Explicit Characterization of Stability Region for Stationary Multi-Queue Multi-Server Systems
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Bibliographic record
Abstract
We derive an explicit characterization of the stability region of stationary multi-queue multi-server (MQMS) queueing system by means of a finite set of linear inequalities. More specifically, we explicitly determine the coefficients of the linear inequalities describing the facet-defining hyperplanes of the stability region polytope. Such a characterization is useful for performance evaluation of certain scheduling algorithms such as maximum weight (MW) policy. Our results can be used for studying the asymptotic behavior of the MW policy and computing bounds for the average queueing delay, as well as limiting moments of the queue sizes in heavy-traffic regime. Furthermore, it may be directly applied as the constraint set of network stochastic optimization problems to provide an offline computational solution for such problems. Finally, we use our methodology to characterize the stability region of a fluid model MQMS system which is described by an infinite number of linear inequalities. For such a model, we present an example and show that depending on the channel distribution, the stability region can be instead characterized by a finite set of non-linear inequalities.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it