A Three-State Node Reliability Model for Sensor Networks
Bibliographic record
Abstract
In this paper we formulate and analyze a model for assessing the reliability of a wireless sensor network (WSN) based on classifying the operating states of each node at any instant into one of three possible states: a state where both the sensing and wireless modules are operating, a state where only the wireless module is operating, and a state where the wireless module is failed. Thus, in the second state a node can only relay traffic among its neighbours without generating its own data. We define the reliability of a WSN as the probability that the sink node can collect data from a number of nodes whose total weight exceeds a specified threshold limit, given that each node can be in any one of the three possible states with a given probability. Existing results in the literature show that a restricted 2-state version of the problem is #P-hard even when the network is a rectangular grid. Nevertheless, for a rectangular W × L grid on n nodes where the sink node lies in one of the corners, the restricted 2-state reliability problem can be solved in O(nL2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</sup> ) time. Thus, the algorithm runs in polynomial time for any fixed W. Our work here derives an exact algorithm for the generalized 3-state reliability model on a generalized class of grids, called diagonalized grids, while maintaining the same O(nL2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</sup> ) running time. We obtain numerical results that illustrate the use of the devised algorithm as a WSN topological design tool.
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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 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".