Statistical inference of boarding and alighting counts in transit systems with incomplete data
Bibliographic record
Abstract
Automatic passenger counting (APC) systems have been widely used in public transit systems to collect boarding and alighting counts, which are essential for understanding travel demand, optimizing transit operations, and improving transit service quality. However, missing boarding and alighting counts remain a pervasive problem due to APC deployment, hardware malfunctions, or operational disruptions. The reconstruction of these missing data is particularly challenging because boarding and alighting counts must satisfy real-world constraints, such as balance conditions and onboard passenger limits. To address this issue, we propose a probabilistic framework that integrates passenger travel behavior and operational constraints to estimate missing boarding and alighting counts. The framework builds a time-varying Poisson model to estimate boarding demand and employs a method to infer time-varying alighting probabilities. Further, the alighting counts are derived by assigning estimated boarding counts to downstream stops with time-varying alighting probabilities, ensuring that the reconstructed data meet operational constraints. We validate the proposed framework using real-world transit data. The results demonstrate the method’s accuracy and robustness in estimating missing APC data, while also providing valuable insights into time-varying passenger travel behaviors, including arrival rates and alighting probabilities. This framework offers a practical and interpretable solution for reconstructing incomplete boarding and alighting data, with significant implications for improving transit planning and operational decision-making.
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How this classification was reachedexpand
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 | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".