An Extended Space‐Time Network With Explicit Incompatibility Modelling for High‐Speed Railway Timetabling
Bibliographic record
Abstract
High‐speed railway systems face increasing operational challenges due to rising passenger demand and complex infrastructure constraints. However, traditional space‐time network models for train timetabling may lack detailed representation of real‐world incompatibility constraints, limiting their practical applicability. This study proposes an extended space‐time network that explicitly incorporates train headway constraints through enhanced incompatibility modelling. The model classifies section arcs into eight operation‐specific types based on train movements at adjacent stations, enabling precise representation of distinct headway constraints. To address the limitations in existing arc incompatibility descriptions, two novel concepts are introduced: N‐incompatible arc sets and pairwise N‐incompatible arc sets. A 0‐1 integer programming formulation is developed to maximize train timetabling profits while strictly enforcing all headway and station capacity constraints. For large‐scale problems, a Lagrangian relaxation algorithm with model reformulation techniques is proposed to efficiently solve real‐world instances. Computational experiments on the Beijing–Shanghai high‐speed railway line demonstrate the model’s ability to generate conflict‐free timetables within acceptable computation time. This work enhances the conceptual framework of incompatibility modelling and bridges the gap between theoretical models and practical timetable generation by explicitly capturing heterogeneous train operations and intricate incompatibility relationships.
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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 | 0.002 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".