Analysis of a Queueing Model for Energy Storage Systems with Self-discharge
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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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".