservable cases, both follow-the-crowd (FTC) and avoid-the-crowd (ATC) behaviors are found to coexist in the customer’s equilibrium joining strategy. Two special models, the classic repair model (when the threshold approaches 0) and the delayed repair model (when the low repair rate approaches 0), are discussed extensively. The classic repair policy maximizes throughput but incurs the highest costs, while delayed repair minimizes costs at the expense of throughput. The proposed congestion-based repair strategy balances these tradeoffs, achieving intermediate throughput and cost levels. Notably, it can increase profits by up to 34.4% compared with classic repair, with its effectiveness amplified under high-cost scenarios. By comparing the unobservable case with the almost unobservable counterpart, we demonstrate that hiding server state information when prices are low and disclosing server information when prices are high can increase profit for the service provider, but at the expense of reducing social welfare.
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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 | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".