Dynamic Transit Passenger Origin/Destination Estimation: A Bilevel Variational Inequality Approach
Bibliographic record
Abstract
Transit origin destination (OD) trip matrices are essential inputs for most problems regarding the planning, operation, and management of public transit systems. Traditionally, OD matrices were obtained statically from passenger surveys. However, due to the need for continuous updates, surveying a representative sample, and the high cost of conducting these surveys, advanced methods estimate transit OD using sensor collected data such as automatic passenger counts (APC). The objective of this research is to formulate a dynamic transit origin estimation (DTOD) estimation model that is transferrable and applicable to scenarios where the available transit data is APC. The proposed methodology is a bi-level optimization model. In this model, each optimization is defined as a distinct level, and each level has its own objectives and constraints. The lower level (follower) seeks to optimize its outcomes, which are then used by the upper level (leader) to optimize its own outcomes. In the bi-level model proposed, the lower level is a dynamic transit assignment model that simultaneously determines the dynamic average travel costs and optimal route choices of passengers in congested transit networks (i.e., estimated passenger flows). The upper level sums passenger route choices from the lower level to obtain transit OD, and minimizes the sum of error measurements between the obtained time-dependent OD matrices and dynamic real passenger counts (APC counts). As a result of considering asymmetric link cost interactions (i.e., the cost of traversing a link in the network is both a function of the flow on the link itself and on surrounding links), the transit assignment is formulated as a variational inequality. The upper level, in contrast, is formulated as a generalized least square estimation. To evaluate the performance of the proposed DTOD estimation model, numerical examples are conducted using MATLAB, in which the model’s solution algorithm is coded. The model is tested on a small theoretical network and a real transit network in Calgary, Alberta, Canada. Sensitivity analyses of the bi-level model to different weighting schemes, link cost function parameters, and congestion levels are performed in which the model converges to unique solutions in minimal times and within acceptable ranges of error.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".