A Short Turning Strategy for Train Scheduling Optimization in an Urban Rail Transit Line: The Case of Beijing Subway Line 4
Bibliographic record
Abstract
In urban rail transit systems, train scheduling plays an important role in improving the transport capacity to alleviate the urban traffic pressure of huge passenger demand and reducing the operation costs for operators. This paper considers the train scheduling with short turning strategy for an urban rail transit line with multiple depots. In addition, the utilization of trains is also taken into consideration. First, we develop a mixed integer nonlinear programming (MINLP) model for the train scheduling, where short turning train services and full-length train services are optimized based on the predefined headway obtained by the passenger demand analysis. The MINLP model is then transformed into a mixed integer linear programming (MILP) model according to several transformation properties. The resulting MILP problem can be solved efficiently by existing solvers, e.g., CPLEX. Two case studies with different scales are constructed to assess the performance of train schedules with the short turning strategy based on the data of Beijing Subway line 4. The simulation results show that the reduction of the utilization of trains is about 20.69%.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| 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".