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 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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".