Queueing System MAP/M/N/N + K Operating in Random Environment as a Model of Call Center
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.
Keywordscall center Markovian arrival process random environment impatient customer
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- 1.Aksin, O.Z., Armony, M., Mehrotra, V.: The modern call centers: a multi-disciplinary perspective on operations management research. Production and Operation Management 16, 655–688 (2007)Google Scholar
- 3.Kim, C., Dudin, S., Taramin, O., Baek, J.: Queueing system MAP/PH/N/N + R with impatient heterogeneous customers as a model of call center. Applied Mathematical Modelling (2012) dx.doi.org/10.1016/j.apm, 03.021Google Scholar
- 9.Cleveland, B.: Call center management on fast forward: succeeding in today’s dynamic customer contact environment. In: ICMI (2006)Google Scholar
- 11.Kesten, H., Runnenburg, J.T.: Priority in waiting line problems. Mathematisch Centrum, Amsterdam (1956)Google Scholar
- 12.van Danzig, D.: Chaines de Markof dans les ensembles abstraits et applications aux processus avec regions absorbantes et au probleme des boucles. Ann. de l’Inst. H. Pioncare 14, 145–199 (1995)Google Scholar