IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v89y2018i1d10.1007_s11134-018-9575-0.html
   My bibliography  Save this article

Many-server Gaussian limits for overloaded non-Markovian queues with customer abandonment

Author

Listed:
  • A. Korhan Aras

    (SAS Institute)

  • Xinyun Chen

    (Wuhan University)

  • Yunan Liu

    (North Carolina State University)

Abstract

Extending Ward Whitt’s pioneering work “Fluid Models for Multiserver Queues with Abandonments, Operations Research, 54(1) 37–54, 2006,” this paper establishes a many-server heavy-traffic functional central limit theorem for the overloaded $$G{/}GI{/}n+GI$$ G / G I / n + G I queue with stationary arrivals, nonexponential service times, n identical servers, and nonexponential patience times. Process-level convergence to non-Markovian Gaussian limits is established as the number of servers goes to infinity for key performance processes such as the waiting times, queue length, abandonment and departure processes. Analytic formulas are developed to characterize the distributions of these Gaussian limits.

Suggested Citation

  • A. Korhan Aras & Xinyun Chen & Yunan Liu, 2018. "Many-server Gaussian limits for overloaded non-Markovian queues with customer abandonment," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 81-125, June.
    • Handle: RePEc:spr:queues:v:89:y:2018:i:1:d:10.1007_s11134-018-9575-0
    DOI: 10.1007/s11134-018-9575-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-018-9575-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11134-018-9575-0?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. Avishai Mandelbaum & Petar Momčilović, 2012. "Queues with Many Servers and Impatient Customers," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 41-65, February.
    2. Yunan Liu & Ward Whitt, 2011. "A Network of Time-Varying Many-Server Fluid Queues with Customer Abandonment," Operations Research, INFORMS, vol. 59(4), pages 835-846, August.
    3. Whitt, Ward, 1985. "Queues with superposition arrival processes in heavy traffic," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 81-91, December.
    4. J. G. Dai & Shuangchi He, 2010. "Customer Abandonment in Many-Server Queues," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 347-362, May.
    5. Ward Whitt, 2006. "Fluid Models for Multiserver Queues with Abandonments," Operations Research, INFORMS, vol. 54(1), pages 37-54, February.
    6. Ward Whitt, 2004. "Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments," Management Science, INFORMS, vol. 50(10), pages 1449-1461, October.
    7. Junfei Huang & Avishai Mandelbaum & Hanqin Zhang & Jiheng Zhang, 2017. "Refined Models for Efficiency-Driven Queues with Applications to Delay Announcements and Staffing," Operations Research, INFORMS, vol. 65(5), pages 1380-1397, October.
    8. Achal Bassamboo & Ramandeep S. Randhawa, 2010. "On the Accuracy of Fluid Models for Capacity Sizing in Queueing Systems with Impatient Customers," Operations Research, INFORMS, vol. 58(5), pages 1398-1413, October.
    9. Avishai Mandelbaum & Sergey Zeltyn, 2009. "Staffing Many-Server Queues with Impatient Customers: Constraint Satisfaction in Call Centers," Operations Research, INFORMS, vol. 57(5), pages 1189-1205, 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. Ward Whitt, 2018. "A broad view of queueing theory through one issue," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 3-14, June.
    2. Ryan Palmer & Martin Utley, 2020. "On the modelling and performance measurement of service networks with heterogeneous customers," Annals of Operations Research, Springer, vol. 293(1), pages 237-268, October.

    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. Shuangchi He, 2020. "Diffusion Approximation for Efficiency-Driven Queues When Customers Are Patient," Operations Research, INFORMS, vol. 68(4), pages 1265-1284, July.
    2. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    3. Junfei Huang & Avishai Mandelbaum & Hanqin Zhang & Jiheng Zhang, 2017. "Refined Models for Efficiency-Driven Queues with Applications to Delay Announcements and Staffing," Operations Research, INFORMS, vol. 65(5), pages 1380-1397, October.
    4. Jeunghyun Kim & Ramandeep S. Randhawa & Amy R. Ward, 2018. "Dynamic Scheduling in a Many-Server, Multiclass System: The Role of Customer Impatience in Large Systems," Manufacturing & Service Operations Management, INFORMS, vol. 20(2), pages 285-301, May.
    5. Avishai Mandelbaum & Petar Momčilović, 2017. "Personalized queues: the customer view, via a fluid model of serving least-patient first," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 23-53, October.
    6. Hongyuan Lu & Guodong Pang & Yuhang Zhou, 2016. "$$G/{ GI}/N(+{ GI})$$ G / G I / N ( + G I ) queues with service interruptions in the Halfin–Whitt regime," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 127-160, February.
    7. Alexander L. Stolyar & Tolga Tezcan, 2011. "Shadow-Routing Based Control of Flexible Multiserver Pools in Overload," Operations Research, INFORMS, vol. 59(6), pages 1427-1444, December.
    8. Max Tschaikowski & Mirco Tribastone, 2017. "A computational approach to steady-state convergence of fluid limits for Coxian queuing networks with abandonment," Annals of Operations Research, Springer, vol. 252(1), pages 101-120, May.
    9. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.
    10. Itai Gurvich & Junfei Huang & Avishai Mandelbaum, 2014. "Excursion-Based Universal Approximations for the Erlang-A Queue in Steady-State," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 325-373, May.
    11. Noa Zychlinski & Avishai Mandelbaum & Petar Momčilović, 2018. "Time-varying tandem queues with blocking: modeling, analysis, and operational insights via fluid models with reflection," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 15-47, June.
    12. Josh Reed & Tolga Tezcan, 2012. "Hazard Rate Scaling of the Abandonment Distribution for the GI/M/n + GI Queue in Heavy Traffic," Operations Research, INFORMS, vol. 60(4), pages 981-995, August.
    13. Kawai, Yosuke & Takagi, Hideaki, 2015. "Fluid approximation analysis of a call center model with time-varying arrivals and after-call work," Operations Research Perspectives, Elsevier, vol. 2(C), pages 81-96.
    14. Jouini, Oualid & Pot, Auke & Koole, Ger & Dallery, Yves, 2010. "Online scheduling policies for multiclass call centers with impatient customers," European Journal of Operational Research, Elsevier, vol. 207(1), pages 258-268, November.
    15. Zhenghua Long & Jiheng Zhang, 2019. "Virtual allocation policies for many-server queues with abandonment," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(3), pages 399-451, December.
    16. Avishai Mandelbaum & Petar Momčilović, 2012. "Queues with Many Servers and Impatient Customers," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 41-65, February.
    17. Bo Zhang & Johan S. H. van Leeuwaarden & Bert Zwart, 2012. "Staffing Call Centers with Impatient Customers: Refinements to Many-Server Asymptotics," Operations Research, INFORMS, vol. 60(2), pages 461-474, April.
    18. Guodong Pang & Yuhang Zhou, 2018. "Two-parameter process limits for infinite-server queues with dependent service times via chaining bounds," Queueing Systems: Theory and Applications, Springer, vol. 88(1), pages 1-25, February.
    19. Rouba Ibrahim & Mor Armony & Achal Bassamboo, 2017. "Does the Past Predict the Future? The Case of Delay Announcements in Service Systems," Management Science, INFORMS, vol. 63(6), pages 1762-1780, June.
    20. Tkachenko Andrey, 2013. "Multichannel queuing systems with balking and regenerative input fl ow," HSE Working papers WP BRP 14/STI/2013, National Research University Higher School of Economics.

    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:spr:queues:v:89:y:2018:i:1:d:10.1007_s11134-018-9575-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.