Existence of a Unique Invariant Measure and Ergodic Property in AIMD-based Multi-resource Allocation
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Bibliographic record
Abstract
Distributed resource allocation arises in many application domains, such as smart energy systems, intelligent transportation systems, cloud computing, edge computing, etcetera. To realize many of these applications, agents in a network may require multiple shared resources to complete a task and aim to maximize the network utility. Additionally, they may demand resources based on their preferences. Furthermore, they may not wish to share their cost functions, partial derivatives of the cost functions, etc., with other agents or a central server; however, they share their resource demands with the central server that aggregates the demands and sends one-bit resource-capacity constraint notification in the network. The single-resource allocation algorithms are inefficient and provide sub-optimal solutions for multi-resource allocations, especially when the cost functions are multi-variate and non-separable. We present additive increase and multiplicative decrease algorithm (AIMD)-based distributed solutions for multi-resource allocation. We formulate the resource allocations problem over finite window sizes and model the system as a homogeneous Markov chain with place-dependent probabilities. We show that the time-averaged allocations over the finite window size converge to a unique invariant measure. We also show that the ergodic property holds for the model.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| 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 it