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A Markovian Model of a Call Center with Time Varying Arrival Rate and Skill Based Routing

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Computer Networks (CN 2009)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 39))

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Abstract

The paper aims at construction and investigation of a practical model serving a call center performance evaluation. The system considered here consists of two queues and three agents’ classes. For such a system we develop a queuing model with the arrival (calling) rate varying with time and a continuous-time Markov chain (CTMC) which provide approximations of system performance measure. The results obtained from the CTMC are compared to results obtained from a simulation of a call-center. The models are applied to determine: average time of answer, probabilities of waiting in queues, average length of queues.

This work was partially supported within the project Metody i modele dla kontroli zatloczenia i oceny efektywnosci mechanizmow jakosci uslug w Internecie nastepnej generacji (N517 025 31/2997).

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References

  1. Bhulai, S., Koole, G.: A queueing model for call blending in call center. IEEE Trans. on Aut. Contr. 48, 1434–1438 (2003)

    Article  MathSciNet  Google Scholar 

  2. Bylina, J., Bylina, B.: Development of a distributed algorithm of matrix generation for Markovian models of congestion control and its performance analysis on a computer cluster. In: Contemporary Aspects of Computer Networks, Wydawnictwa Komunikacji i Łaczności, Warszawa, vol. 2, pp. 251–258 (2008)

    Google Scholar 

  3. Deslauriers, A., L’Ecuyer, P., Pichitlamken, J., Ingolfsson, A., Avramidis, A.N.: Markov chain models of a telephone call center with call blending. Computers & OR 34(6), 1616–1645 (2007)

    Article  MATH  Google Scholar 

  4. Gans, N., Koole, G., Mandelbaum, A.: Telephone Call Centers: tutorial. Review and Research Prospects, Manufact. and Service Oper. Manag. 5, 79–141 (2003)

    Google Scholar 

  5. Ingolfsson, A.: Modeling the M(t)/M/s(t) Queue with an Exhaustive Discipline (submitted)

    Google Scholar 

  6. Koole, G., Amndelbaum, A.: Queueing Models of Call Centers. An Introduction. Ann. of Oper. Res. 113, 41–55 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Perrone, L.F., Wieland, F.P., Liu, J., Lawson, B.G., Nicol, D.M., Fujimoto, R.M. (eds.): Variance Reduction in the Simulation of Call Centers. In: Proceedings of the 2006 Winter Simulation Conference (2006)

    Google Scholar 

  8. Pichitlamken, J., Deslauriers, A., L’Ecuyer, P., Avramidis, A.N.: Modelling and simulation of a telephone call center. In: Proceedings of the 2003 Winter Simulation Conference, pp. 1805–1812 (2003)

    Google Scholar 

  9. Skaraczyński, T., Zoła, A.: Komponentowy system modelowania kolejek w zastosowaniu do telefonicznych centrów obsługi. Współczesne aspekty sieci komputerowych, Wydawnictwa Komunikacji i Łaczności, Warszawa, vol. 1, pp. 89–96 (2008) (in Polish)

    Google Scholar 

  10. Skaraczyński, T., Zoła, A.: Optimizing employment in telephone call centers. Theor. and Appl. Inform. 20(1), 39–47 (2008)

    Google Scholar 

  11. Skaraczyński, T., Zoła, A., Bylina, J., Bylina, B.: Markovian method of modeling call-centers. In: Computer Science and Information Technologies (Proceedings of CSIT 2008), Lviv, pp. 51–54 (2008)

    Google Scholar 

  12. Stewart, W.J.: An Introduction to the Numerical Solution of Markov chains. Princeton University Press, New York (1994)

    MATH  Google Scholar 

  13. Whitt, W.: Engineering Solution of a Basic Call-Center Model. Manag. Sci. 51(2), 221–235 (2005)

    Article  MATH  Google Scholar 

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Bylina, J., Bylina, B., Zoła, A., Skaraczyński, T. (2009). A Markovian Model of a Call Center with Time Varying Arrival Rate and Skill Based Routing. In: Kwiecień, A., Gaj, P., Stera, P. (eds) Computer Networks. CN 2009. Communications in Computer and Information Science, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02671-3_4

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  • DOI: https://doi.org/10.1007/978-3-642-02671-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02670-6

  • Online ISBN: 978-3-642-02671-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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