Estimating Primary Demand in Bike-sharing Systems

Abstract

In operating modern bike-sharing systems, understanding rider demand and behaviors is of significant importance. A key challenge in estimating demand is to account for the choice substitution effect, where a rider may substitute a trip for stations nearby when the first-choice location for picking up or returning a bike is not available. In this paper, we study and analyze a locational demand model to account for substitution behaviors that are determined by proximity. The model assumes that riders originate from a region in space, and each has a heterogeneous consideration radius to find stations with available bikes in the order of closeness to their locations. We study a natural parameterization of this model with distance rankings, each corresponding to a distance ordering of stations within the consideration radius of a rider from a particular origin. We characterize the conditions under which the model is identifiable and its parameters can be consistently estimated. By exploiting the locational structure and sparsity in stock-out patterns, which are inherent to bike-sharing systems, we find sparse representations of the model parameters and develop efficient first-order methods for estimating the parameters. Our approach is tractable on a city scale and has good empirical performance, which we demonstrate on a bike-sharing system in the Boston metropolitan area.