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Analysis of batch arrival queue with randomized vacation policy and an un-reliable server

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Abstract

This paper examines an M[x]/G/1 queueing system with an unreliable server and a delayed repair, in which the server operates a randomized vacation policy with multiple vacations. Whenever the system is empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be immediately activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 −p. Whenever one or more customers arrive when the server is idle, the server immediately starts providing service for the arrivals. The server may also meet an unpredictable breakdown and the repair may be delayed. For such a system the authors derive the distributions of some important system characteristics, such as the system size distribution at a random epoch and at a departure epoch, the system size distribution at the busy period initiation epoch, and the distribution of the idle period and the busy period. The authors perform a numerical analysis for changes in the system characteristics, along with changes in specific values of the system parameters. A cost effectiveness maximization model is constructed to explain the benefits of such a queueing system.

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Authors and Affiliations

  1. Department of Applied Statistics, National Taichung University of Science and Technology, Taichung, 404, Taiwan, China

    Jau Chuan Ke

  2. Department of Engineering Information System Development, Ardebtec Corporation Ltd., Hsin Chu, Taiwan, 30351, China

    Kai Bin Huang

Authors
  1. Jau Chuan Ke
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  2. Kai Bin Huang
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Correspondence to Jau Chuan Ke.

Additional information

This paper was recommended for publication by Editor Shouyang WANG.

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Ke, J.C., Huang, K.B. Analysis of batch arrival queue with randomized vacation policy and an un-reliable server. J Syst Sci Complex 25, 759–777 (2012). https://doi.org/10.1007/s11424-012-9154-0

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  • DOI: https://doi.org/10.1007/s11424-012-9154-0

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