The complexity of computing virtual-time in weighted fair queuing schedulers
Bibliographic record
Abstract
This paper presents two fundamental theorems that show that the O(N) complexity for updating the virtual time in a weighted fair queuing (WFQ) scheduler with N sessions is caused mainly by simultaneous departures of packets, and not by iterated deletion as was previously claimed. Iterated deletion is caused by an "avalanche" of consecutive, but not necessarily simultaneous, departures that incur more departures due to increments in available bandwidth from idling sessions. Iterated deletion potentially leads to large numbers of consecutive departures within a given time period. The number of departures is, however, a function of such implementation details as the resolution of the time-stamp and the scheduler clock. On the other hand, the problem of simultaneous time-stamps can not be solved by an increase in the time resolution of virtual-time update. Essentially, all equal time-stamps must be processed during a single virtual-time update operation. We present a proof to show that O(N) simultaneous departures can occur during a single virtual-time update. We also show that this is a fundamental property of WFQ that holds even under the most restrictive conditions, viz. all packets arrive serially to the scheduler (no simultaneous arrivals), and the input bit-rate does not exceed the output bit-rate.
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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 | 0.004 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.005 | 0.010 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".