Achieving Optimal Traffic Engineering Using a Generalized Routing Framework
Bibliographic record
Abstract
The open shortest path first (OSPF) protocol has been widely applied to intra-domain routing in today's Internet. Since a router running OSPF distributes traffic uniformly over equal-cost multi-path (ECMP), the OSPF-based optimal traffic engineering (TE) problem (i.e., deriving optimal link weights for a given traffic demand) is computationally intractable for large-scale networks. Therefore, many studies resort to multi-protocol label switching (MPLS) based approaches to solve the optimal TE problem. In this paper we present a generalized routing framework to realize the optimal TE, which can be potentially implemented via OSPFor MPLS-based approaches. We start with viewing the conventional optimal TE problem in a fresh way, i.e., optimally allocating the residual capacity to every link. Then we make a generalization of network utility maximization (NUM) to close this problem, where the network operator is associated with a utility function of the residual capacity to be maximized. We demonstrate that under this framework, the optimal routes resulting from the optimal TE are also the shortest paths in terms of a set of non-negative link weights that are explicitly determined by the optimal residual capacity and the objective function. The network entropy maximization theory is employed to enable routers to exponentially, instead of uniformly, split traffic over ECMP. The shortest-path penalizing exponential flow-splitting (SPEF) is designed as a link-state protocol with hop-by-hop forwarding to implement our theoretical findings. An alternative MPLS-based implementation is also discussed here. Numerical simulation results have demonstrated the effectiveness of the proposed framework as well as SPEF.
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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 | 0.002 |
| 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 | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".