Multiclass state‐dependent service systems with returns
Bibliographic record
Abstract
Abstract In this paper, we consider a service system facing several classes of customers in which the arrival rate and service time depend on the workload in the system, while the chance of return is a function of the service time. We first model the problem as a multiclass multiserver queueing network and investigate its stability by examining the conditions under which the Markov chain representing the network is positive recurrent. We then examine the impact of the relationship among the workload, service time, arrival rate, and the chance of return on the dynamics of the system using a fluid approach. We first characterize all equilibria of the system and show that the system may shift between several equilibrium states. We establish that all equilibria can be easily determined and demonstrate conditions under which an equilibrium is stable. We then prove that, surprisingly, the stability of an equilibrium and the congestion in the system may depend on the amount of time a customer spends outside of the system before returning for rework. However, we show that if the relationship between the workload and service time in a system facing a single class of customers is nondecreasing, the long‐run behavior of the system is not affected by how long it takes until a customer returns.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| 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".