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Geom/G1, G2/1/1 repairable Erlang loss system with catastrophe and second optional service

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Abstract

This paper studies a single server discrete-time Erlang loss system with Bernoulli arrival process and no waiting space. The server in the system is assumed to provide two different types of services, namely essential and optional services, to the customer. During the operation of the system, the arrival of the catastrophe will break the system down and simultaneously induce customer to leave the system immediately. Using a new type discrete supplementary variable technique, the authors obtain some performance characteristics of the queueing system, including the steady-state availability and failure frequency of the system, the steady-state probabilities for the server being idle, busy, breakdown and the loss probability of the system etc. Finally, by the numerical examples, the authors study the influence of the system parameters on several performance measures.

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Author information

Authors and Affiliations

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

    Yinghui Tang & Miaomiao Yu

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

    Miaomiao Yu

  3. Department of Information and Computer Science, Chengdu Electro-Mechanical College, Chengdu, 610032, China

    Cailiang Li

Authors
  1. Yinghui Tang
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  2. Miaomiao Yu
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  3. Cailiang Li
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Corresponding author

Correspondence to Yinghui Tang.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 70871084, Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 200806360001, and the Scientific Research Fund of Sichuan Provincial Education Department under Grant No. 10ZA136.

This paper was recommended for publication by Editor Shouyang WANG.

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Tang, Y., Yu, M. & Li, C. Geom/G1, G2/1/1 repairable Erlang loss system with catastrophe and second optional service. J Syst Sci Complex 24, 554–564 (2011). https://doi.org/10.1007/s11424-011-8339-2

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  • DOI: https://doi.org/10.1007/s11424-011-8339-2

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