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A discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times

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Abstract

The authors discuss a discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times. As soon as the orbit is empty, the server takes a vacation. However, the server is allowed to take a maximum number J of vacations, if the system remains empty after the end of a vacation. If there is at least one customer in the orbit at the end of a vacation, the server begins to serve the new arrivals or the arriving customers from the orbit. For this model, the authors focus on the steady-state analysis for the considered queueing system. Firstly, the authors obtain the generating functions of the number of customers in the orbit and in the system. Then, the authors obtain the closed-form expressions of some performance measures of the system and also give a stochastic decomposition result for the system size. Besides, the relationship between this discrete-time model and the corresponding continuous-time model is also investigated. Finally, some numerical results are provided.

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Authors and Affiliations

  1. College of Science, Yanshan University, Qinhuangdao, 066004, China

    Dequan Yue

  2. College of Economics and Management, Yanshan University, Qinhuangdao, 066004, China

    Feng Zhang

  3. College of Science, North University of China, Taiyuan, 030051, China

    Feng Zhang

Authors
  1. Dequan Yue
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  2. Feng Zhang
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Correspondence to Dequan Yue.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 71071133.

This paper was recommended for publication by Editor ZHANG Hanqin.

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Yue, D., Zhang, F. A discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times. J Syst Sci Complex 26, 556–571 (2013). https://doi.org/10.1007/s11424-013-1121-x

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  • DOI: https://doi.org/10.1007/s11424-013-1121-x

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