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Fluid and Diffusion Limits for Bike Sharing Systems

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Queueing Theory and Network Applications (QTNA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10591))

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Abstract

Bike sharing systems have rapidly developed around the world, and they are served as a promising strategy to improve urban traffic congestion and to decrease polluting gas emissions. So far performance analysis of bike sharing systems always exists many difficulties and challenges under some more general factors. In this paper, a more general large-scale bike sharing system is discussed by means of heavy traffic approximation of multiclass closed queueing networks with non-exponential factors. Based on this, the fluid scaled equations and the diffusion scaled equations are established by means of the numbers of bikes both at the stations and on the roads, respectively. Furthermore, the scaling processes for the numbers of bikes both at the stations and on the roads are proved to converge in distribution to a semimartingale reflecting Brownian motion (SRBM) in a \(N^{2}\)-dimensional box, and also the fluid and diffusion limit theorems are obtained. Furthermore, performance analysis of the bike sharing system is provided. Thus the results and methodology of this paper provide new highlight in the study of more general large-scale bike sharing systems.

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under grant Nos. 71671158 and 71471160, and Natural Science Foundation of Hebei under grant No. G2017203277.

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Authors and Affiliations

  1. School of Economics and Management Sciences, Yanshan University, Qinhuangdao, 066004, China

    Quan-Lin Li, Zhi-Yong Qian & Rui-Na Fan

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  1. Quan-Lin Li
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  2. Zhi-Yong Qian
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  3. Rui-Na Fan
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Correspondence to Quan-Lin Li .

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Editors and Affiliations

  1. Konan University, Kobe, Japan

    Wuyi Yue

  2. Yanshan University, Qinhuangdao, China

    Quan-Lin Li

  3. Yanshan University, Qinhuangdao, China

    Shunfu Jin

  4. Yanshan University, Qinhuangdao, China

    Zhanyou Ma

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Li, QL., Qian, ZY., Fan, RN. (2017). Fluid and Diffusion Limits for Bike Sharing Systems. In: Yue, W., Li, QL., Jin, S., Ma, Z. (eds) Queueing Theory and Network Applications. QTNA 2017. Lecture Notes in Computer Science(), vol 10591. Springer, Cham. https://doi.org/10.1007/978-3-319-68520-5_14

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  • DOI: https://doi.org/10.1007/978-3-319-68520-5_14

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-68520-5

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