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A STOCHASTIC ANALYSIS OF BIKE-SHARING SYSTEMS

Published online by Cambridge University Press:  27 July 2020

Shuang Tao  and
Jamol Pender Open the ORCID record for Jamol Pender [Opens in a new window]
Shuang Tao
Affiliation:
School of Operations Research and Information Engineering, Cornell University, 293 Rhodes Hall, Ithaca, NY14853, USA E-mail: st754@cornell.edu; jjp274@cornell.edu
Jamol Pender
Affiliation:
School of Operations Research and Information Engineering, Cornell University, 293 Rhodes Hall, Ithaca, NY14853, USA E-mail: st754@cornell.edu; jjp274@cornell.edu
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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 (BSS), 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 BSSs with stations having a finite capacity. By an appropriate scaling of our stochastic model, we prove a mean-field limit and a central limit theorem for an empirical process of the number of stations with k bikes. The mean-field limit and the central limit theorem provide insight on the mean, variance, and sample path dynamics of large-scale BSSs. 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 BSSs.

Keywords

applied probabilityoperations researchprobabilistic networksqueueing theorystochastic modeling
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 4 , October 2021 , pp. 781 - 838
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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