The Impact of Smartphone Apps on Bike Sharing Systems

Abstract

Bike-sharing systems are exploding in cities around the world as more people are adopting sustainable transportation solutions for their everyday commutes. However, as more people use the system, riders often encounter that bikes or docks might not be available when they arrive to a station. As a result, many systems like CitiBike and Divvy provide riders with information about the network via smartphone apps so that riders can find stations with available bikes. However, not all customers have adopted the use of these smartphone apps for their station selection. By combining customer choice modeling and finite capacity queueing models, we explore the impact of the smartphone app technology to increase throughput and reduce blocking in bike sharing systems. To this end, we prove a mean-field limit and a central limit theorem for an empirical process of the number of stations with $k$ bikes. We also prove limit theorems for a new process called the ratio process, which characterizes the proportion of stations whose bike availability ratio lies within a particular partition of the interval [0,1]. For the mean field limit, we prove that the equilibrium exists, is unique, and that the stationary distribution of the empirical measure converges to a Dirac mass at the same equilibrium, thus showing an interchange of limits result ($\lim_{t\rightarrow \infty}\lim_{N\rightarrow \infty}=\lim_{N\rightarrow \infty}\lim_{t\rightarrow \infty}$). Our limit theorems provide insight on the mean, variance, and sample path dynamics of large scale bike-sharing systems. Our results illustrate that if we increase the proportion of customers that use smartphone app information, the entropy of the bike sharing network is reduced, and riders experience less blocking in the network.