Bibliographic record
Abstract
We consider two parallel queues. There is one server tending to each queue and the capacity of each queue is K . The network is fed by a single Poisson arrival stream of rate λ, and the two servers are identical exponential servers working at rate µ. A new arrival is routed to the queue with the smaller number of customers. If both have the same number of customers then the arrival is routed randomly, with the probability of joining either queue being 1/2. If there are more than 2 K customers in the system, further arrivals are turned away and lost. We let ρ = λ/µ and take K →∞, and consider the cases ρ 2 and ρ − 2 = O ( K − 1 ). We shall obtain asymptotic approximations to the joint steady state distribution of finding m customers in the first queue and n in the second. The asymptotic approximations are shown to be quite accurate numerically. We shall identify precisely for what ranges of m and n can the finite capacity model be approximated by the infinite capacity one. We will also show that the marginal distribution of finding n customers in the second queue undergoes a transition when ρ = 4. Key words: Shortest queue problem; Finite capacity; Poisson arrival stream; Analytical approximations
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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 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".