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Inhomogeneous CTMC model of a call center with balking and abandonment

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Warianty tytułu
EN
Modelowanie call center jako systemu kolejkowego z wykorzystaniem łańcuchów markowa z niejednorodnym czasem ciągłym
Języki publikacji
EN
Abstrakty
EN
This paper considers a nonstationary multiserver queuing model with abandonment and balking for inbound call centers. We present a continuous time Markov chain (CTMC) model which captures the important characteristics of an inbound call center and obtain a numerical solution for its transient state probabilities using uniformization method with steady-state detection.
PL
Artykuł opisuje zastosowanie CTMC do modelowania Call Center z klientami o ograniczonej cierpliwości.
Czasopismo
Rocznik
Strony
23--34
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
  • West Pomeranian University of Technology, Applied Informatics
Bibliografia
  • 1. Aksin Z., Armony M., Mehrotra V.: The modern call center: A multi-disciplinary perspective on operations management research. Production and Operations Management 16(6) (Nov 2007), 665-688.
  • 2. Gans N., Koole G., Mandelbaum A.: Telephone call centers: Tutorial, review, and research prospects. Manufacturing & Service Operations Management 5(2) (Apr 2003), 79-141.
  • 3. Brown L., Gans N., Mandelbaum A., Sakov A., Shen H., Zeltyn S., Zhao L.: Statistical analysis of a telephone call center. Journal of the American Statistical Association 100(469) (Mar 2005), 36-50.
  • 4. Deslauriers A., L’Ecuyer P., Pichitlamken J., Ingolfsson A., Avramidis A. N.: Markov chain models of a telephone call center with call blending. Computers & Operations Research 34(6) (Jun 2007), 1616-1645.
  • 5. Phung-Duc T., Kawanishi K.: Performance analysis of call centers with abandonment, retrial and after-call work. Performance Evaluation 80 (Oct 2014), 43-62.
  • 6. Green L.V., Kolesar P.J., Whitt W.: Coping with time-varying demand when setting staffing requirements for a service system. Production and Operations Management 16(1) (Jan 2007), 13-39.
  • 7. Ingolfsson A., Campello F., Wu X., Cabral E.: Combining integer programming and the randomization method to schedule employees. European Journal of Operational Research 202(1) (Apr 2010), 153-163.
  • 8. Ingolfsson A., Akhmetshina E., Budge S., Li Y., Wu X.: A survey and experimental comparison of service-level-approximation methods for nonstationary m(t)/m/s(t) queueing systems with exhaustive discipline. INFORMS Journal on Computing 19(2) (May 2007), 201-214.
  • 9. Bylina J., Bylina B., Zoła A., Skaraczyński T.: A markovian model of a call center with time varying arrival rate and skill based routing. In: Computer Networks. Springer Science Business Media (2009), 26-33.
  • 10. Burak M.: Multi-step uniformization with steady-state detection in nonstationary m/m/s queuing systems. arXiv preprint arXiv:1410.0804 (2014).
  • 11. Czachórski T., Fourneau J. M., Nycz T., Pekergin F.: Diffusion approximation model of multiserver stations with losses. Electronic Notes in Theoretical Computer Science 232 (Mar 2009), 125-143.
  • 12. Czachórski T., Nycz T., Nycz M., Pekergin F.: Traffic engineering: Erlang and engset models revisited with diffusion approximation. In: Information Sciences and Systems 2014. Springer Science – Business Media (2014), 249-256.
  • 13. Mandelbaum A., Zeltyn S.: Staffing many-server queues with impatient customers: Constraint satisfaction in call centers. Operations Research 57(5) (Oct 2009),1189-1205.
  • 14. Whitt W.: Sensitivity of performance in the Erlang-a queueing model to changes in the model parameters. Operations Research 54(2) (Apr 2006), 247-260.
  • 15. Artalejo J., Pla V.: On the impact of customer balking, impatience and retrials in telecommunication systems. Computers & Mathematics with Applications 57(2) (Jan 2009), 217-229.
  • 16. Rindos A., Woolet S., Viniotis I., Trivedi K.: Exact methods for the transient analysis of nonhomogeneous continuous time Markov chains. In: Computations with Markov Chains. Springer US (1995), 121-133.
  • 17. Gross D., Miller D. R.: The randomization technique as a modeling tool and solution procedure for transient Markov processes. Operations Research 32(2) (Apr 1984), 343-361.
  • 18. Van Dijk N. M.: Uniformization for nonhomogeneous Markov chains. Operations Research Letters 12(5) (Nov 1992), 283-291.
  • 19. Van Moorsel A.P., Wolter K.: Numerical solution of non-homogeneous Markov processes through uniformization. In: ESM. (1998), 710-717.
  • 20. Arns M., Buchholz P., Panchenko A.: On the numerical analysis of inhomogeneous continuous-time Markov chains. INFORMS Journal on Computing 22(3) (Aug 2010), 416-432.
  • 21. Andreychenko A., Crouzen P., Mikeev L., Wolf V.: On-the-fly uniformization of timeinhomogeneous infinite Markov population models. arXiv preprint:1006.4425 (2010).
  • 22. Grassmann W.: Transient solutions in markovian queueing systems. Computers & Operations Research 5(2) (Jan 1978), 161.
  • 23. Reibman A., Trivedi K.: Numerical transient analysis of Markov models. Computers & Operations Research 15(1) (Jan 1988), 19-36.
  • 24. Muppala J. K., Trivedi K. S.: Numerical transient solution of finite markovian queueing systems. Oxford Statistical Science Series (1992), 262-262.
  • 25. Malhotra M., Muppala J. K., Trivedi K. S.: Stiffness-tolerant methods for transient analysis of stiff Markov chains. Microelectronics Reliability 34(11) (Nov 1994), 1825-1841.
  • 26. Stewart W.J.: Probability, Markov chains, queues, and simulation: the mathematical basis of performance modeling. Princeton University Press (2009).
  • 27. Ò Leary D. P., Stewart G. W., Vandergraft J. S.: Estimating the largest eigenvalue of a positive definite matrix. Mathematics of Computation 33(148) (Oct 1979), 1289.
  • 28. Van Moorsel A., Sanders W.: Transient solution of Markov models by combining adaptive and standard uniformization. IEEE Transactions on Reliability 46(3) (1997), 430-440.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b5a88e83-817c-4d0f-8cbe-0587177723b6
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