Randomized routing schemes for large processor sharing systems with multiple service rates
Bibliographic record
Abstract
We consider randomized job routing techniques for a system consisting of a large number of parallel processor sharing servers with heterogeneous server speeds. In particular, a scheme, that routes an incoming job request to the server providing the highest instantaneous processing rate per job among two servers, chosen uniformly at random, is proposed. We show that, unlike the homogeneous case, in the heterogeneous case, such randomized dynamic schemes need not always perform better than the optimal static scheme (in which jobs are assigned to servers with fixed probabilities independent of server states) in terms of reducing the mean response time of jobs. Specifically, we show that the stability region under the proposed scheme is a subset of that under the optimal static routing scheme. We also obtain the stationary tail distribution of server occupancies for the proposed scheme in the limit as the system size grows to infinity. This distribution has been shown to be insensitive to job length distribution and decay super-exponentially.
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How this classification was reachedexpand
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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.000 | 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 teacher head, 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".