Multimodal pricing and optimal design of urban public transport: The interplay between traffic congestion and bus crowding

• A social welfare maximisation model with crowding externalities is developed.
• The interplay between congestion and crowding in the design of bus systems is exposed.
• Optimal frequency is the result of crowding and congestion acting as colliding forces.
• If crowding matters to users, buses should have as many seats as possible.
• Crowding externalities increase optimal bus fare and reduce optimal subsidy.

The interplay between congestion and crowding externalities in the design of urban bus systems is identified and analysed. A multimodal social welfare maximisation model with spatially disaggregated demand is developed, in which users choose between travelling by bus, car or walking in a transport corridor. Optimisation variables are bus fare, congestion toll, bus frequency, bus size, fare collection system, bus boarding policy and the number of seats inside buses. We find that optimal bus frequency results from a trade-off between the level of congestion inside buses, i.e., passengers’ crowding, and the level of congestion outside buses, i.e., the effect of frequency on slowing down both buses and cars in mixed-traffic roads. A numerical application shows that optimal frequency is quite sensitive to the assumptions on crowding costs, impact of buses on traffic congestion, and overall congestion level. If crowding matters to users, buses should have as many seats as possible, up to a minimum area that must be left free of seats. If for any other reason planners decide to have buses with fewer seats than optimal (e.g., to increase bus capacity), frequency should be increased to compensate for the discomfort imposed on public transport users. Finally, the consideration of crowding externalities (on both seating and standing) imposes a sizeable increase in the optimal bus fare, and consequently, a reduction of the optimal bus subsidy.