Performance Analysis and Optimization of a Queueing Model for a Multi-skill Call Center in M-Design

  • Dequan YueEmail author
  • Chunyan Li
  • Wuyi Yue
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 383)


This paper studies a queuing model of a multi-skill call center in M-design. In this model, there are two types of customers and three groups of servers who have different skills. Servers in Group 1 can only serve type 1 customers, servers in Group 2 can only serve type 2 customers, and servers in Group 3 can serve both type 1 and type 2 customers. We obtain the state-transition rates by using results from M/M/c/c and M/M/c queueing systems. Then, we establish equations for the steady-state probabilities of the system. Finally, we obtain the computational formula for the service level and we present an optimization of a staffing problem.


Multi-skill call center Queuing model Steady-state probabilities Service level Optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Koole, G., Mandelbaum, A.: Queueing models of call centers: an introduction. Annals of Operations Research 113, 41–59 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Gans, N., Koole, G., Mandelbaum, A.: Telephone call centers: tutorial, review, and research prospects. Manufacturing & Service Operation Management 5(2), 79–141 (2003)CrossRefGoogle Scholar
  3. 3.
    Aksin, Z., Armony, M., Mehrotra, V.: The modern call-center: a multi-disciplinary perspective on operations management research. Production and Operations Management 16, 655–688 (2007)Google Scholar
  4. 4.
    Perry, M., Nilsson A.: Performance modeling of automatic call distributors: assignable grade of service staffing. In: Proceedings of the 14th International Switching Symposium, pp. 294–298 (1992)Google Scholar
  5. 5.
    Bhulai, S., Koole, G.: A queueing model for call blending in call centers. IEEE Transactions on Automatic Control 48, 1434–1438 (2003)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gans, N., Zhou, Y.: A call-routing problem with service-level constraints. Operations Research 51(2), 255–271 (2003)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Örmeci, L.E.: Dynamic admission control in a call center with one shared and two dedicated service facilities. IEEE Transactions on Automatic Control 49(7), 1157–1161 (2004)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Gross, D., Harris, C.M.: Fundamentals of Queueing Theory, 2nd edn. Wiley, New York (1985)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.College of ScienceYanshan UniversityQinhuangdaoChina
  2. 2.School of Economics and ManagementYanshan UniversityQinhuangdaoChina
  3. 3.Zhijiang College of Zhejiang University of TechnologyHangzhouChina
  4. 4.Department of Intelligence and InformaticsKonan UniversityKobeJapan

Personalised recommendations