Explicit Characterization of Stability Region for Stationary Multi-Queue\n Multi-Server Systems
Bibliographic record
Abstract
In this paper, we characterize the network stability region (capacity region)\nof multi-queue multi-server (MQMS) queueing systems with stationary channel\ndistribution and stationary arrival processes. The stability region is\nspecified by a finite set of linear inequalities. We first show that the\nstability region is a polytope characterized by the finite set of its facet\ndefining hyperplanes. We explicitly determine the coefficients of the linear\ninequalities describing the facet defining hyperplanes of the stability region\npolytope. We further derive the necessary and sufficient conditions for the\nstability of the system for general arrival processes with finite first and\nsecond moments. For the case of stationary arrival processes, the derived\nconditions characterize the system stability region. Furthermore, we obtain an\nupper bound for the average queueing delay of Maximum Weight (MW) server\nallocation policy which has been shown in the literature to be a throughput\noptimal policy for MQMS systems. Using a similar approach, we can characterize\nthe stability region for a fluid model MQMS system. However, the stability\nregion of the fluid model system is described by an infinite number of linear\ninequalities since in this case the stability region is a convex surface. We\npresent an example where we show that in some cases depending on the channel\ndistribution, the stability region can be characterized by a finite set of\nnon-linear inequalities instead of an infinite number of linear inequalities.\n
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".