IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v20y2017i2d10.1007_s10951-015-0456-7.html
   My bibliography  Save this article

Scheduling of multi-class multi-server queueing systems with abandonments

Author

Listed:
  • Urtzi Ayesta

    (CNRS, LAAS
    IKERBASQUE — Basque Foundation for Science
    Univ. de Toulouse, LAAS
    University of the Basque Country)

  • Peter Jacko

    (Lancaster University)

  • Vladimir Novak

    (CERGE-EI, Politickych veznu 7)

Abstract

Many real-world situations involve queueing systems in which customers may abandon if service does not start sufficiently quickly. We study a comprehensive model of multi-class queue scheduling accounting for customer abandonment, with the objective of minimizing the total discounted or time-average sum of linear waiting costs, completion rewards, and abandonment penalties of customers in the system. We assume the service times and abandoning times are exponentially distributed. We solve analytically the case in which there is one server and there are one or two customers in the system and obtain an optimal policy. For the general case, we use the framework of restless bandits to analytically design a novel simple index rule with a natural interpretation. We show that the proposed rule achieves near-optimal or asymptotically optimal performance both in single- and multi-server cases, both in overload and underload regimes, and both in idling and non-idling systems.

Suggested Citation

  • Urtzi Ayesta & Peter Jacko & Vladimir Novak, 2017. "Scheduling of multi-class multi-server queueing systems with abandonments," Journal of Scheduling, Springer, vol. 20(2), pages 129-145, April.
  • Handle: RePEc:spr:jsched:v:20:y:2017:i:2:d:10.1007_s10951-015-0456-7
    DOI: 10.1007/s10951-015-0456-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-015-0456-7
    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/s10951-015-0456-7?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. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    2. Nam Kyoo Boots & Henk Tijms, 1999. "A Multiserver Queueing System with Impatient Customers," Management Science, INFORMS, vol. 45(3), pages 444-448, March.
    3. Dennis W. Fife, 1965. "Scheduling with Random Arrivals and Linear Loss Functions," Management Science, INFORMS, vol. 11(3), pages 429-437, January.
    4. Oualid Jouini & Auke Pot & Ger Koole & Yves Dallery, 2010. "Online Scheduling Policies for Multiclass Call Centers with Impatient Customers," Post-Print hal-00565528, HAL.
    5. J. Michael Harrison & Assaf Zeevi, 2004. "Dynamic Scheduling of a Multiclass Queue in the Halfin-Whitt Heavy Traffic Regime," Operations Research, INFORMS, vol. 52(2), pages 243-257, April.
    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. Meilijson, Isaac & Weiss, Gideon, 1977. "Multiple feedback at a single-server station," Stochastic Processes and their Applications, Elsevier, vol. 5(2), pages 195-205, May.
    8. P. H. Brill & M. J. M. Posner, 1977. "Level Crossings in Point Processes Applied to Queues: Single-Server Case," Operations Research, INFORMS, vol. 25(4), pages 662-674, August.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    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. Francis de Véricourt & Otis B. Jennings, 2008. "Dimensioning Large-Scale Membership Services," Operations Research, INFORMS, vol. 56(1), pages 173-187, February.
    2. 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.
    3. B. Krishna Kumar & R. Sankar & R. Navaneetha Krishnan & R. Rukmani, 2022. "Performance Analysis of Multi-processor Two-Stage Tandem Call Center Retrial Queues with Non-Reliable Processors," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 95-142, March.
    4. Opher Baron & Joseph Milner, 2009. "Staffing to Maximize Profit for Call Centers with Alternate Service-Level Agreements," Operations Research, INFORMS, vol. 57(3), pages 685-700, June.
    5. Avishai Mandelbaum & Petar Momčilović, 2008. "Queues with Many Servers: The Virtual Waiting-Time Process in the QED Regime," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 561-586, August.
    6. Legros, Benjamin & Jouini, Oualid, 2019. "On the scheduling of operations in a chat contact center," European Journal of Operational Research, Elsevier, vol. 274(1), pages 303-316.
    7. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    8. Terry James & Kevin Glazebrook & Kyle Lin, 2016. "Developing Effective Service Policies for Multiclass Queues with Abandonment: Asymptotic Optimality and Approximate Policy Improvement," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 251-264, May.
    9. Noah Gans & Haipeng Shen & Yong-Pin Zhou & Nikolay Korolev & Alan McCord & Herbert Ristock, 2015. "Parametric Forecasting and Stochastic Programming Models for Call-Center Workforce Scheduling," Manufacturing & Service Operations Management, INFORMS, vol. 17(4), pages 571-588, October.
    10. Achal Bassamboo & J. Michael Harrison & Assaf Zeevi, 2006. "Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method," Operations Research, INFORMS, vol. 54(3), pages 419-435, June.
    11. Achal Bassamboo & Assaf Zeevi, 2009. "On a Data-Driven Method for Staffing Large Call Centers," Operations Research, INFORMS, vol. 57(3), pages 714-726, June.
    12. Itai Gurvich & Ohad Perry, 2012. "Overflow Networks: Approximations and Implications to Call Center Outsourcing," Operations Research, INFORMS, vol. 60(4), pages 996-1009, August.
    13. J. G. Dai & Tolga Tezcan, 2011. "State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 271-320, May.
    14. Guodong Pang & Ohad Perry, 2015. "A Logarithmic Safety Staffing Rule for Contact Centers with Call Blending," Management Science, INFORMS, vol. 61(1), pages 73-91, January.
    15. J. Michael Harrison & Assaf Zeevi, 2005. "A Method for Staffing Large Call Centers Based on Stochastic Fluid Models," Manufacturing & Service Operations Management, INFORMS, vol. 7(1), pages 20-36, September.
    16. Shuangchi He, 2020. "Diffusion Approximation for Efficiency-Driven Queues When Customers Are Patient," Operations Research, INFORMS, vol. 68(4), pages 1265-1284, July.
    17. Yoshiaki Inoue & Onno Boxma & David Perry & Shelley Zacks, 2018. "Analysis of $$\hbox {M}^{\mathrm {x}}/\hbox {G}/1$$ M x / G / 1 queues with impatient customers," Queueing Systems: Theory and Applications, Springer, vol. 89(3), pages 303-350, August.
    18. Rouba Ibrahim & Ward Whitt, 2009. "Real-Time Delay Estimation in Overloaded Multiserver Queues with Abandonments," Management Science, INFORMS, vol. 55(10), pages 1729-1742, October.
    19. Ward Whitt, 2006. "Fluid Models for Multiserver Queues with Abandonments," Operations Research, INFORMS, vol. 54(1), pages 37-54, February.
    20. Noah Gans & Yong-Pin Zhou, 2007. "Call-Routing Schemes for Call-Center Outsourcing," Manufacturing & Service Operations Management, INFORMS, vol. 9(1), pages 33-50, May.

    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:jsched:v:20:y:2017:i:2:d:10.1007_s10951-015-0456-7. 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.