IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v309y2022i2d10.1007_s10479-021-04140-x.html
   My bibliography  Save this article

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

Author

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-021-04140-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-021-04140-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Saif Benjaafar & Daniel Jiang & Xiang Li & Xiaobo Li, 2022. "Dynamic Inventory Repositioning in On-Demand Rental Networks," Management Science, INFORMS, vol. 68(11), pages 7861-7878, November.
    2. Gilbert Laporte & Frédéric Meunier & Roberto Wolfler Calvo, 2018. "Shared mobility systems: an updated survey," Annals of Operations Research, Springer, vol. 271(1), pages 105-126, December.
    3. Zhou, Yaoming & Lin, Zeyu & Guan, Rui & Sheu, Jiuh-Biing, 2023. "Dynamic battery swapping and rebalancing strategies for e-bike sharing systems," Transportation Research Part B: Methodological, Elsevier, vol. 177(C).
    4. Negahban, Ashkan, 2019. "Simulation-based estimation of the real demand in bike-sharing systems in the presence of censoring," European Journal of Operational Research, Elsevier, vol. 277(1), pages 317-332.
    5. Çelebi, Dilay & Yörüsün, Aslı & Işık, Hanife, 2018. "Bicycle sharing system design with capacity allocations," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 86-98.
    6. Legros, Benjamin, 2019. "Dynamic repositioning strategy in a bike-sharing system; how to prioritize and how to rebalance a bike station," European Journal of Operational Research, Elsevier, vol. 272(2), pages 740-753.
    7. Sharon Datner & Tal Raviv & Michal Tzur & Daniel Chemla, 2019. "Setting Inventory Levels in a Bike Sharing Network," Service Science, INFORMS, vol. 53(1), pages 62-76, February.
    8. Fu, Chenyi & Ma, Shoufeng & Zhu, Ning & He, Qiao-Chu & Yang, Hai, 2022. "Bike-sharing inventory management for market expansion," Transportation Research Part B: Methodological, Elsevier, vol. 162(C), pages 28-54.
    9. 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.
    10. Long He & Guangrui Ma & Wei Qi & Xin Wang, 2021. "Charging an Electric Vehicle-Sharing Fleet," Manufacturing & Service Operations Management, INFORMS, vol. 23(2), pages 471-487, March.
    11. Chen, Qingxin & Fu, Chenyi & Zhu, Ning & Ma, Shoufeng & He, Qiao-Chu, 2023. "A target-based optimization model for bike-sharing systems: From the perspective of service efficiency and equity," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 235-260.
    12. Ruijing Wu & Shaoxuan Liu & Zhenyang Shi, 2019. "Customer Incentive Rebalancing Plan in Free-Float Bike-Sharing System with Limited Information," Sustainability, MDPI, vol. 11(11), pages 1-24, May.
    13. Santiago R. Balseiro & David B. Brown & Chen Chen, 2021. "Dynamic Pricing of Relocating Resources in Large Networks," Management Science, INFORMS, vol. 67(7), pages 4075-4094, July.
    14. Gu, Wei & Li, Meng & Wang, Chen & Shang, Jennifer & Wei, Lirong, 2021. "Strategic sourcing selection for bike-sharing rebalancing: An evolutionary game approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 156(C).
    15. Li, Shukai & Luo, Qi & Hampshire, Robert Cornelius, 2021. "Optimizing large on-demand transportation systems through stochastic conic programming," European Journal of Operational Research, Elsevier, vol. 295(2), pages 427-442.
    16. Mohammed Elhenawy & Hesham A. Rakha & Youssef Bichiou & Mahmoud Masoud & Sebastien Glaser & Jack Pinnow & Ahmed Stohy, 2021. "A Feasible Solution for Rebalancing Large-Scale Bike Sharing Systems," Sustainability, MDPI, vol. 13(23), pages 1-19, December.
    17. Anton Braverman & J. G. Dai & Xin Liu & Lei Ying, 2019. "Empty-Car Routing in Ridesharing Systems," Operations Research, INFORMS, vol. 67(5), pages 1437-1452, September.
    18. Bruno Albert Neumann-Saavedra & Teodor Gabriel Crainic & Bernard Gendron & Dirk Christian Mattfeld & Michael Römer, 2020. "Integrating Resource Management in Service Network Design for Bike-Sharing Systems," Transportation Science, INFORMS, vol. 54(5), pages 1251-1271, September.
    19. Kaspi, Mor & Raviv, Tal & Tzur, Michal & Galili, Hila, 2016. "Regulating vehicle sharing systems through parking reservation policies: Analysis and performance bounds," European Journal of Operational Research, Elsevier, vol. 251(3), pages 969-987.
    20. Liangpeng Gao & Yanjie Ji & Xingchen Yan & Yao Fan & Weihong Guo, 2021. "Incentive measures to avoid the illegal parking of dockless shared bikes: the relationships among incentive forms, intensity and policy compliance," Transportation, Springer, vol. 48(2), pages 1033-1060, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:309:y:2022:i:2:d:10.1007_s10479-021-04140-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.