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Number Of Retrials In A Finite Source Retrial Queue With Unreliable Server

Author

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  • VELIKA I. DRAGIEVA

    (Department of Mathematics and Physics, University of Forestry, 10 Kliment Ohridski Boulevard, Sofia 1756, Bulgaria)

Abstract

The object of this paper is to continue investigation of a single server retrial queue with finite number of sources in which the server is subjected to breakdowns and repairs. The server life time as well as the intervals between repetitions are exponentially distributed, while the repair and the service times are generally distributed. Using the formulas for the stationary system state distributions, obtained by Wang et al. [in Wang, J, L Zhao and F Zhang (2011). Analysis of the finite source retrial queues with server breakdowns and repairs. Journal of Industrial and Management Optimization, 7, 655–676.] we investigate the distribution of the number of retrials, made by a customer before he reaches the server free. Recurrent schemes for computing this distribution in steady state as well as any arbitrary of its moments are established. Numerical results for five different distributions of the service and repair times are also presented.

Suggested Citation

  • Velika I. Dragieva, 2014. "Number Of Retrials In A Finite Source Retrial Queue With Unreliable Server," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-23.
    • Handle: RePEc:wsi:apjorx:v:31:y:2014:i:02:n:s0217595914400053
    DOI: 10.1142/S0217595914400053
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    Cited by:

    1. Anatoly Nazarov & János Sztrik & Anna Kvach & Tamás Bérczes, 2019. "Asymptotic analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs," Annals of Operations Research, Springer, vol. 277(2), pages 213-229, June.
    2. Anatoly Nazarov & János Sztrik & Anna Kvach & Ádám Tóth, 2020. "Asymptotic sojourn time analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs," Annals of Operations Research, Springer, vol. 288(1), pages 417-434, May.
    3. Anatoly Nazarov & János Sztrik & Anna Kvach & Ádám Tóth, 2022. "Asymptotic Analysis of Finite-Source M/GI/1 Retrial Queueing Systems with Collisions and Server Subject to Breakdowns and Repairs," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1503-1518, September.

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