Analysis of a Queueing Model for Energy Storage Systems with Self-discharge
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Bibliographic record
Abstract
This article presents an analysis of a recently proposed queueing system model for energy storage with discharge. Even without a load, energy storage systems experience a reduction of the stored energy through self-discharge . In some storage technologies, the rate of self-discharge can exceed 50% of the stored energy per day. We consider a queueing model, referred to as leakage queue , where, in addition to an arrival and a service process, there is a leakage process that reduces the buffer content by a factor ɣ ( 0 < ɣ < 1) in each time slot. When the average drift is positive, we discover that the leakage queue operates in one of two regimes, each with distinct characteristics. In one of the regimes, the stored energy always stabilizes at a point that lies below the storage capacity, and the stored energy closely follows a Gaussian distribution. In the other regime, the storage system behaves similar to a conventional finite capacity system. For both regimes, we derive expressions for the probabilities of underflow and overflow. In particular, we develop a new martingale argument to estimate the probability of underflow in the second regime. The methods are validated in a numerical example where the energy supply resembles a wind energy source.
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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