Cordon toll pricing in a multi-modal linear monocentric city with stochastic auto travel time

This paper proposes an analytical model to determine the optimal cordon toll pricing scheme in a linear monocentric city with a competitive railway/highway system. It is assumed that the daily commuting time by rail mode is deterministic, while that by auto is stochastic and location dependent across the city. The travel time uncertainty could affect residents' residential location choices and thus the urban spatial structure due to a long-term adjustment. In order to hedge against travel time variability on highway, commuters by auto often consider a travel time budget longer than the expected trip time to avoid late arrivals. It shows that ignorance of auto travel time variation may cause a significant bias in the prediction of the urban spatial structure in terms of residential distribution and city size. The implementation of cordon toll pricing scheme can rationalize the urban residential distribution and increase the social welfare of the urban system.