Copula Analysis of Temporal Dependence Structure in Markov Modulated Poisson Process and Its Applications
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Bibliographic record
Abstract
The Markov Modulated Poisson Process (MMPP) has been extensively studied in random process theory and widely applied in various applications involving Poisson arrivals whose rate varies following a Markov process. Despite the rich literature on MMPP, very little is known on its intricate temporal dependence structure. No exact solution is available so far to capture the functional temporal dependence of MMPP at the stationary state over slotted times. This article tackles the above challenges with copula analysis. It not only presents a novel analytical framework to capture the temporal dependence of MMPP but also provides the exact copula-based solutions for single MMPP as well as the aggregate of independent MMPP. This theoretical contribution discloses functional dependence structure of MMPP. It also lays the foundation for many applications that rely on the temporal dependence of MMPP for adaptive control or predictive resource provisioning. We demonstrate case studies, with real-world trace data as well as simulation, to illustrate the practical significance of our analytical results.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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)
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