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On retrial queueing model with fuzzy parameters

Author

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  • Ke, Jau-Chuan
  • Huang, Hsin-I
  • Lin, Chuen-Horng

Abstract

This work constructs the membership functions of the system characteristics of a retrial queueing model with fuzzy customer arrival, retrial and service rates. The α-cut approach is used to transform a fuzzy retrial-queue into a family of conventional crisp retrial queues in this context. By means of the membership functions of the system characteristics, a set of parametric non-linear programs is developed to describe the family of crisp retrial queues. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the system characteristics are expressed and governed by the membership functions, more information is provided for use by management. By extending this model to the fuzzy environment, fuzzy retrial-queue is represented more accurately and analytic results are more useful for system designers and practitioners.

Suggested Citation

  • Ke, Jau-Chuan & Huang, Hsin-I & Lin, Chuen-Horng, 2007. "On retrial queueing model with fuzzy parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 272-280.
    • Handle: RePEc:eee:phsmap:v:374:y:2007:i:1:p:272-280
    DOI: 10.1016/j.physa.2006.05.057
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    References listed on IDEAS

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    1. Chen, Shih-Pin, 2004. "Parametric nonlinear programming for analyzing fuzzy queues with finite capacity," European Journal of Operational Research, Elsevier, vol. 157(2), pages 429-438, September.
    2. Chen, Shih-Pin, 2005. "Parametric nonlinear programming approach to fuzzy queues with bulk service," European Journal of Operational Research, Elsevier, vol. 163(2), pages 434-444, June.
    3. J. Artalejo, 1999. "A classified bibliography of research on retrial queues: Progress in 1990–1999," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 187-211, December.
    4. Dudin, A. N. & Krishnamoorthy, A. & Joshua, V. C. & Tsarenkov, G. V., 2004. "Analysis of the BMAP/G/1 retrial system with search of customers from the orbit," European Journal of Operational Research, Elsevier, vol. 157(1), pages 169-179, August.
    5. Diamond, Jeffrey E. & Alfa, Attahiru Sule, 1999. "Approximation method for M/PH/1 retrial queues with phase type inter-retrial times," European Journal of Operational Research, Elsevier, vol. 113(3), pages 620-631, March.
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    Cited by:

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    3. Sanga, Sudeep Singh & Jain, Madhu, 2019. "FM/FM/1 double orbit retrial queue with customers’ joining strategy: A parametric nonlinear programing approach," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    4. Blanc, J.P.C. & den Hertog, D., 2008. "On Markov Chains with Uncertain Data," Discussion Paper 2008-50, Tilburg University, Center for Economic Research.

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