Dynamic Scheduling with Convex Delay Costs: The Generalized CU Rule
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Bibliographic record
Abstract
We consider a general single-server multiclass queueing system that incurs a delay cost Ck(Tk) for each class k job that resides Tk units of time in the system. This paper derives a scheduling policy that minimizes the total cumulative delay cost when the system operates during a finite time horizon. Denote the marginal delay cost function and the (possibly non-stationary) average processing time of class k by ck = C'k and 1/uk, respectively, and let ak(t) be the age or time that the oldest class k job has been waiting at time t. We call the scheduling policy that at time t serves the oldest waiting job of that class k with the highest index uk(t)ck(ak(t)), the generalized cu rule. As a dynamic priority rule that depends on very little data, the generalized cu rule is attractive to implement. We show that, with nondecreasing convex delay costs, the generalized cu rule is asymptotically optimal if the system operates in heavy traffic and give explicit expressions for the associated performance characteristics: the delay (throughput time) process and the minimum cumulative delay cost. The optimality result is robust in that it holds for a countable number of classes and several homogeneous servers in a nonstationary, deterministic or stochastic environment where arrival and service processes can be general and interdependent.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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