Job Scheduling with Battery Recharging Constraints: Applications to UAV Flight Planning
Bibliographic record
Abstract
The need to understand job scheduling on devices with intermittent availability is of significant interest today because of the use of battery-powered devices - including electric vehicles - that rely on recharging intervals or energy harvesting. In some recent work by Islam and Nirjon, effective heuristics were proposed for scheduling recurring tasks with deadlines on such intermittently available devices. The broader computational complexity of job scheduling has not been explored in this setting where there is a relationship between job durations and energy consumption. We provide a richer understanding of this problem space. We consider two recharging approaches, one where the battery has to be fully charged during a recharging interval (sometimes considered better for extending battery lifetime) and another where the battery can be partially charged, and we study different scheduling objectives: minimizing the sum of completion times, minimizing the maximum tardiness, and minimizing the number of tardy jobs. We also consider four different relationships between job duration and energy consumption: (i) energy consumption is equal for all jobs irrespective of job length; (ii) job length is equal for all jobs irrespective of energy consumption; (iii) energy consumption is directly proportional to job length; and (iv) there is an arbitrary relationship between job length and energy consumption. In effect, we consider 24 different scheduling problems, and establish that most problems subject to a complete recharging requirement are NP-Hard but that most problems can be solved in polynomial time when partial recharging is permitted. Interestingly, we have been unable to resolve the computational complexity for the one case of minimizing the sum of completion times subject to partial recharging.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 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) | 0.003 | 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".