IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v35y2018i05ns0217595918500380.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595918500380
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595918500380?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. 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.
    2. 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.
    3. 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.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    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. Sigrún Andradóttir & Hayriye Ayhan & Douglas G. Down, 2007. "Compensating for Failures with Flexible Servers," Operations Research, INFORMS, vol. 55(4), pages 753-768, August.
    2. Eser Kırkızlar & Sigrún Andradóttir & Hayriye Ayhan, 2010. "Robustness of efficient server assignment policies to service time distributions in finite‐buffered lines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(6), pages 563-582, September.
    3. Yi‐Chun Tsai & Nilay Tanık Argon, 2008. "Dynamic server assignment policies for assembly‐type queues with flexible servers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(3), pages 234-251, April.
    4. Tuğçe Işık & Sigrún Andradóttir & Hayriye Ayhan, 2016. "Optimal control of queueing systems with non-collaborating servers," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 79-110, October.
    5. Peng Wang & Kai Pan & Zhenzhen Yan & Yun Fong Lim, 2022. "Managing Stochastic Bucket Brigades on Discrete Work Stations," Production and Operations Management, Production and Operations Management Society, vol. 31(1), pages 358-373, January.
    6. Eser Kırkızlar & Sigrún Andradóttir & Hayriye Ayhan, 2012. "Flexible Servers in Understaffed Tandem Lines," Production and Operations Management, Production and Operations Management Society, vol. 21(4), pages 761-777, July.
    7. Gabriel Zayas-Cabán & Jingui Xie & Linda V. Green & Mark E. Lewis, 2016. "Dynamic control of a tandem system with abandonments," Queueing Systems: Theory and Applications, Springer, vol. 84(3), pages 279-293, December.
    8. Down, Douglas G. & Karakostas, George, 2008. "Maximizing throughput in queueing networks with limited flexibility," European Journal of Operational Research, Elsevier, vol. 187(1), pages 98-112, May.
    9. Yun Fong Lim & Bingnan Lu & Rowan Wang & Wenjia Zhang, 2020. "Flexibly Serving A Finite Number of Heterogeneous Jobs in A Tandem System," Production and Operations Management, Production and Operations Management Society, vol. 29(6), pages 1431-1447, June.
    10. Emmett J. Lodree & Nezih Altay & Robert A. Cook, 2019. "Staff assignment policies for a mass casualty event queuing network," Annals of Operations Research, Springer, vol. 283(1), pages 411-442, December.
    11. Gregory Dobson & Tolga Tezcan & Vera Tilson, 2013. "Optimal Workflow Decisions for Investigators in Systems with Interruptions," Management Science, INFORMS, vol. 59(5), pages 1125-1141, May.
    12. Zhao, Yaping & Xu, Xiaoyun & Li, Haidong & Liu, Yanni, 2016. "Prioritized customer order scheduling to maximize throughput," European Journal of Operational Research, Elsevier, vol. 255(2), pages 345-356.
    13. Dimitrios G. Pandelis, 2014. "Optimal control of noncollaborative servers in two‐stage tandem queueing systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(6), pages 435-446, September.
    14. Ramesh Arumugam & Maria Mayorga & Kevin Taaffe, 2009. "Inventory based allocation policies for flexible servers in serial systems," Annals of Operations Research, Springer, vol. 172(1), pages 1-23, November.
    15. Eugene Furman & Adam Diamant & Murat Kristal, 2021. "Customer Acquisition and Retention: A Fluid Approach for Staffing," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 4236-4257, November.
    16. S.M.R. Iravani & J.A. Buzacott & M.J.M. Posner, 2005. "A robust policy for serial agile production systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(1), pages 58-73, February.
    17. Tuğçe Işık & Sigrún Andradóttir & Hayriye Ayhan, 2022. "Dynamic Control of Non‐Collaborative Workers When Reassignment Is Costly," Production and Operations Management, Production and Operations Management Society, vol. 31(3), pages 1332-1352, March.
    18. Nilay Tanık Argon & Sigrún Andradóttir, 2017. "Pooling in tandem queueing networks with non-collaborative servers," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 345-377, December.
    19. Sigrún Andradóttir & Hayriye Ayhan & Douglas G. Down, 2011. "TECHNICAL NOTE---Queueing Systems with Synergistic Servers," Operations Research, INFORMS, vol. 59(3), pages 772-780, June.
    20. Sennott, Linn I. & Van Oyen, Mark P. & Iravani, Seyed M.R., 2006. "Optimal dynamic assignment of a flexible worker on an open production line with specialists," European Journal of Operational Research, Elsevier, vol. 170(2), pages 541-566, 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:wsi:apjorx:v:35:y:2018:i:05:n:s0217595918500380. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    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.