A STOCHASTIC ANALYSIS OF BIKE-SHARING SYSTEMS. Issue 4 (October 2021)

• Record Type: Journal Article
• Authors: Tao, Shuang; Pender, Jamol
• Is Part Of: Probability in the engineering and informational sciences. Volume 35:Issue 4(2021)
• Page Start: 781
• Page End: 838
• Publication Date: 2021-10
• Subjects: applied probability -- operations research -- probabilistic networks -- queueing theory -- stochastic modeling; Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S0269964820000297
• Languages: English
• ISSNs: 0269-9648

Abstract

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.