Diffusion Approximations for Some Multiclass Queueing Networks with FIFO Service Disciplines
Bibliographic record
Abstract
The diffusion approximation is proved for a class of multiclass queueing networks under FIFO service disciplines. In addition to the usual assumptions for a heavy traffic limit theorem, a key condition that characterizes this class is that a J × J matrix G, known as the workload contents matrix, has a spectral radius less than unity, where J represents the number of service stations. The (j, 𝓁)th component of matrix Gcan be interpreted as the long-run average amount of future work for station j that is embodied in a unit of immediate work at station 𝓁. This class includes, as a special case, the feedforward multiclass queueing network and the Rybko-Stolyar network under FIFO service discipline. A new approach is taken in establishing the diffusion limit theorem. The traditional approach is based on an oblique reflection mapping, but such a mapping is not well defined for the network under consideration. Our approach takes two steps: Arst establishing the C-tightness of the scaled queueing processes, and then completing the proof for the convergence of the scaled queueing processes by invoking the weak uniqueness for the limiting processes, which are semimartingale reflecting Brownian motions.
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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 | 0.004 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| 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".