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Queueing Network with Moving Servers as a Model of Car Sharing Systems

Author

Listed:
  • Chesoong Kim

    (Department of Industrial Engineering, Sangji University, Wonju, Kangwon 26339, Korea)

  • Sergei Dudin

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4 Nezavisimosti Ave., Minsk 220030, Belarus
    Applied Mathematics and Communications Technology Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russia)

  • Olga Dudina

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4 Nezavisimosti Ave., Minsk 220030, Belarus
    Applied Mathematics and Communications Technology Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russia)

Abstract

We consider a queueing network with a finite number of nodes and servers moving between the nodes as a model of car sharing. The arrival process of customers to various nodes is defined by a marked Markovian arrival process. The customer that arrives at a certain node when there is no idle server (car) is lost. Otherwise, he/she is able to start the service. With known probability, which depends on the node and the number of available cars, this customer can balk the service and leave the system. The service time of a customer has an exponential distribution. Location of the server in the network after service completion is random with the known probability distribution. The behaviour of the network is described by a multi-dimensional continuous-time Markov chain. The generator of this chain is derived which allows us to compute the stationary distribution of the network states. The formulas for computing the key performance indicators of the system are given. Numerical results are presented. They characterize the dependence of some performance measures of the network and the nodes on the total number of cars (fleet size of the car sharing system) and correlation in the arrival process.

Suggested Citation

  • Chesoong Kim & Sergei Dudin & Olga Dudina, 2019. "Queueing Network with Moving Servers as a Model of Car Sharing Systems," Mathematics, MDPI, vol. 7(9), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:825-:d:264766
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    References listed on IDEAS

    as
    1. Aili (Alice) Zou & Douglas G. Down, 2018. "Asymptotically Maximal Throughput in Tandem Systems with Flexible and Dedicated Servers," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-15, October.
    2. Perboli, Guido & Ferrero, Francesco & Musso, Stefano & Vesco, Andrea, 2018. "Business models and tariff simulation in car-sharing services," Transportation Research Part A: Policy and Practice, Elsevier, vol. 115(C), pages 32-48.
    3. 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.
    4. Baumann, Hendrik & Sandmann, Werner, 2017. "Multi-server tandem queue with Markovian arrival process, phase-type service times, and finite buffers," European Journal of Operational Research, Elsevier, vol. 256(1), pages 187-195.
    5. Dhingra, Vibhuti & Kumawat, Govind Lal & Roy, Debjit & Koster, René de, 2018. "Solving semi-open queuing networks with time-varying arrivals: An application in container terminal landside operations," European Journal of Operational Research, Elsevier, vol. 267(3), pages 855-876.
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    Cited by:

    1. Mohamed Amjath & Laoucine Kerbache & James MacGregor Smith, 2024. "A Closed Queueing Networks Approach for an Optimal Heterogeneous Fleet Size of an Inter-Facility Bulk Material Transfer System," Logistics, MDPI, vol. 8(1), pages 1-38, March.

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