Stochastic Model of Train Running Time and Arrival Delay: A Case Study of Wuhan–Guangzhou High-Speed Rail
Bibliographic record
Abstract
Train operations are subject to stochastic variations, reducing service punctuality and thus the quality of service (QoS). Models of such variations are needed to evaluate and predict the potential impact of disturbances and to avoid service punctuality reduction in train service management and timetabling. In this paper, through a case study of the Wuhan–Guangzhou (WH–GZ) high-speed rail (HSR), we show how a wealth of train operation records can be used to model the stochastic nature of train operations at each level, section and station. Specifically, we examine different distribution models for running times of individual sections and show that the Log-logistic probability density function is the best distributional form to approximate the empirical distribution of running times on the specified line. Next, we show that the distribution of running times in each section can be used to accurately infer arrival delays. Consequently, we construct the underlying analytical model and derive the respective arrival delay distribution at the downstream stations. The results support the correctness of the model presented and show that the proposed model is suitable for constructing the distribution of arrival delays at every station of the specified line. We show that the integrated distribution models of running times and arrival delays, driven by empirical data, can also be used to evaluate the QoS at individual track sections.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".