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A DISCRETE-TIMEGeo/G/1RETRIAL QUEUE WITH SERVER BREAKDOWNS

Author

Listed:
  • IVAN ATENCIA

    (Departamento de Matemática Aplicada, E.T.S.I. de Telecomunicación, Universidad de Málaga, Málaga 29071, Spain)

  • PILAR MORENO

    (Departamento de Economía, Métodos Cuantitativos, e Historia Económica, Facultad de Ciencias Empresariales, Universidad Pablo de Olavide, Sevilla 41013, Spain)

Abstract

This paper discusses a discrete-timeGeo/G/1retrial queue with the server subject to breakdowns and repairs. The customer just being served before server breakdown completes his remaining service when the server is fixed. The server lifetimes are assumed to be geometrical and the server repair times are arbitrarily distributed. We study the Markov chain underlying the considered queueing system and present its stability condition as well as some performance measures of the system in steady-state. Then, we derive a stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions of our system and the corresponding system without retrials. Also, we introduce the concept of generalized service time and develop a recursive procedure to obtain the steady-state distributions of the orbit and system size. Finally, we prove the convergence to the continuous-time counterpart and show some numerical results.

Suggested Citation

  • Ivan Atencia & Pilar Moreno, 2006. "A DISCRETE-TIMEGeo/G/1RETRIAL QUEUE WITH SERVER BREAKDOWNS," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 247-271.
    • Handle: RePEc:wsi:apjorx:v:23:y:2006:i:02:n:s0217595906000929
    DOI: 10.1142/S0217595906000929
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    Citations

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    Cited by:

    1. Lan Shaojun & Tang Yinghui, 2017. "Performance Analysis of a Discrete-Time Queue with Working Breakdowns and Searching for the Optimum Service Rate in Working Breakdown Period," Journal of Systems Science and Information, De Gruyter, vol. 5(2), pages 176-192, April.
    2. Rein Nobel, 2016. "Retrial queueing models in discrete time: a short survey of some late arrival models," Annals of Operations Research, Springer, vol. 247(1), pages 37-63, December.

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