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Mathematical Model of Call Center in the Form of Multi-Server Queueing System

Author

Listed:
  • Anatoly Nazarov

    (Institute of Applied Mathematics and Computer Science, Tomsk State University, 634050 Tomsk, Russia)

  • Alexander Moiseev

    (Institute of Applied Mathematics and Computer Science, Tomsk State University, 634050 Tomsk, Russia)

  • Svetlana Moiseeva

    (Institute of Applied Mathematics and Computer Science, Tomsk State University, 634050 Tomsk, Russia)

Abstract

The paper considers the model of a call center in the form of a multi-server queueing system with Poisson arrivals and an unlimited waiting area. In the model under consideration, incoming calls do not differ in terms of service conditions, requested service, and interarrival periods. It is assumed that an incoming call can use any free server and they are all identical in terms of capabilities and quality. The goal problem is to find the stationary distribution of the number of calls in the system for an arbitrary recurrent service. This will allow us to evaluate the performance measures of such systems and solve various optimization problems for them. Considering models with non-exponential service times provides solutions for a wide class of mathematical models, making the results more adequate for real call centers. The solution is based on the approximation of the given distribution function of the service time by the hyperexponential distribution function. Therefore, first, the problem of studying a system with hyperexponential service is solved using the matrix-geometric method. Further, on the basis of this result, an approximation of the stationary distribution of the number of calls in a multi-server system with an arbitrary distribution function of the service time is constructed. Various issues in the application of this approximation are considered, and its accuracy is analyzed based on comparison with the known analytical result for a particular case, as well as with the results of the simulation.

Suggested Citation

  • Anatoly Nazarov & Alexander Moiseev & Svetlana Moiseeva, 2021. "Mathematical Model of Call Center in the Form of Multi-Server Queueing System," Mathematics, MDPI, vol. 9(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2877-:d:677541
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    References listed on IDEAS

    as
    1. Ger Koole & Avishai Mandelbaum, 2002. "Queueing Models of Call Centers: An Introduction," Annals of Operations Research, Springer, vol. 113(1), pages 41-59, July.
    2. Ward Whitt, 2004. "A Diffusion Approximation for the G/GI/n/m Queue," Operations Research, INFORMS, vol. 52(6), pages 922-941, December.
    3. O. J. Boxma & J. W. Cohen & N. Huffels, 1979. "Approximations of the Mean Waiting Time in an M / G / s Queueing System," Operations Research, INFORMS, vol. 27(6), pages 1115-1127, December.
    4. Sem Borst & Avi Mandelbaum & Martin I. Reiman, 2004. "Dimensioning Large Call Centers," Operations Research, INFORMS, vol. 52(1), pages 17-34, February.
    5. Neuts, Marcel F., 1984. "Matrix-analytic methods in queuing theory," European Journal of Operational Research, Elsevier, vol. 15(1), pages 2-12, January.
    6. 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.
    7. Toshikazu Kimura, 1983. "Diffusion Approximation for an M / G / m Queue," Operations Research, INFORMS, vol. 31(2), pages 304-321, April.
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    Cited by:

    1. Anatoly Nazarov & Alexander Dudin & Alexander Moiseev, 2022. "Pseudo Steady-State Period in Non-Stationary Infinite-Server Queue with State Dependent Arrival Intensity," Mathematics, MDPI, vol. 10(15), pages 1-12, July.

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