Self-Stabilizing Balls and Bins in Batches:The Power of Leaky Bins
Bibliographic record
Abstract
A fundamental problem in distributed computing is the distribution of requests to a set of uniform servers without a centralized controller. Classically, such problems are modelled as static balls into bins processes, where m balls (tasks) are to be distributed among n bins (servers). In a seminal work, Azar et al. [4] proposed the sequential strategy Greedy[d] for n = m. Each ball queries the load of d random bins and is allocated to a least loaded of them. Azar et al. showed that d = 2 yields an exponential improvement compared to d = 1. Berenbrink et al. [7] extended this to m n, showing that for d = 2 the maximal load difference is independent of m (in contrast to the d = 1 case). We propose a new variant of an infinite balls-into-bins process. In each round an expected number of λn new balls arrive and are distributed (in parallel) to the bins, and each non-empty bin deletes one of its balls. This setting models a set of servers processing incoming requests, where clients can query a server’s current load but receive no information about parallel requests. We study the Greedy[d] distribution scheme in this setting and show a strong self-stabilizing property: for any arrival rate λ = λ(n) < 1, the system load is time-invariant. Moreover, for any (even super-exponential) round t, the maximum system load is (w.h.p.) O 1 1−λ· log n 1−λ for d = 1 and O log n 1−λ for d = 2. In particular, Greedy[2] has an exponentially smaller system load for high arrival rates.
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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 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".