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A mean-field matrix-analytic method for bike sharing systems under Markovian environment

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Listed:
  • Quan-Lin Li

    (Beijing University of Technology)

  • Rui-Na Fan

    (Fudan University)

Abstract

This paper proposes a novel mean-field matrix-analytic method in the study of bike sharing systems, in which a Markovian environment is constructed to express time-inhomogeneity and asymmetry of processes that customers rent and return bikes. To achieve effective computability of this mean-field method, this study provides a unified framework through the following three basic steps. The first one is to deal with a major challenge encountered in setting up mean-field block-structured equations in general bike sharing systems. Accordingly, we provide an effective technique to establish a necessary reference system, which is a time-inhomogeneous queue with block structures. The second one is to prove asymptotic independence (or propagation of chaos) in terms of martingale limits. Note that asymptotic independence ensures and supports that we can construct a nonlinear quasi-birth-and-death (QBD) process, such that the stationary probability of problematic stations can be computed under a unified nonlinear QBD framework. Lastly, in the third step, we use some numerical examples to show the effectiveness and computability of the mean-field matrix-analytic method, and also to provide valuable observation of the influence of some key parameters on system performance. We are optimistic that the methodology and results given in this paper are applicable in the study of general large-scale bike sharing systems.

Suggested Citation

  • Quan-Lin Li & Rui-Na Fan, 2022. "A mean-field matrix-analytic method for bike sharing systems under Markovian environment," Annals of Operations Research, Springer, vol. 309(2), pages 517-551, February.
    • Handle: RePEc:spr:annopr:v:309:y:2022:i:2:d:10.1007_s10479-021-04140-x
    DOI: 10.1007/s10479-021-04140-x
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    References listed on IDEAS

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    1. Tal Raviv & Ofer Kolka, 2013. "Optimal inventory management of a bike-sharing station," IISE Transactions, Taylor & Francis Journals, vol. 45(10), pages 1077-1093.
    2. Christine Fricker & Nicolas Gast, 2016. "Incentives and redistribution in homogeneous bike-sharing systems with stations of finite capacity," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 261-291, August.
    3. Mor Kaspi & Tal Raviv & Michal Tzur, 2017. "Bike-sharing systems: User dissatisfaction in the presence of unusable bicycles," IISE Transactions, Taylor & Francis Journals, vol. 49(2), pages 144-158, February.
    4. Jia Shu & Mabel C. Chou & Qizhang Liu & Chung-Piaw Teo & I-Lin Wang, 2013. "Models for Effective Deployment and Redistribution of Bicycles Within Public Bicycle-Sharing Systems," Operations Research, INFORMS, vol. 61(6), pages 1346-1359, December.
    5. Long He & Zhenyu Hu & Meilin Zhang, 2020. "Robust Repositioning for Vehicle Sharing," Manufacturing & Service Operations Management, INFORMS, vol. 22(2), pages 241-256, March.
    6. Kou, Zhaoyu & Cai, Hua, 2019. "Understanding bike sharing travel patterns: An analysis of trip data from eight cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 785-797.
    7. Daniel Adelman, 2007. "Price-Directed Control of a Closed Logistics Queueing Network," Operations Research, INFORMS, vol. 55(6), pages 1022-1038, December.
    8. George, David K. & Xia, Cathy H., 2011. "Fleet-sizing and service availability for a vehicle rental system via closed queueing networks," European Journal of Operational Research, Elsevier, vol. 211(1), pages 198-207, May.
    9. Christine Fricker & Nicolas Servel, 2016. "Two-choice regulation in heterogeneous closed networks," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 173-197, February.
    10. Schuijbroek, J. & Hampshire, R.C. & van Hoeve, W.-J., 2017. "Inventory rebalancing and vehicle routing in bike sharing systems," European Journal of Operational Research, Elsevier, vol. 257(3), pages 992-1004.
    11. Ariel Waserhole & Vincent Jost, 2016. "Pricing in vehicle sharing systems: optimization in queuing networks with product forms," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 293-320, August.
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