Erik Chromy, Ivan Baronak



Mathematical Model of the Contact Center

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The paper deals with the contact center modeling with emphasis on the optimal number of agents. The contact center belongs to the queueing systems and its mathematical model can be described by various quality of service parameters. The Erlang C formula is a suitable tool for the modeling of QoS parameters of contact centers. The contact center consist of IVR system and service groups and we propose also two new parameters – downtime and administrative task duration. These parameters are useful for better determination of the optimal number of contact center agents. Based on these parameters we propose a mathematical model for contact centers also with repeated calls.


Contact Center, Erlang C Formula, Interactive Voice Response, Optimization, Quality of Service


[1] G. Bolch, “Queueing Networks and Markov Chains - Modeling and Performance Evaluation with Computer Science Applications,” 2nd ed., New Jersey: John Wiley & Sons, 2006.

[2] A. Budhiraja, A. Ghosh and X. Liu, “Scheduling control for Markov-modulated single-server multiclass queueing systems in heavy traffic,” Queueing Systems, vol. 78, no. 1, pp. 57– 97, 2014.

[3] B. Buke and H. Chen, “Stabilizing policies for probabilistic matching systems,” Queueing Systems, vol. 80, no. 1-2, pp. 35–69, 2015.

[4] V. Shah and G. de Veciana, “Asymptotic independence of servers activity in queueing systems with limited resource pooling,” Queueing Systems, vol. 83, no. 1, pp. 13–28, 2016.

[5] M. Budhiraja, “Invariance of workload in queueing systems,” Queueing Systems, vol. 83, no. 1, pp. 181–192, 2016.

[6] A. Kovac, M. Halas and M. Orgon, “E-model MOS estimate improvement through jitter buffer packet loss modelling,” Advances in Electrical and Electronic Engineering, vol. 9, no. 5, pp. 233–242, 2011.

[7] J. Misurec and M. Orgon, “Modeling of power line transfer of data for computer simulation,” International Journal of Communication Networks and Information Security, vol. 3, no. 2, pp. 104-111, 2011.

[8] H.S. Nguyen, T.-S. Nguyen and M. Voznak, “Successful transmission probability of cognitive device-to-device communications underlaying cellular networks in the presence of hardware impairments,” Eurasip Journal on Wireless Communications and Networking, vol. 2017, no. 1, 2017, Article number 208.

[9] S. Klucik and M. Lackovic, “Modelling of H.264 MPEG2 TS traffic source, ” Advances in Electrical and Electronic Engineering, vol. 11, no. 5, pp. 404–409, 2013.

[10] R. Roka, “The environment of fixed transmission media and their negative influences in the simulation,” International Journal of Mathematics and Computers in Simulation, vol. 9, pp. 190–205, 2015.

[11] F. Certik and R. Roka, “Possibilities for Advanced Encoding Techniques at Signal Transmission in the Optical Transmission Medium,” Journal of Engineering (United States), vol. 2016.

[12] J. Frnda, M. Voznak and L. Sevcik, “Impact of packet loss and delay variation on the quality of real-time video streaming,” Telecommunication Systems, vol. 62, no. 2, pp. 265–275, 2016.

[13] A. Brezavscek and A. Baggia, “Optimization of a Call Centre Performance Using the Stochastic Queueing Models,” Business Systems Research, vol. 5, no. 3, pp. 6–18, 2014.

[14] S. Ding, G. Koole and R. D. Mei, “On the Estimation of the True Demand in Call Centers with Redials and Reconnects,” European Journal of Operational Research, vol. 246, no. 1, pp. 250– 262, 2015.

[15] J. Zan, J. Hasenbein and D. Morton, “Asymptotically optimal staffing of service systems with joint QoS constraints,” Queueing Systems, vol. 78, no. 4, pp. 359–386, 2014.

[16] B. Legros, O. Jouini and G. Koole, “Optimal scheduling in call centers with a callback option,” Performance Evaluation, vol. 95, pp. 1– 40, 2016.

[17] G. Koole, B. Nielsen and T. Nielsen, “Optimization of overflow policies in call centers. Probability in the Engineering and Informational Sciences,” Cambridge University Press, vol. 29, no. 3, pp. 461–471, 2015.

[18] J. F. Hayes, “Modeling and Analysis of Telecommunications Networks,” New Jersey: John Wiley & Sons, 2004.

[19] E. Chromy, T. Misuth and M. Kavacky, “Erlang C Formula and Its Use In the Call Centers,” Advances in Electrical and Electronic Engineering, vol. 9, no. 1, pp. 7–13, 2011.

[20] J. P. C. Blanc, “Queueing Models: Analytical and Numerical Methods. Course 35M2C8,” Departement of Econometrics and Operations Research, 226 p., 2011.

Cite this paper

Erik Chromy, Ivan Baronak. (2018) Mathematical Model of the Contact Center. International Journal of Internet of Things and Web Services, 3, 17-23


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