IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-04452674.html
   My bibliography  Save this paper

The Transient Blended Queue

Author

Listed:
  • B. Legros

    (Métis Lab EM Normandie - EM Normandie - École de Management de Normandie)

Abstract

This study aims to determine the transient behavior of the blended queue. Priority customers arrive over time and benefit from a threshold reservation policy, while non-priority ones can be contacted at any time. We show how to compute the Laplace transforms of the transient probabilities. Using the uniformization technique, we prove some monotonicty properties of the expected number of customers in the queue, explaining why the optimal transient reservation threshold should be lower than the stationary one. \textcopyright 2022 Elsevier B.V.

Suggested Citation

  • B. Legros, 2022. "The Transient Blended Queue," Post-Print hal-04452674, HAL.
    • Handle: RePEc:hal:journl:hal-04452674
    DOI: 10.1016/j.orl.2022.03.001
    Note: View the original document on HAL open archive server: https://normandie-univ.hal.science/hal-04452674
    as

    Download full text from publisher

    File URL: https://normandie-univ.hal.science/hal-04452674/document
    Download Restriction: no
    File URL: https://libkey.io/10.1016/j.orl.2022.03.001?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
    ---><---

    References listed on IDEAS

    as
    1. Benjamin Legros, 2021. "Transient analysis of an affine Queue-Hawkes process," Post-Print hal-03605436, HAL.
    2. Benjamin Legros & Oualid Jouini & Ger Koole, 2015. "Adaptive threshold policies for multi-channel call centers," IISE Transactions, Taylor & Francis Journals, vol. 47(4), pages 414-430, April.
    3. Linda V. Green & Peter J. Kolesar & João Soares, 2001. "Improving the Sipp Approach for Staffing Service Systems That Have Cyclic Demands," Operations Research, INFORMS, vol. 49(4), pages 549-564, August.
    4. 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.
    5. Noah Gans & Yong-Pin Zhou, 2003. "A Call-Routing Problem with Service-Level Constraints," Operations Research, INFORMS, vol. 51(2), pages 255-271, April.
    6. Tuan Phung-Duc & Wouter Rogiest & Yutaka Takahashi & Herwig Bruneel, 2016. "Retrial queues with balanced call blending: analysis of single-server and multiserver model," Annals of Operations Research, Springer, vol. 239(2), pages 429-449, April.
    7. W. David Kelton & Averill M. Law, 1985. "The Transient Behavior of the M / M / s Queue, with Implications for Steady-State Simulation," Operations Research, INFORMS, vol. 33(2), pages 378-396, April.
    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. Dietz, Dennis C., 2011. "Practical scheduling for call center operations," Omega, Elsevier, vol. 39(5), pages 550-557, October.
    2. Kraig Delana & Nicos Savva & Tolga Tezcan, 2021. "Proactive Customer Service: Operational Benefits and Economic Frictions," Manufacturing & Service Operations Management, INFORMS, vol. 23(1), pages 70-87, 1-2.
    3. 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.
    4. Júlíus Atlason & Marina A. Epelman & Shane G. Henderson, 2008. "Optimizing Call Center Staffing Using Simulation and Analytic Center Cutting-Plane Methods," Management Science, INFORMS, vol. 54(2), pages 295-309, February.
    5. 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.
    6. Alex Roubos & Ger Koole & Raik Stolletz, 2012. "Service-Level Variability of Inbound Call Centers," Manufacturing & Service Operations Management, INFORMS, vol. 14(3), pages 402-413, July.
    7. Benjamin Legros & Sihan Ding & Rob Mei & Oualid Jouini, 2017. "Call centers with a postponed callback offer," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1097-1125, October.
    8. Castillo, Ignacio & Joro, Tarja & Li, Yong Yue, 2009. "Workforce scheduling with multiple objectives," European Journal of Operational Research, Elsevier, vol. 196(1), pages 162-170, July.
    9. Legros, Benjamin & Jouini, Oualid & Akşin, O. Zeynep & Koole, Ger, 2020. "Front-office multitasking between service encounters and back-office tasks," European Journal of Operational Research, Elsevier, vol. 287(3), pages 946-963.
    10. Benjamin Legros, 2021. "Agents’ Self‐Routing for Blended Operations to Balance Inbound and Outbound Services," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3599-3614, October.
    11. 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.
    12. Ran Liu & Xiaolan Xie, 2018. "Physician Staffing for Emergency Departments with Time-Varying Demand," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 588-607, August.
    13. Robbins, Thomas R. & Harrison, Terry P., 2010. "A stochastic programming model for scheduling call centers with global Service Level Agreements," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1608-1619, December.
    14. 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.
    15. Joseph M. Milner & Tava Lennon Olsen, 2008. "Service-Level Agreements in Call Centers: Perils and Prescriptions," Management Science, INFORMS, vol. 54(2), pages 238-252, February.
    16. Yue Zhang & Martin L. Puterman & Matthew Nelson & Derek Atkins, 2012. "A Simulation Optimization Approach to Long-Term Care Capacity Planning," Operations Research, INFORMS, vol. 60(2), pages 249-261, April.
    17. Ingolfsson, Armann & Campello, Fernanda & Wu, Xudong & Cabral, Edgar, 2010. "Combining integer programming and the randomization method to schedule employees," European Journal of Operational Research, Elsevier, vol. 202(1), pages 153-163, April.
    18. Ta, Thuy Anh & Chan, Wyean & Bastin, Fabian & L’Ecuyer, Pierre, 2021. "A simulation-based decomposition approach for two-stage staffing optimization in call centers under arrival rate uncertainty," European Journal of Operational Research, Elsevier, vol. 293(3), pages 966-979.
    19. Sandjai Bhulai & Taoying Farenhorst-Yuan & Bernd Heidergott & Dinard Laan, 2012. "Optimal balanced control for call centers," Annals of Operations Research, Springer, vol. 201(1), pages 39-62, December.
    20. Barış Ata & Xiaoshan Peng, 2020. "An Optimal Callback Policy for General Arrival Processes: A Pathwise Analysis," Operations Research, INFORMS, vol. 68(2), pages 327-347, March.

    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:hal:journl:hal-04452674. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.