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Multi-server queueing system with a generalized phase-type service time distribution as a model of call center with a call-back option

Author

Listed:
  • Alexander Dudin

    (Belarusian State University)

  • Chesoong Kim

    (Sangji University)

  • Olga Dudina

    (Belarusian State University)

  • Sergey Dudin

    (Belarusian State University)

Abstract

A multi-server queueing system with a Markovian arrival process and finite and infinite buffers to model a call center with a call-back option is investigated. If all servers are busy during the customer arrival epoch, the customer may leave the system forever or move to the buffer (such a customer is referred to as a real customer), or, alternatively, request for call-back (such a customer is referred to as a virtual customer). During a waiting period, a real customer can be impatient and may leave the system without service or request for call-back (becomes a virtual customer). The service time of a customer and the dial time to a virtual customer for a server have a phase-type distribution. To simplify the investigation of the system we introduce the notion of a generalized phase-type service time distribution. We determine the stationary distribution of the system states and derive the Laplace–Stieltjes transforms of the sojourn and waiting time distributions for real and virtual customers. Some key performance measures are calculated and numerical results are presented.

Suggested Citation

  • Alexander Dudin & Chesoong Kim & Olga Dudina & Sergey Dudin, 2016. "Multi-server queueing system with a generalized phase-type service time distribution as a model of call center with a call-back option," Annals of Operations Research, Springer, vol. 239(2), pages 401-428, April.
    • Handle: RePEc:spr:annopr:v:239:y:2016:i:2:d:10.1007_s10479-014-1626-2
    DOI: 10.1007/s10479-014-1626-2
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    References listed on IDEAS

    as
    1. Che Kim & Vilena Mushko & Alexander Dudin, 2012. "Computation of the steady state distribution for multi-server retrial queues with phase type service process," Annals of Operations Research, Springer, vol. 201(1), pages 307-323, December.
    2. Mor Armony & Constantinos Maglaras, 2004. "On Customer Contact Centers with a Call-Back Option: Customer Decisions, Routing Rules, and System Design," Operations Research, INFORMS, vol. 52(2), pages 271-292, April.
    3. Ger Koole & Avishai Mandelbaum, 2002. "Queueing Models of Call Centers: An Introduction," Annals of Operations Research, Springer, vol. 113(1), pages 41-59, July.
    4. Mor Armony & Constantinos Maglaras, 2004. "Contact Centers with a Call-Back Option and Real-Time Delay Information," Operations Research, INFORMS, vol. 52(4), pages 527-545, August.
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    Cited by:

    1. Yi Peng, 2017. "On the MAP/PH/c retrial queueing system with two types of nonpersistent calls," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 537-557, September.
    2. A. N. Dudin & S. A. Dudin & O. S. Dudina, 2023. "Randomized Threshold Strategy for Providing Flexible Priority in Multi-Server Queueing System with a Marked Markov Arrival Process and Phase-Type Distribution of Service Time," Mathematics, MDPI, vol. 11(12), pages 1-23, June.
    3. Sally McClean, 2021. "Using Markov Models to Characterize and Predict Process Target Compliance," Mathematics, MDPI, vol. 9(11), pages 1-12, May.

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