Time-dependent transit fare optimization with elastic and spatially distributed demand

Motivated by the lack of microeconomic models that optimize time-dependent transit fares based on realistic demand formulations, this paper presents a microeconomic model for the design of a time-dependent transit pricing scheme considering elastic and spatiotemporally distributed demand. To model the spatial distribution of demand, a transit line with multiple origin-destination pairs is considered. To model the cyclical demand fluctuations, transit operations in one day are divided into multiple time periods. In the proposed model we optimize fares, headway, vehicle capacity, and maximum fleet size, with the objective of maximizing social welfare, subject to fleet size and vehicle capacity constraints. We find time-dependent pricing could avoid crosssubsidization among travelers in different time periods. Under both pricing schemes, the timedependent headways satisfy the same optimality condition: the total rider waiting cost equals the total fixed cost on the supplier side. We also demonstrate that both resource constraints (vehicle capacity and fleet size) can be binding in multiple time periods, unlike the usual assumption in the literature that resource constraints are binding only in the period with the highest demand. Two extensions (considering a financial constraint and a variable roundtrip time) are also investigated. The developed models can be used to facilitate the design of timedependent pricing schemes for practical applications.

Automated summary

This paper presents a microeconomic model for designing time-dependent transit pricing schemes considering elastic and spatiotemporally distributed demand. The model optimizes fares, headway, vehicle capacity, and fleet size to maximize social welfare.