Time-dependent transit fare optimization with elastic and spatially distributed demand: Fid-Bau Portal

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

Guo, Qianwen / Sun, Yanshuo / Schonfeld, Paul / Li, Zhongfei

Highlights • We optimize time-dependent transit pricing considering elastic and spatiotemporally distributed demand. • Time-dependent pricing could avoid cross-subsidization among travelers in different time periods. • A zero fare is warranted in a time period where no constraints (e.g., capacity and financial) are binding. • Resource constraints can be binding in multiple periods rather than in a single so-called “peak” period. • The total rider waiting cost equals the total fixed cost on the supplier side regardless of pricing schemes.

Abstract 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 cross-subsidization among travelers in different time periods. Under both pricing schemes, the time-dependent 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 time-dependent pricing schemes for practical applications.