Efficient Online Strategies for Renting Servers in the Cloud
Bibliographic record
Abstract
In Cloud systems, we often deal with jobs that arrive and depart in an online manner. Upon its arrival, a job should be assigned to a server. Each job has a size which defines the amount of resources that it needs. Servers have uniform capacity and, at all times, the total size of jobs assigned to a server should not exceed the capacity. This setting is closely related to the classic bin packing problem. The difference is that, in bin packing, the objective is to minimize the total number of used servers. In the Cloud, however, the charge for each server is proportional to the length of the time interval it is rented for, and the goal is to minimize the cost involved in renting all used servers. Recently, certain bin packing strategies were considered for renting servers in the Cloud [Li et al. SPAA'14]. There, it is proved that all Any-Fit bin packing strategy has a competitive ratio of at least $μ$, where $μ$ is the max/min interval length ratio of jobs. It is also shown that First Fit has a competitive ratio of $2μ+ 13$ while Best Fit is not competitive at all. We observe that the lower bound of $μ$ extends to all online algorithms. We also prove that, surprisingly, Next Fit algorithm has competitive ratio of at most $2 μ+1$. We also show that a variant of Next Fit achieves a competitive ratio of $K \times max\{1,μ/(K-1)\}+1$, where $K$ is a parameter of the algorithm. In particular, if the value of $μ$ is known, the algorithm has a competitive ratio of $μ+2$; this improves upon the existing upper bound of $μ+8$. Finally, we introduce a simple algorithm called Move To Front (MTF) which has a competitive ratio of at most $6μ+ 7$ and also promising average-case performance. We experimentally study the average-case performance of different algorithms and observe that the typical behaviour of MTF is distinctively better than other algorithms.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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".