Morning commuting pattern and crowding pricing in a many-to-one public transit system with heterogeneous users

Document Type

Journal Article

Publication Date


Subject Area

ridership - commuting, policy - fares, operations - crowding, mode - rail


Many-to-one, Crowding cost, Heterogeneous user, Commuting pattern, Crowding fare


This paper examines the morning commuting flow patterns in a many-to-one public transit line. Multi-class commuters with different degrees of sensitivity towards crowding are considered. At user equilibrium, trains arriving at the destination at approximately the work start time are found to be either more or less congested at the intermediate stations, depending on the spatial distribution of commuter class at each station. In addition, the system optimal crowding fare is found to be train-dependent and may fluctuate over time at each station. Finally, the theoretical properties of morning commuting flow patterns and crowding fare are illustrated through numerical examples.


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


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