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Multiserver call center retrial queue under Bernoulli vacation schedule with two-way communication and orbital search

Author

Listed:
  • B. Krishna Kumar

    (Vellore Institute of Technology
    Anna University)

  • R. Sankar

    (Anna University)

  • R. Navaneetha Krishnan

    (Anna University)

  • R. Rukmani

    (Pachaiyappa’s College)

Abstract

This article deals with the steady-state behaviour of a finite orbit capacity multiserver call center retrial queue with Bernoulli vacation schedule in which the servers not only accept incoming calls but also make outgoing calls after some exponentially distributed idle time. In addition, upon each service completion of the outgoing call, the servers search for orbital calls, if any, with some probability or take a single vacation with the complementary probability. Search time is assumed to be negligible. Under the Markovian assumptions, the steady-state joint probability distribution of the number of incoming calls in the orbit and the status of the servers is determined by adopting matrix analytic methods. The three types of retrials, namely ideal retrial, vain retrial, and successful retrial for incoming calls are also discussed. The expressions for the Laplace–Stieltjes transforms (LSTs) of the busy period length of the system and the waiting time distribution of a tagged incoming call in the orbit are obtained. Moreover, the probability generating function for the number of retrials made by an incoming call is investigated. Some vital performance characteristics of the system and various moments of quantities of interest are studied. Finally, extensive numerical illustrations are presented to show the impact of the system parameters on the selected performance measures.

Suggested Citation

  • B. Krishna Kumar & R. Sankar & R. Navaneetha Krishnan & R. Rukmani, 2023. "Multiserver call center retrial queue under Bernoulli vacation schedule with two-way communication and orbital search," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 84(1), pages 23-51, September.
    • Handle: RePEc:spr:telsys:v:84:y:2023:i:1:d:10.1007_s11235-023-01025-1
    DOI: 10.1007/s11235-023-01025-1
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    References listed on IDEAS

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    1. B. Krishna Kumar & A. Thanikachalam & V. Kanakasabapathi & R. Rukmani, 2016. "Performance analysis of a multiprogramming–multiprocessor retrial queueing system with orderly reattempts," Annals of Operations Research, Springer, vol. 247(1), pages 319-364, December.
    2. 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.
    3. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, March.
    4. Aguir, M. Salah & Aksin, O. Zeynep & Karaesmen, Fikri & Dallery, Yves, 2008. "On the interaction between retrials and sizing of call centers," European Journal of Operational Research, Elsevier, vol. 191(2), pages 398-408, December.
    5. Falin, G. I. & Artalejo, J. R., 1998. "A finite source retrial queue," European Journal of Operational Research, Elsevier, vol. 108(2), pages 409-424, July.
    6. 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.
    7. 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.
    8. B. Kumar & J Raja, 2006. "On multiserver feedback retrial queues with balking and control retrial rate," Annals of Operations Research, Springer, vol. 141(1), pages 211-232, January.
    9. Hiroyuki Sakurai & Tuan Phung-Duc, 2015. "Two-way communication retrial queues with multiple types of outgoing calls," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 466-492, July.
    10. Tuan Phung-Duc & Ken'Ichi Kawanishi, 2014. "An Efficient Method For Performance Analysis Of Blended Call Centers With Redial," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-33.
    11. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
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