A New Dependence Model for Heterogeneous Markov Modulated Poisson Processes
Bibliographic record
Abstract
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. The most general form of aggregated MMPP is the superposition of heterogeneous MMPPs (HeMMPP), in which each constituent MMPP has different parameters. Due to the generality of HeMMPP, studying its temporal dependence will benefit network traffic monitoring and traffic prediction. Modeling the temporal dependence of HeMMPP, however, is extremely hard because the total number of states in a HeMMPP increases exponentially with the number of states in constituent MMPPs. This paper tackles the above challenge with copula analysis. It not only presents a novel framework to capture the functional dependence structure of HeMMPP, but also provides a recursive algorithm to effectively calculate HeMMPP copula values. The theoretical analysis and the algorithms together offer a complete solution for modeling the temporal dependence of HeMMPP. Another contribution of the paper is the application of HeMMPP copula for traffic prediction.
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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 | 0.006 |
| 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 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".