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| Notation | Definition |
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| Set of train services |
| Set of stations |
| Set of operation periods |
| Index of train services |
| Index of stations |
| Train load factor between stations i and i + 1 for train service k |
| Dwell time at station i for train service |
| Dwell-time coefficient |
| Number of passengers that alight train service k at station i |
| Number of passengers that board train service k at station i |
| Minimal dwell time at station i |
| Departure time of train service k at station i |
| Arrival time of train service k at station i |
| Minimal running time from station i to station i + 1 |
| Maximal running time from station i to station i + 1 |
| Minimal train departure interval at station i |
| Maximal train departure interval at station i |
| Train running time of full-length routing |
| Minimal train running time of full-length routing |
| Maximal train running time of full-length routing |
| Train running time of short-turn routing |
| Minimal train running time of short-turn routing |
| Maximal train running time of short-turn routing |
| Average train running time of full-length routing |
| Average train running time of short-turn routing |
| Number of trains for full-length routing |
| Number of trains for short-turn routing |
| Number of trains available |
| Train operation proportion of full-length and short-turn routings |
| Average train departure interval of full-length routing |
| Average train departure interval of short-turn routing |
| Number of passengers onboard train service k at station i after the boarding process has completed |
| Number of passengers onboard train service k at station i before the start of the boarding process |
| Number of passengers onboard train service k at station i with destination station j |
| Number of passengers arriving at station i with destination station j during time period |
| Arrival time at station i of last passenger to board train service k |
| Number of passengers onboard train service k at time t |
| Maximum allowable train loading factor |
| Capacity of trains in terms of maximum number of onboard passengers |
| Number of passengers arriving at station i during time period |
| Passenger arrival rate at station i with destination station j at time t |
| Number of passengers waiting at station i after the boarding process has completed for train service k at station i |
| Number of passengers waiting at station i with destination station j after the boarding process has completed for train service k at station i |
| Train turn-back time at reversal station |
| Maximum loading rate of all the trains passing through each station |
| Running time from station i to station i + 1 for train service |
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