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Abstract
In this paper, we propose step fare schemes for a rail transit line connecting a residential district with a central business district (CBD). The proposed fare schemes aim to reduce the total system cost (TSC) while ensuring revenue-neutrality for the rail operator. The user equilibrium (UE) principle in terms of generalized trip cost is adopted to formulate commuters’ departure time choice problems with late arrival under the proposed fare schemes. The equilibrium flow patterns and trip costs are analytically derived. It is found that passengers’ departure times present more even distribution under the schemes with more fare steps, resulting in a lower TSC. Besides, the optimal train schedule and the optimal number and capacity of trains are analyzed. Finally, numerical examples are provided to illustrate the performance of the proposed transit fare schemes.
Acknowledgements
The authors are grateful to the four reviewers for their constructive comments.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
4 In fact, a train (service run) is composed of multiple train units (subway cars). Passengers are unevenly distributed across all train units. However, in this paper, we focus on the average crowding degrees of different runs. The average crowding degree may involve all possible states: with a good seat or a bad seat, having to stand in a spacious carriage or a seriously crowded vehicle, etc.. Similar treatments can be found in Tian, Huang, and Yang (Citation2007) and De Palma, Lindsey, and Monchambert (Citation2017).
5 Note that the incomes from subway fares are eliminated from the TSTC, because it is usually supposed that the government incomes from charges will return to commuters via another form for the net social benefit maximization. Readers interested can refer to the work of Huang (Citation2002).