WAITING TIME ANALYSIS OF MULTI-CLASS QUEUES WITH IMPATIENT CUSTOMERS
Bibliographic record
Abstract
In this paper, we study three delay systems where different classes of impatient customers arrive according to independent Poisson processes. In the first system, a single server receives two classes of customers with general service time requirements, and follows a non-preemptive priority policy in serving them. Both classes of customers abandon the system when their exponentially distributed patience limits expire. The second system comprises parallel and identical servers providing the same type of service for both classes of impatient customers under the non-preemptive priority policy. We assume exponential service times and consider two cases depending on the time-to-abandon distribution being exponentially distributed or deterministic. In either case, we permit different reneging rates or patience limits for each class. Finally, we consider the first-come-first-served policy in single- and multi-server settings. In all models, we obtain the Laplace transform of the virtual waiting time for each class by exploiting the level-crossing method. This enables us to compute the steady-state system performance measures.
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How this classification was reachedexpand
Direct model labels (unvalidated)
Per-model category and study-design labels from the labeling rounds. They are machine output, unvalidated, and the disagreement between models ships as data. No study design here is MEDLINE-validated yet.
| Model arm | Categories | Study design | Confidence |
|---|---|---|---|
| gemma | no category Domain: not available · Genre: Empirical About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | low |
| gpt | no category Domain: not available · Genre: Empirical About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | high |
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 | 0.006 |
| 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 | 0.001 |
| 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, unvalidatedLabeled directly by 2 models reading the full record.
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".