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| Parameters | Description |
|
| , | Index of urban metro stations |
| Index of trains |
| Index of urban metro lines |
| Index of time windows |
| Set of alternative stations |
| Set of ordinary stations |
| Crowding station |
| The number of passengers boarding train at station and alighting the train at station |
| The arriving rate of passengers at station , whose destination is station |
| Train travel time between station and station |
| Walking time from station to station |
| Dwell time of a train at a station |
| Headway between consecutive trains of a line |
| The area of the crowd gathering place |
| Area of the roads connecting the alternative station and the crowding station , |
| Safety threshold of crowd density and pedestrian density |
| Variables | Description |
| The binary variable that determines whether train stops at station (i.e., if , train stops at station , otherwise if train skips station ) |
| The number of passengers skipped by train but waiting for the next train that stops at both station and station |
| The number of passengers skipped by previous trains who intend to board train at station and alight at station |
| The number of passengers boarding train at station |
| The number of passengers alighting train at station |
| The number of passengers skipped by train , who intend to walk from station to station |
| The number of passengers walking on the roads connecting alternative station and the crowding station during time window , |
| Arrival time of train at station |
| Departure time of train at station |
| Number of passengers at the crowd gathering place during time window |
| Increase of the number of passengers at the crowd gathering place during time window |
| Crowd density at the crowd gathering place during time window |
| Pedestrian density on the roads connecting alternative station and the crowding station during time window , |
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