A Stochastic Analysis of Bike Sharing Systems

TL;DR

This paper models and analyzes the stochastic behavior of large-scale bike sharing systems with finite station capacities, providing theoretical insights and practical performance estimates to improve system design and operation.

Contribution

It introduces a stochastic model with a central limit theorem for bike sharing systems, offering new analytical tools for understanding system dynamics and performance.

Findings

Proves a central limit theorem for the empirical process of station bike counts.

Provides confidence intervals for system performance metrics.

Offers insights into variance and sample path dynamics of large systems.

Abstract

As more people move back into densely populated cities, bike sharing is emerging as an important mode of urban mobility. In a typical bike sharing system, riders arrive at a station and take a bike if it is available. After retrieving a bike, they ride it for a while, then return it to a station near their final destinations. Since space is limited in cities, each station has a finite capacity of docks, which cannot hold more bikes than its capacity. In this paper, we study bike sharing systems with stations having a finite capacity. By an appropriate scaling of our stochastic model, we prove a central limit theorem for an empirical process of the number of stations with $k$ bikes. The central limit theorem provides insight on the variance, and sample path dynamics of large scale bike sharing systems. We also leverage our results to estimate confidence intervals for various performance measures such as the proportion of empty stations, the proportion of full stations, and the number of bikes in circulation. These performance measures have the potential to inform the operations and design of future bike sharing systems.