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This paper proposes an equilibrium bus boarding model to investigate optimal pricing and service for peak-period bus commuting inefficiency of boarding queuing congestion. Commuters are assumed to choose their optimal time-of-use decision from home or the workplace to the bus. We found that: (1) when the earliest commuter boards the bus as soon as the bus arrives at the bus station, the dynamic boarding queuing congestion toll that eliminates the boarding queuing congestion creates social optimal equilibrium and the optimal bus departure interval during the peak period; (2) the optimal bus departure interval during the peak period is the time that the preceding bus riders spend on boarding, which means the relationship between service frequency and ridership does not conform to the square root principle: the optimal bus frequency is proportional to the square root of the number of commuters.

Optimal Pricing and Service for the Peak-Period Bus Commuting Inefficiency of Boarding Queuing Congestion