TECHNICAL NOTE—Queueing Systems with Synergistic Servers
Bibliographic record
Abstract
We consider tandem lines with finite buffers and flexible, heterogeneous servers that are synergistic in that they work more effectively in teams than on their own. Our objective is to determine how the servers should be assigned dynamically to tasks in order to maximize the long-run average throughput. In particular, we investigate when it is better to take advantage of synergy among servers, rather than exploiting the servers' special skills, to achieve the best possible system throughput. We show that when there is no trade-off between server synergy and servers' special skills (because the servers are generalists who are equally skilled at all tasks), the optimal policy has servers working in teams of two or more at all times. Moreover, for Markovian systems with two stations and two servers, we provide a complete characterization of the optimal policy and show that, depending on how well the servers work together, the optimal policy either takes full advantage of servers' special skills, or full advantage of server synergy (and hence there is no middle ground in this case). Finally, for a class of larger Markovian systems, we provide sufficient conditions that guarantee that the optimal policy should take full advantage of server synergy at all times.
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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 | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 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 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".