On the Planning and Design Problem of Fog Computing Networks
Bibliographic record
Abstract
This paper proposes an exact model for the planning and design problem of fog networks. More precisely, a mathematical model is proposed to simultaneously determine the optimal location, the capacity and the number of fog node(s) as well as the interconnection between the installed fog nodes and the cloud. The goal of the model is to minimize the delay in the network and the amount of traffic sent to the cloud data center. To address this multi-objective optimization problem, three optimization techniques are used: the weighted sum, the hierarchical and the trade-off methods. The weighted sum method aggregates all the lone objective functions into a single objective by applying a weighted vector. The hierarchical method takes a sequential approach by tightly constraining the more important objective function. The trade-off method solves a single objective function and translates all other objective functions into constraints. These methods are then compared in terms of average delay, amount of traffic sent to the cloud and amount of CPU time required to find optimal solution(s). Since we are dealing with a multi-objective optimization problem and that multiple optimal solutions can be found, the fuzzy-based mechanism and the hypervolume indicator have been used. Computational results show that as the problem size increases, the delay and the traffic also increase in a linear form; whereas, the solution time increases in non-polynomial time. The weighted sum method was able to achieve the best trade-off results for the delay and the traffic, whereas the hierarchical method was able to return minimum delay but with worse traffic going to the cloud. As the model considers realistic edge device traffic parameters, constraints, and various topology aspects, it can be helpful for the planning and deployment of fog networks and how they operate within a cloud infrastructure.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".