Modeling and optimizing a fare incentive strategy to manage queuing and crowding in mass transit systems

Document Type

Journal Article

Publication Date


Subject Area

mode - mass transit, mode - rail, place - europe, ridership - commuting, ridership - behaviour, operations - crowding, policy - fares, planning - methods


Incentive, Departure time choice, Queuing and crowding, Mass transit system, Bilevel model


This paper solves the problem of optimizing a surcharge-reward scheme and analyzes equilibrium properties incorporating commuters’ departure time choice to relieve crowding and queuing congestion in mass transit systems. The surcharge-reward scheme incentivizes commuters to switch departure times from a pre-specified central period to shoulder periods. We formulate a bilevel model to design and optimize the surcharge-reward scheme. The upper-level problem minimizes the total equilibrium costs by determining the refundable surcharges, the rewards, and the corresponding central charging period. The lower-level problem determines the equilibrium of commuters’ departure times with respect to generalized travel costs. Equilibrium properties are analyzed and a sequential iterative solution algorithm is developed. We found that the existence of an optimal solution depends on the scheme design and there exists a lower bound on the surcharge to achieve the system optimum. Numerical studies are conducted on a commuting rail line in Copenhagen. The proposed algorithm converges efficiently, and the fare incentive scheme can simultaneously reduce the individual trip costs, total crowding costs, and total queuing time costs. The performance of the scheme increases with the rewards and surcharges up to a point and beyond which it stays unchanged.


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


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