Headway Optimisation for Metro Lines Based on Timetable Simulation and Simulated Annealing
Bibliographic record
Abstract
To improve the capacity of metro systems, it is important to evaluate and minimise headway, which is defined as the time interval calculated from “head to head” between two successive trains in this paper. With existing approaches for headway optimisation, the headway for moving block systems is often calculated based on the safe braking distance. However, the blocking time at movable elements (e.g., switches and crossings) and stops has special characteristics. Since train separation is dominated by a signalling system, the distance between two successive trains at movable elements and stops exceeds the safe braking distance. In this work, the theory for building a blocking time model and calculating line headway for moving block systems is investigated. A workflow to minimise line headway is designed to derive an optimised velocity profile before the identified bottlenecks. Several different optimisation algorithms, including grid search, Monte Carlo, and simulated annealing, are developed and compared. Among them, simulated annealing shows the best optimisation capability with the least computational effort. The designed algorithm has been tested for Hefei-Metro Line 1, and the line headway can be reduced from 116.776 seconds to 105.806 seconds. If the acceptable rate of the increased transport is set at 1%, the line capacity will increase by 6.5%.
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".