Multiservice Function Chain Embedding With Delay Guarantee: A Game-Theoretical Approach
Bibliographic record
Abstract
Through network function virtualization (NFV), virtual network functions (VNFs) can be mapped onto substrate networks as service function chains (SFCs) to provide customized services with guaranteed Quality of Service (QoS). In this article, we solve a multi-SFC embedding problem by a game-theoretical approach considering the heterogeneity of NFV nodes, the effect of processing-resource sharing among various VNFs, and the capacity constraints of NFV nodes. Specifically, each SFC is treated as a player whose objective is to minimize the overall latency experienced by the supported service flow, while satisfying the capacity constraints of all NFV nodes. Due to processing-resource sharing, additional delay is incurred and incorporated into the overall latency for each SFC. The capacity constraints of NFV nodes are considered by adding a penalty term into the cost function of each player, and are guaranteed by a prioritized admission control mechanism. We prove that the formulated resource-constrained multi-SFC embedding game (RC-MSEG) is an exact potential game admitting at least one pure Nash equilibrium (NE) and has the finite improvement property (FIP). Two iterative algorithms are developed, namely, the best response (BR) algorithm with fast convergence and the spatial adaptive play (SAP) algorithm with great potential to obtain the best NE. Simulations are conducted to demonstrate the effectiveness of the proposed game-theoretical approach.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".