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Analysis of G-Queue with Pseudo-Fault and Multiple Working Vacations

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Abstract

This paper presents a new model of discrete time Geo/Geo/1 repairable queueing system with pseudo-fault, negative customers and multiple working vacations. The authors assume that system service may be interrupted by breakdown or pseudo-fault, this system may become disabled only when it is in a regular busy period, and negative customers adopt two types of typical killing strategies. In this paper, the authors know that the evolution of the system can be described by a two-dimensional Markov chain, and the two-dimensional Markov chain satisfies the condition of quasi birth and death chains. Based on the method of matrix-geometric solution, the authors obtain distributions for the stationary queue length in RCH and RCE strategy, respectively. Moreover, the reliability of the system is analyzed and the number of customers and waiting time of a customer in the system in steady state are obtained. The authors analyze the impact of two killing strategies on the system comparatively. This paper studies the individually and socially optimal behaviors of positive customers, and presents a pricing policy for positive customers, therefore, the authors obtain the socially optimal arrival rate. Various numerical results are provided to show the change of performance measures.

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Author information

Authors and Affiliations

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

    Zhanyou Ma

  2. LiRen College, Yanshan University, Qinhuangdao, 066004, China

    Li Chen

  3. School of Transportation Science and Engineering, Beihang University, Beijing, 100000, China

    Pengcheng Wang

Authors
  1. Zhanyou Ma
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  2. Li Chen
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  3. Pengcheng Wang
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Corresponding author

Correspondence to Zhanyou Ma.

Additional information

This paper was supported by the National Natural Science Foundation of China under Grant Nos. 61973261, 61872311, the Natural Science Foundation of Hebei Province under Grant No. A2018203088, Key Foundation of Higher Education Science and Technology Research of Hebei Province under Grant No. ZD2017079.

This paper was recommended for publication by Editor WANG Shouyang.

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Ma, Z., Chen, L. & Wang, P. Analysis of G-Queue with Pseudo-Fault and Multiple Working Vacations. J Syst Sci Complex 33, 1144–1162 (2020). https://doi.org/10.1007/s11424-020-8117-0

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  • DOI: https://doi.org/10.1007/s11424-020-8117-0

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