Analytic and Computational Analysis of GI/Ma,b/c Queueing System
Bibliographic record
Abstract
Bulk-service queueing systems have been widely applied in many areas in real life. While single-server queueing systems work in some cases, multi-servers can efficiently handle most complex applications. Bulk-service, multi-server queueing systems (compared to well-developed single-server queueing systems) are more complex and harder to deal with, especially when the inter-arrival time distributions are arbitrary. This paper deals with analytic and computational analyses of queue-length distributions for a complex bulk-service, multi-server queueing system GI/Ma,b/c, wherein inter-arrival times follow an arbitrary distribution, a is the quorum, and b is the capacity of each server; service times follow exponential distributions. The introduction of quorum a further increases the complexity of the model. In view of this, a two-dimensional Markov chain has to be involved. Currently, it appears that this system has not been addressed so far. An elegant analytic closed-form solution and an efficient algorithm to obtain the queue-length distributions at three different epochs, i.e., pre-arrival epoch (p.a.e.), random epoch (r.e.), and post-departure epoch (p.d.e.) are presented, when the servers are in busy and idle states, respectively.
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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 | 0.001 | 0.005 |
| 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 | 0.001 |
| Open science | 0.001 | 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".