On Optimal Server Allocation for a Loss System With Moldable Jobs
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Bibliographic record
Abstract
A large proportion of jobs submitted to modern computing clusters and data centers are parallelizable and capable of running on a flexible number of computing cores or servers. Although allocating more servers to such a job results in a higher speed-up in the job’s execution, it reduces the number of servers available to other jobs, which in the worst case, can result in an incoming job not finding any available server to run immediately upon arrival. Hence, a key question to address is: how to optimally allocate servers to jobs such that (i) the average execution time across jobs is minimized and (ii) almost all jobs find at least one server immediately upon arrival. To address this question, we consider a system with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> servers, where jobs are parallelizable up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d^{(n)}$</tex-math> </inline-formula> servers and the speed-up function of jobs is concave and increasing. Jobs not finding any available servers upon entry are blocked and lost. We propose a simple server allocation scheme that achieves the minimum average execution time of accepted jobs while ensuring that the blocking probability of jobs vanishes as the system becomes large (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n \to \infty $</tex-math> </inline-formula>). This result is established for various traffic conditions as well as for heterogeneous workloads. To prove our result, we employ Stein’s method which also yields non-asymptotic bounds on the blocking probability and the mean execution time. Furthermore, our simulations show that the performance of the scheme is insensitive to the distribution of job execution times.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 it