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Asymptotically Maximal Throughput in Tandem Systems with Flexible and Dedicated Servers

Author

Listed:
  • Aili (Alice) Zou

    (Department of Computing and Software, McMaster University, 1280 Main Street, West Hamilton, Ontario L8S 4L7, Canada)

  • Douglas G. Down

    (Department of Computing and Software, McMaster University, 1280 Main Street, West Hamilton, Ontario L8S 4L7, Canada)

Abstract

For a system of two tandem queues with a finite intermediate buffer, we study the asymptotically maximal throughput as the number of servers in each station grows to infinity. First, we study the system with only dedicated servers, and then we examine the system with both dedicated and flexible servers. We assume that travel times between the two stations are negligible and that each server can only work on one customer at a time. We model the system as a birth–death Markov process, derive a closed form solution for the stationary distribution, and quantify the maximal asymptotic normalized throughput as the number of servers grows to infinity. We show that flexibility is more favorable for small systems, and as the number of servers grows, the benefits of flexibility decrease. Furthermore, we prove that when the number of servers goes to infinity, there is no need of flexibility at all, as the maximum value of the throughput is obtained. However, flexibility still has a secondary beneficial effect — a little flexibility (on the order of the square root of the number of dedicated servers at each station) guarantees that all dedicated servers are busy and results in faster convergence to the maximum throughput.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:05:n:s0217595918500380
    DOI: 10.1142/S0217595918500380
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    References listed on IDEAS

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    1. René Bekker & Ger Koole & Dennis Roubos, 2017. "Flexible bed allocations for hospital wards," Health Care Management Science, Springer, vol. 20(4), pages 453-466, December.
    2. Sigrún Andradóttir & Hayriye Ayhan, 2005. "Throughput Maximization for Tandem Lines with Two Stations and Flexible Servers," Operations Research, INFORMS, vol. 53(3), pages 516-531, June.
    3. Mohammad H. Yarmand & Douglas G. Down, 2015. "Maximizing throughput in zero-buffer tandem lines with dedicated and flexible servers," IISE Transactions, Taylor & Francis Journals, vol. 47(1), pages 35-49, January.
    4. Sigrún Andradóttir & Hayriye Ayhan & Douglas G. Down, 2003. "Dynamic Server Allocation for Queueing Networks with Flexible Servers," Operations Research, INFORMS, vol. 51(6), pages 952-968, December.
    5. Sigrún Andradóttir & Hayriye Ayhan & Douglas G. Down, 2001. "Server Assignment Policies for Maximizing the Steady-State Throughput of Finite Queueing Systems," Management Science, INFORMS, vol. 47(10), pages 1421-1439, October.
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    Cited by:

    1. 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.

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