Rate-based randomized routing in large heterogeneous processor sharing systems
Bibliographic record
Abstract
Randomized load balancing techniques are effective solutions to reduce mean waiting time of jobs in large web server farms, where obtaining state information of all the servers becomes costly. The classical power-of-two routing scheme, which has already been analyzed for systems of identical servers, requires the instantaneous state information of two randomly selected servers at each job-arrival instant. In this paper, we consider variants of the classical power-of-two scheme for multiserver systems where the servers may have different service rates. We modify the classical power-of-two scheme for the heterogeneous system so that it now incorporates server speeds into the criterion for server selection. We analytically characterize the stability region, stationary load distribution, and the mean sojourn time of jobs of this modified scheme. It is shown that, in the heterogeneous case, the stability region of the modified scheme may be a subset of the maximum achievable stability region. To improve the stability region, we propose and analyze another scheme which combines the power-of-two routing scheme with randomized state independent routing scheme. We show that this new scheme achieves the maximum stability region and results in the least mean sojourn time of jobs among all the schemes considered in the paper.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".