Asymptotically optimal scheduling of random malleable demands in smart grid
Bibliographic record
Abstract
We study the problem of scheduling random energy demands within a fixed normalized time horizon. Each demand has to be serviced without interruption at a constant intensity, while its duration is bounded by a pair of malleability constraints. Such constraints are assumed to be characterized by an i.i.d random vector that follows a general distribution. At each time instance, the total power consumption is computed as the sum of the intensities of all demands being serviced at that moment. Our objective is to minimize both the maximum and the total convex cost of the power consumption of the grid. The problem is considered in the asymptotic regime. In this regime, the number of demands is assumed to be large, and their (random) energy requirements are inversely proportional to the number of demands. Such setting allows us to introduce a linear-time scheduling policy and shows its asymptotic optimality with respect to both cost criteria. We first study the optimization problem in the case where all demands are available a priori, i.e., before scheduling starts. Then we extend our approach for the case of demand scheduling in an arbitrary length time horizon, where the demands arrive randomly during this time interval.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".