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| Notation | Description |
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| Elements and sets for infrastructures and trains |
| Station element and station set |
| Segment element and segment set |
| Platform track element and platform track set of station |
| Train element and candidate train set |
| Station set that train traverse by |
| , | Origin and destination station of train |
| The segment set that train traverse by |
| Event type, , “A” denotes arrival, and “D” denotes departure |
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| Elements and sets for time-space network |
| Time index (discrete time stamp) |
| Generic node of the time-space-state network |
| , | Origin and sink virtual node of train |
| Time-space node of train at station at the moment with event |
| Node of the time-space-state network belongs to train |
| , | Generic arc of the time-space-state network |
| , | Origin and sink virtual arc |
| Running arc |
| Dwelling arc |
| , | Arc set entering/leaving node |
| The arc set belongs to train |
| The dwelling arc set belongs to train |
| Train group categorized by multiobjective function |
| Train group set |
| Train set that belongs to group |
| Time-space resource |
| Arc set that occupies time-space resource |
| value of train group |
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| Parameters (numbers) |
| [, ] | The time range of train operation |
| Running time of train through segment |
| Free flow running time through segment |
| , | Acceleration and deceleration time loss for train stopping at station |
| Binary indicator denoting whether train stops at station . 1 for stop, 0 otherwise |
| The time range of train dwells at station |
| The departure time window for train |
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| Decision variables |
| Binary variable, if train is scheduled, 0 otherwise |
| Binary variable, if the time-space arc is selected, 0 otherwise |
| Total number of scheduled trains in train group |
| The Lagrangian multiplier for time-space resource |
| The Lagrangian multiplier for train group |
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| Elements and sets for timetable performance indexes calculation |
| Successfully scheduled train set |
| Passenger set |
| Assigned passenger set |
| Train set that in which the passenger assigned |
| Passenger set that travels with train at segment |
| The th train during passenger ’ journey |
| Available train connection set for passenger |
| Successive train pair set running at segment |
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| Parameters (numbers) for timetable performance indexes calculation |
| , | Arrival and departure time of train at station |
| Binary indicator, 1 denotes that there exists a train service from to |
| The length of segment |
| The earliest departure time of passenger |
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