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Reliability indices of discrete-time Geox/G/1 queueing system with unreliable service station and multiple adaptive delayed vacations

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Abstract

This paper considers the discrete-time GeoX/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research. Following problems will be discussed: 1) The probability that the server is in a “generalized busy period” at time n; 2) The probability that the service station is in failure at time n, i.e., the transient unavailability of the service station, and the steady state unavailability of the service station; 3) The expected number of service station failures during the time interval (0, n], and the steady state failure frequency of the service station; 4) The expected number of service station breakdowns in a server’s “generalized busy period”. Finally, the authors demonstrate that some common discrete-time queueing models with unreliable service station are special cases of the model discussed in this paper.

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Author information

Authors and Affiliations

  1. School of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, China

    Yinghui Tang

  2. School of Science, Sichuan University of Science and Engineering, Zigong, 643000, China

    Miaomiao Yu

  3. School of Mathematics, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Xi Yun & Shujuan Huang

Authors
  1. Yinghui Tang
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  2. Miaomiao Yu
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  3. Xi Yun
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  4. Shujuan Huang
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Corresponding author

Correspondence to Yinghui Tang.

Additional information

This research was supported in part by the National Natural Science Foundation of China under Grant Nos. 71171138, 70871084, and the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 200806360001.

This paper was recommended for publication by Editor Hanqin ZHANG.

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Tang, Y., Yu, M., Yun, X. et al. Reliability indices of discrete-time Geox/G/1 queueing system with unreliable service station and multiple adaptive delayed vacations. J Syst Sci Complex 25, 1122–1135 (2012). https://doi.org/10.1007/s11424-012-1062-9

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  • DOI: https://doi.org/10.1007/s11424-012-1062-9

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