Managing rail transit peak-hour congestion with a fare-reward scheme

Document Type

Journal Article

Publication Date


Subject Area

mode - rail, operations - performance, policy - fares, policy - congestion, ridership - commuting


Rail transit bottleneck, Queuing congestion, Fare-reward scheme, Departure time choice, User equilibrium


This paper describes a new fare-reward scheme for managing a commuter's departure time choice in a rail transit bottleneck, which aims to incentivize a shift in departure time to the shoulder periods of the peak hours to relieve queuing congestion at transit stations. A framework of the rail transit bottleneck is provided and the user equilibrium with a uniform-fare and the social optimum with service run-dependent fares are determined. A fare-reward scheme (FRS) is then introduced that rewards a commuter with one free trip during shoulder periods after a certain number of paid trips during the peak hours. For a given number of peak-hour commuters and ex-ante uniform fare, the FRS determines the free fare intervals and the reward ratio (the ratio of the free trips to the total number of trips, which is equivalent to the ratio of the number of rewarded commuters to the total number of commuters on each day during the peak hours). The new fare under the FRS is determined so that the transit operator's revenue remains unchanged before and after introducing the FRS. Our study indicates that, depending on the original fare, FRS results in an optimal reward ratio up to 50% and yields a reduction of system total time costs and average equilibrium trip costs by at least 25% and 20%, respectively.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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