Integrating Queueing Theory and Scheduling for Dynamic Scheduling Problems
Bibliographic record
Abstract
Dynamic scheduling problems consist of both challenging combinatorics, as found in classical scheduling problems, and stochastics due to uncertainty about the arrival times, resource requirements, and processing times of jobs. To address these two challenges, we investigate the integration of queueing theory and scheduling. The former reasons about long-run stochastic system characteristics, whereas the latter typically deals with short-term combinatorics. We investigate two simple problems to isolate the core differences and potential synergies between the two approaches: a two-machine dynamic flowshop and a flexible queueing network. We show for the first time that stability, a fundamental characteristic in queueing theory, can be applied to approaches that periodically solve combinatorial scheduling problems. We empirically demonstrate that for a dynamic flowshop, the use of combinatorial reasoning has little impact on schedule quality beyond queueing approaches. In contrast, for the more complicated flexible queueing network, a novel algorithm that combines long-term guidance from queueing theory with short-term combinatorial decision making outperforms all other tested approaches. To our knowledge, this is the first time that such a hybrid of queueing theory and scheduling techniques has been proposed and evaluated.
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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 | 0.006 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| 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".