Queueing System MAP/M/N/N + K Operating in Random Environment as a Model of Call Center

  • Olga Dudina
  • Sergey Dudin
Part of the Communications in Computer and Information Science book series (CCIS, volume 356)


A multi-server queueing system with a Markovian Arrival Process (MAP), a finite buffer and impatient customers operating in random environment as a model of a call center 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 with probability that depends on the number of customers in the buffer. During a waiting period, a customer can be impatient and can leave the system without the service. System parameters depend on the state of the random environment. An efficient algorithm for calculating the stationary probabilities of system states is proposed. Some key performance measures are calculated. The Laplace-Stieltjes transforms of the sojourn and waiting time distributions are derived.


call center Markovian arrival process random environment impatient customer 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Olga Dudina
    • 1
  • Sergey Dudin
    • 1
  1. 1.Belarusian State UniversityMinskBelarus

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