A Stochastic Analysis of Bike Sharing Systems

63 Pages Posted: 29 Aug 2017 Last revised: 22 Apr 2020

See all articles by Shuang Tao

Shuang Tao

Cornell University - Operations Research & Industrial Engineering

Jamol Pender

Cornell University - School of Operations Research and Industrial Engineering

Date Written: August 27, 2017

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.

Suggested Citation

Tao, Shuang and Pender, Jamol, A Stochastic Analysis of Bike Sharing Systems (August 27, 2017). Available at SSRN: https://ssrn.com/abstract=3026324 or http://dx.doi.org/10.2139/ssrn.3026324

Shuang Tao (Contact Author)

Cornell University - Operations Research & Industrial Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States

Jamol Pender

Cornell University - School of Operations Research and Industrial Engineering ( email )

Ithaca, NY
United States

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