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A Discrete‐Time Geo/G/1 Retrial Queue with J Vacations and Two Types of Breakdowns

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  • Feng Zhang
  • Zhifeng Zhu

Abstract

This paper is concerned with a discrete‐time Geo/G/1 retrial queueing model with J vacations and two types of breakdowns. If the orbit is empty, the server takes at most J vacations repeatedly until at least one customer appears in the orbit upon returning from a vacation. It is assumed that the server is subject to two types of different breakdowns and is sent immediately for repair. We analyze the Markov chain underlying the considered queueing system and derive the system state distribution as well as the orbit size and the system size distributions in terms of their generating functions. Then, we obtain some performance measures through the generating functions. Moreover, the stochastic decomposition property and the corresponding continuous‐time queueing system are investigated. Finally, some numerical examples are provided to illustrate the effect of vacations and breakdowns on several performance measures of the system.

Suggested Citation

  • Feng Zhang & Zhifeng Zhu, 2013. "A Discrete‐Time Geo/G/1 Retrial Queue with J Vacations and Two Types of Breakdowns," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:834731
    DOI: 10.1155/2013/834731
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    References listed on IDEAS

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    1. Li, Hui & Yang, Tao, 1995. "A single-server retrial queue with server vacations and a finite number of input sources," European Journal of Operational Research, Elsevier, vol. 85(1), pages 149-160, August.
    2. 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.
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    Cited by:

    1. Shunfu Jin & Wuyi Yue & Xiaofei Zhang, 2014. "Performance Analysis of the Sleep Mode in WiMAX 2 Networks with Multimedia Application," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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