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A functional approximation for retrial queues with two way communication

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  • Sofiane Ouazine

    (University of Bejaia)

  • Karim Abbas

    (University of Bejaia)

Abstract

In this paper we consider retrial queues with two way communication and finite orbit. We will develop a functional approximation of the stationary performances of this queue where the parameter of interest is the outgoing rate. Specifically, we will apply the Taylor series expansion method to propagate parametric uncertainty to performance measures. We provide an analysis of the $$\hbox {M}_{1},\, \hbox {M}_{2}/\hbox {G}_{1},\, \hbox {G}_{2}/1$$ M 1 , M 2 / G 1 , G 2 / 1 retrial queue with two way communication and finite orbit. The sensitivity analysis is carried out by considering several numerical examples. More specifically, this paper proposes a numerical approach based on Taylor series expansion with a statistical aspect for analyzing the stationary performances of the considered queueing model, where we assume that the outgoing rate is not assessed in a perfect manner. Additionally, approximate expressions of the probability density functions, the expectation and the variance of the performance measures are obtained and compared to the corresponding Monte Carlo simulations results.

Suggested Citation

  • Sofiane Ouazine & Karim Abbas, 2016. "A functional approximation for retrial queues with two way communication," Annals of Operations Research, Springer, vol. 247(1), pages 211-227, December.
    • Handle: RePEc:spr:annopr:v:247:y:2016:i:1:d:10.1007_s10479-015-2083-2
    DOI: 10.1007/s10479-015-2083-2
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    References listed on IDEAS

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    1. Srinivas R. Chakravarthy & Alexander N. Dudin & Valentina I. Klimenok, 2010. "A Retrial Queueing Model With Map Arrivals, Catastrophic Failures With Repairs, And Customer Impatience," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(06), pages 727-752.
    2. Yang, T. & Posner, M. J. M. & Templeton, J. G. C. & Li, H., 1994. "An approximation method for the M/G/1 retrial queue with general retrial times," European Journal of Operational Research, Elsevier, vol. 76(3), pages 552-562, August.
    3. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    4. Artalejo, J. R. & Gomez-Corral, A. & Neuts, M. F., 2001. "Analysis of multiserver queues with constant retrial rate," European Journal of Operational Research, Elsevier, vol. 135(3), pages 569-581, December.
    5. J.R. Artalejo & M. Pozo, 2002. "Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue," Annals of Operations Research, Springer, vol. 116(1), pages 41-56, October.
    6. 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.
    7. J. R. Artalejo & J. A. C. Resing, 2010. "Mean Value Analysis Of Single Server Retrial Queues," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(03), pages 335-345.
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    Cited by:

    1. Muthukrishnan Senthil Kumar & Aresh Dadlani & Kiseon Kim, 2020. "Performance analysis of an unreliable M/G/1 retrial queue with two-way communication," Operational Research, Springer, vol. 20(4), pages 2267-2280, December.

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