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Bounds and limit theorems for a layered queueing model in electric vehicle charging

Author

Listed:
  • Angelos Aveklouris

    (Eindhoven University of Technology)

  • Maria Vlasiou

    (Eindhoven University of Technology)

  • Bert Zwart

    (Eindhoven University of Technology
    Centrum Wiskunde en Informatica)

Abstract

The rise of electric vehicles (EVs) is unstoppable due to factors such as the decreasing cost of batteries and various policy decisions. These vehicles need to be charged and will therefore cause congestion in local distribution grids in the future. Motivated by this, we consider a charging station with finitely many parking spaces, in which electric vehicles arrive in order to get charged. An EV has a random parking time and a random charging time. Both the charging rate per vehicle and the charging rate possible for the station are assumed to be limited. Thus, the charging rate of uncharged EVs depends on the number of cars charging simultaneously. This model leads to a layered queueing network in which parking spaces with EV chargers have a dual role, of a server (to cars) and a customer (to the grid). We are interested in the performance of the aforementioned model, focusing on the fraction of vehicles that get fully charged. To do so, we develop several bounds and asymptotic (fluid and diffusion) approximations for the vector process which describes the total number of EVs and the number of not fully charged EVs in the charging station, and we compare these bounds and approximations with numerical outcomes.

Suggested Citation

  • Angelos Aveklouris & Maria Vlasiou & Bert Zwart, 2019. "Bounds and limit theorems for a layered queueing model in electric vehicle charging," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 83-137, October.
    • Handle: RePEc:spr:queues:v:93:y:2019:i:1:d:10.1007_s11134-019-09616-z
    DOI: 10.1007/s11134-019-09616-z
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    References listed on IDEAS

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    1. Zhang, Lidong & Jiang, Chunmei, 2009. "Stationary distribution of reflected O-U process with two-sided barriers," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 177-181, January.
    2. Aldous, David, 1986. "Some interesting processes arising as heavy traffic limits in an M/M/[infinity] storage process," Stochastic Processes and their Applications, Elsevier, vol. 22(2), pages 291-313, July.
    3. Maria Remerova & Josh Reed & Bert Zwart, 2014. "Fluid Limits for Bandwidth-Sharing Networks with Rate Constraints," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 746-774, August.
    4. H. Christian Gromoll & Philippe Robert & Bert Zwart, 2008. "Fluid Limits for Processor-Sharing Queues with Impatience," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 375-402, May.
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    Cited by:

    1. Ghotge, Rishabh & van Wijk, Ad & Lukszo, Zofia, 2021. "Off-grid solar charging of electric vehicles at long-term parking locations," Energy, Elsevier, vol. 227(C).
    2. Legros, Benjamin & Fransoo, Jan C., 2023. "Admission and pricing optimization of on-street parking with delivery bays," Other publications TiSEM 6d41ee5c-27dc-4d34-aff1-4, Tilburg University, School of Economics and Management.
    3. Legros, Benjamin & Fransoo, Jan C., 2024. "Admission and pricing optimization of on-street parking with delivery bays," European Journal of Operational Research, Elsevier, vol. 312(1), pages 138-149.
    4. Hung, Ying-Chao & PakHai Lok, Horace & Michailidis, George, 2022. "Optimal routing for electric vehicle charging systems with stochastic demand: A heavy traffic approximation approach," European Journal of Operational Research, Elsevier, vol. 299(2), pages 526-541.
    5. Jiaqi Zhou & Ilya O. Ryzhov, 2021. "Equilibrium analysis of observable express service with customer choice," Queueing Systems: Theory and Applications, Springer, vol. 99(3), pages 243-281, December.

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