Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Kim, J.W., Park, S.C.: Outsourcing strategy in two-stage call centers. Computers & Operations Research 37, 790–805 (2010)
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, 03.021
Dudin, S., Dudina, O.: Call center operation model as a MAP/PH/N/R − N system with impatient customers. Problems of Information Transmission 47, 364–377 (2011)
Kim, C., Dudin, A., Klimenok, V., Khramova, V.: Erlang loss queueing system with batch arrivals operating in a random environment. Computers & Operations Research 36(3), 674–697 (2009)
Kim, C., Klimenok, V., Mushko, V., Dudin, A.: The BMAP/PH/N retrial queueing system operating in Markovian random environment. Computers & Operations Research 37(7), 1228–1237 (2010)
He, Q.M.: Queues with marked customers. Advances in Applied Probability 28, 567–587 (1996)
Kim, C.S., Dudin, S.A.: Priority tandem queueing model with admission control. Computers & Industrial Engineering 61, 131–140 (2011)
Cleveland, B.: Call center management on fast forward: succeeding in today’s dynamic customer contact environment. In: ICMI (2006)
Graham, A.: Kronecker products and matrix calculus with applications. Ellis Horwood, Cichester (1981)
Kesten, H., Runnenburg, J.T.: Priority in waiting line problems. Mathematisch Centrum, Amsterdam (1956)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dudina, O., Dudin, S. (2013). Queueing System MAP/M/N/N + K Operating in Random Environment as a Model of Call Center. In: Dudin, A., Klimenok, V., Tsarenkov, G., Dudin, S. (eds) Modern Probabilistic Methods for Analysis of Telecommunication Networks. BWWQT 2013. Communications in Computer and Information Science, vol 356. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35980-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-35980-4_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35979-8
Online ISBN: 978-3-642-35980-4
eBook Packages: Computer ScienceComputer Science (R0)