The two-mode problem with bottleneck queuing and transit crowding: How should congestion be priced using tolls and fares?

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, mode - car, ridership - commuting, ridership - mode choice, policy - congestion, policy - fares, operations - crowding, operations - scheduling


Two-mode problem, Bottleneck model, Time-varying scheduling preferences, In-bus passenger crowding externality, Time-varying and step congestion charging


This paper proposes a bi-modal bottleneck model with time-varying scheduling preferences for investigating the two-mode problem with bottleneck queuing and transit crowding. In the proposed model, the activity scheduling utilities of commuters at home and at work vary by the time of day, and two kinds of congestion externalities (i.e., traffic congestion among vehicles at the bottleneck and in-bus passenger crowding discomfort) are considered. Commuters choose their travel modes and departure times from home to work during the morning commute to minimize their own generalized travel cost. The properties of the proposed bi-modal bottleneck model are analytically explored. Particularly, the relationship between the departure intervals of auto and bus commuters is revealed. The time-varying charging schemes and step charging schemes for reducing the congestion externalities are also investigated. A critical condition for passenger shift from one mode to the other mode with congestion charging schemes is identified, and the effects of congestion charging schemes with and without internalizing the bus-related congestion externalities (including the bottleneck congestion externality induced by auto and bus interaction and the in-bus passenger crowding externality) on the bottleneck system are compared.


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


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