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An Efficient Method For Performance Analysis Of Blended Call Centers With Redial

Author

Listed:
  • TUAN PHUNG-DUC

    (Tokyo Institute of Technology, Ookayama, Tokyo 152-8552, Japan)

  • KEN'ICHI KAWANISHI

    (Gunma University, Kiryu, Gunma 376-8515, Japan)

Abstract

This paper considers a multiserver retrial queue with two-way communication for blended call centers. Primary incoming calls arrive at the servers according to a Poisson process and request an exponentially distributed service time. Incoming calls that find all the servers fully occupied join the orbit and retry to occupy a server again after some random time. A retrial incoming call behaves the same as a primary incoming call. A server not only serves as an incoming call but also makes an outgoing call after some random idle time. We assume that the distribution of the duration of outgoing calls is different from that of incoming calls. Artalejo and Phung-Duc (2012) have extensively studied the single server case and have obtained some preliminary results for the multiserver model. In this paper, we present an extensive analysis for the multiserver model in which, we propose a new formulation by a level-dependent quasi birth-and-death (QBD) process, whose block matrices have some special block structure. Based on a matrix continued fraction approach and a censoring technique, we develop an efficient algorithm utilizing the special structure for computing the stationary distribution. Furthermore, we derive explicit formulae for the mean number of incoming calls and that of outgoing calls in the servers. Through various numerical results, we study the characteristics of the queueing system and find some insights into the optimal outgoing call rate.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:apjorx:v:31:y:2014:i:02:n:s0217595914400089
    DOI: 10.1142/S0217595914400089
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    Citations

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    Cited by:

    1. 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.
    2. Shin, Yang Woo, 2015. "Algorithmic approach to Markovian multi-server retrial queues with vacations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 287-297.
    3. Jingui Xie & Taozeng Zhu & An-Kuo Chao & Shuaian Wang, 2017. "Performance analysis of service systems with priority upgrades," Annals of Operations Research, Springer, vol. 253(1), pages 683-705, June.
    4. 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.
    5. Hiroyuki Sakurai & Tuan Phung-Duc, 2016. "Scaling limits for single server retrial queues with two-way communication," Annals of Operations Research, Springer, vol. 247(1), pages 229-256, December.

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