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Analysis of the State-Dependent Queueing Model and Its Application to Battery Swapping and Charging Stations

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  • Doo Il Choi

    (Department of Applied Mathematics, Halla University, 28 Halla University-gil, Wonju-si, Gangwon-do 26404, Korea)

  • Dae-Eun Lim

    (Department of Industrial Engineering, Kangwon National University, 1 Kangwondaehak-gil, Chuncheon-si, Gangwon-do 24341, Korea)

Abstract

This study analyzes the performance of a queue length-dependent overload control policy using a leaky bucket (LB) scheme. This queueing model is applied to the operation of a battery swapping and charging station for electric vehicles (EVs). In addition to the LB scheme, we propose two congestion control policies based on EV queue length thresholds. With these policies, the model determines both EV-arrival and battery-supply intervals, and these depend on the number of EVs waiting in the queue. The queue length distributions, including those at arbitrary epochs, are derived using embedded Markov chain and supplementary variable methods. Performance measures such as blocking probability and mean waiting time are investigated using numerical examples. We study the characteristics of the system using numerical examples and use a cost analysis to investigate situations in which the application of each congestion control policy is advantageous.

Suggested Citation

  • Doo Il Choi & Dae-Eun Lim, 2020. "Analysis of the State-Dependent Queueing Model and Its Application to Battery Swapping and Charging Stations," Sustainability, MDPI, vol. 12(6), pages 1-15, March.
    • Handle: RePEc:gam:jsusta:v:12:y:2020:i:6:p:2343-:d:333618
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    References listed on IDEAS

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    1. Tony T. Lee, 1984. "M / G /1/ N Queue with Vacation Time and Exhaustive Service Discipline," Operations Research, INFORMS, vol. 32(4), pages 774-784, August.
    2. Zou, Bipan & Xu, Xianhao & Gong, Yeming (Yale) & De Koster, René, 2018. "Evaluating battery charging and swapping strategies in a robotic mobile fulfillment system," European Journal of Operational Research, Elsevier, vol. 267(2), pages 733-753.
    3. Eline Cuypere & Koen Turck & Dieter Fiems, 2018. "A queueing model of an energy harvesting sensor node with data buffering," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 67(2), pages 281-295, February.
    4. Bogdan Ovidiu Varga & Arsen Sagoian & Florin Mariasiu, 2019. "Prediction of Electric Vehicle Range: A Comprehensive Review of Current Issues and Challenges," Energies, MDPI, vol. 12(5), pages 1-19, March.
    5. A.D. Banik, 2015. "Some aspects of stationary characteristics and optimal control of the BMAP ∕ G − G ∕ 1 ∕ N( ∞ ) oscillating queueing system," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(2), pages 204-230, March.
    6. Feyijimi Adegbohun & Annette von Jouanne & Kwang Y. Lee, 2019. "Autonomous Battery Swapping System and Methodologies of Electric Vehicles," Energies, MDPI, vol. 12(4), pages 1-14, February.
    7. Bipan Zou & Xianhao Xu & Yeming Gong & René de Koster, 2018. "Evaluating battery charging and swapping strategies in a robotic mobile fulfillment system," Post-Print hal-02312110, HAL.
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    Cited by:

    1. Liu, Yanwei & Liang, Ziyong & Zhong, Wei & Xue, Yu & Wang, Yue & Tao, Naian & Lu, Yanbo, 2025. "Multi-objective predictive cruise control for electric heavy-duty trucks considering fleet battery swapping under cyber-physical system," Energy, Elsevier, vol. 321(C).
    2. Benoliel, Peter & Taylor, Margaret & Coburn, Timothy & Desai, Ranjit R. & Schey, Stephen & Gerdes, Mindy & Peng, Peng, 2025. "Soft costs and EVSE – Knowledge gaps as a barrier to successful projects," Applied Energy, Elsevier, vol. 389(C).
    3. Karumbathil Rasmi & Machuveettil Joseph Jacob & Alexander S. Rumyantsev & Achyutha Krishnamoorthy, 2021. "A Multi-Server Heterogeneous Queuing-Inventory System with Class-Dependent Inventory Access," Mathematics, MDPI, vol. 9(9), pages 1-23, May.
    4. Yu Feng & Xiaochun Lu, 2021. "Construction Planning and Operation of Battery Swapping Stations for Electric Vehicles: A Literature Review," Energies, MDPI, vol. 14(24), pages 1-19, December.
    5. Long Zeng & Si-Zhe Chen & Zebin Tang & Ling Tian & Tingting Xiong, 2023. "An Electric Vehicle Charging Method Considering Multiple Power Exchange Modes’ Coordination," Sustainability, MDPI, vol. 15(13), pages 1-17, July.

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