Queueing System MAP/M/N as a Model of Call Center with Call-Back Option

  • Chesoong Kim
  • Olga Dudina
  • Alexander Dudin
  • Sergey Dudin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7314)


A multi-server queueing system with a Markovian Arrival Process (MAP), an infinite buffer and impatient customers useful in modeling a call center with a call-back option is investigated. The service time of a customer by a server has an exponential distribution. If all servers are busy at a 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, the real customer can be impatient and can leave the system without the service or request for call-back (becomes a virtual customer). An efficient algorithm for calculating the stationary probabilities of system states is proposed. Some key performance measures are calculated. The Laplace-Stieltjes transform of the sojourn time distribution for virtual customers is derived. Some numerical results are presented.


Call Center Call-Back Markovian Arrival Process Multi-Server Queueing System 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Chesoong Kim
    • 1
  • Olga Dudina
    • 2
  • Alexander Dudin
    • 2
  • Sergey Dudin
    • 2
  1. 1.Sangji UniversityWonjuKorea
  2. 2.Belarusian State UniversityMinskBelarus

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