Impact of the Frequency of Control for the Multiclass Queue Scheduling Problem
Bibliographic record
Abstract
Optimal control of stochastic queueing networks and their applications in, e.g., service, healthcare, and telecommunication systems have been extensively studied. The literature largely focuses on continuous-time control. In many settings, however, decisions can only be made at discrete points in time. We study a discrete-time finite-horizon multiclass queue scheduling problem, where server assignments can only be adjusted at the beginning of discrete intervals or review periods. Our objective is to examine the value of control as a function of the review period length. To this end, we analyze a sequence of fluid control problems parameterized by the review period and characterize the first- and second-order sensitivity of the value function. For the two-class case, we derive explicit expressions for the first and second derivatives and show when they are positive or negative. We discuss the extension of our results to more classes and numerically examine generalizability to the stochastic setting.
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How this classification was reachedexpand
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 teacher head, 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".