On the online fault-tolerant server consolidation problem
Bibliographic record
Abstract
In the server consolidation problem, the goal is to minimize the number of servers needed to host a set of clients. The clients appear in an online manner and each of them has a certain load. The servers have uniform capacity and the total load of clients assigned to a server must not exceed this capacity. Additionally, to have a fault-tolerant solution, the load of each client should be distributed between at least two different servers so that failure of one server avoids service interruption by migrating the load to the other servers hosting the respective second loads. In a simple setting, upon receiving a client, an online algorithm needs to select two servers and assign half of the load of the client to each server. We analyze the problem in the framework of competitive analysis. First, we provide upper and lower bounds for the competitive ratio of two well known heuristics which are introduced in the context of tenant placement in the cloud. In particular, we show their competitive ratios are no better than 2. We then present a new algorithm called Horizontal Harmonic and show that it has an improved competitive ratio which converges to 1.59. The simplicity of this algorithm makes it a good choice for use by cloud service providers. Finally, we prove a general lower bound that shows any online algorithm for the online fault-tolerant server consolidation problem has a competitive ratio of at least 1.42.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.002 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| 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".