Applications of maximum queue lengths to call center management. (English) Zbl 1102.90015
Summary: This paper deals with the distribution of the maximum queue length in two-dimensional Markov models. In this framework, two typical assumptions are: (1) the stationary regime, and (2) the system homogeneity (i.e., homogeneity of the underlying infinitesimal generator). In the absence of these assumptions, the computation of the stationary queue length distribution becomes extremely intricate or, even, intractable. The use of maximum queue lengths provides an alternative queueing measure overcoming these problems. We apply our results to some problems arising from call center management.
MSC:
| 90B22 | Queues and service in operations research |
Keywords:
call center; maximum queue length; level dependent quasi-birth-and-death processes; customer behavior; routing rulesReferences:
| [1] | Gans, N.; Koole, G.; Mandelbaum, A., Telephone call centerstutorial, review and research prospects, Manufacturing and Service Operations Management, 5, 79-141 (2003) |
| [2] | Koole, G.; Mandelbaum, A., Queueing models of call centersan introduction, Annals of Operations Research, 113, 41-59 (2002) · Zbl 1013.90090 |
| [3] | Brandt A, Brandt M, Spahl G, Weber D. Modelling and optimization of call distribution systems. In: Ramaswami, V, Wirth, PE. editors, Proceedings of the 15th International Teletraffic Congress. Elsevier Science B.V., 1997. p.133-144.; Brandt A, Brandt M, Spahl G, Weber D. Modelling and optimization of call distribution systems. In: Ramaswami, V, Wirth, PE. editors, Proceedings of the 15th International Teletraffic Congress. Elsevier Science B.V., 1997. p.133-144. |
| [4] | Srinivasan, R.; Talim, J.; Wang, J., Performance analysis of a call center with interactive voice response units, Top, 12, 91-110 (2004) · Zbl 1076.60083 |
| [5] | Aguir, S.; Karaesmen, F.; Akşin, O. Z.; Chauvet, F., The impact of retrials on call center performance, OR Spectrum, 26, 353-376 (2004) · Zbl 1109.90019 |
| [6] | Whitt, W., Improving service by informing customers about anticipated delays, Management Science, 45, 192-207 (1999) · Zbl 1231.90285 |
| [7] | Falin, G. I.; Templeton, J. G.C., Retrial queues (1997), Chapman and Hall: Chapman and Hall London · Zbl 0944.60005 |
| [8] | Artalejo, J. R., Accessible bibliography on retrial queues, Mathematical and Computer Modelling, 30, 1-6 (1999) · Zbl 1009.90001 |
| [9] | Serfozo, R. F., Extreme values of birth and death processes and queues, Stochastic Processes and their Applications, 27, 291-306 (1988) · Zbl 0637.60098 |
| [10] | Neuts, M. F., The distribution of the maximum length of a Poisson queue during a busy period, Operations Research, 12, 281-285 (1964) · Zbl 0127.35101 |
| [11] | Masi, D. M.B.; Fischer, M. J.; Harris, C. M., Computation of steady-state probabilities for resource-sharing call-center queueing systems, Stochastic Models, 17, 191-214 (2001) · Zbl 0994.90014 |
| [12] | Shumsky, R. A., Approximation and analysis of a call center with flexible and specialized servers, OR Spectrum, 26, 307-330 (2004) · Zbl 1109.90025 |
| [13] | Latouche, G.; Ramaswami, V., Introduction to Matrix Analytic Methods in Stochastic Modeling (1999), ASA-SIAM: ASA-SIAM Philadelphia · Zbl 0922.60001 |
| [14] | Artalejo JR, Economou A, Lopez-Herrero MJ. Algorithmic analysis of the maximum queue length in a busy period for the \(M / M / c\); Artalejo JR, Economou A, Lopez-Herrero MJ. Algorithmic analysis of the maximum queue length in a busy period for the \(M / M / c\) · Zbl 1241.90028 |
| [15] | Green, L., A queueing system with general-use and limited-use servers, Operations Research, 33, 168-182 (1985) · Zbl 0587.60092 |
| [16] | Stanford, D. A.; Grassmann, W. K., The bilingual server system: a queueing model featuring fully and partially qualified servers, INFOR, 31, 261-277 (1993) · Zbl 0799.90056 |
| [17] | Ciarlet, P. G., Introduction to Numerical Linear Algebra and Optimization (1989), Cambridge University Press: Cambridge University Press Cambridge |
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