Revisiting Scheduling in Heterogeneous Networks When the Backhaul Is Limited
Bibliographic record
Abstract
We study the impact of the limited capacity of backhaul links on downlink user scheduling in a heterogeneous network comprising macro base stations and small cells. Assuming a tree topology of the backhaul network, we formulate a backhaulaware global α-fair time-domain user scheduling problem and study it under three different scenarios of backhaul limitations. For the scenario where the backhaul links are not the bottleneck, we derive closed-form scheduling solutions to the scheduling problem under certain assumptions. For the scenario where the backhaul links between the macro base station and the small cells are the bottleneck, we show that the global α-fair user scheduling problem can be decomposed into a set of independent local α-fair user scheduling problems. However, unlike the previous case, a local scheduler in this case is not of a unique type but can be of one of three types, depending on the available backhaul capacity. We completely characterize these three types and also propose a simple heuristic for optimal α-fair scheduling. When the link between the macro base station and the core network is a potential bottleneck, we show how each base station can still perform a local scheduling as in the previous case as long as there is a master problem that allocates feasible virtual backhaul capacities to each BS. However, computing the optimal virtual capacities is complex and expensive in terms of the amount and frequency of information exchanges. For this scenario, we propose realization-agnostic heuristic schemes that are simple to implement and perform quite well.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| 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".