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Math. Comput. Appl. 2017, 22(1), 15; doi:10.3390/mca22010015

An M/G/1 Retrial G-Queue with General Retrial Times and Working Breakdowns

1
School of Science, Shandong University of Technology, Zibo 255049, China
2
School of Business, Shandong University of Technology, Zibo 255049, China
*
Author to whom correspondence should be addressed.
Academic Editor: Fazal M. Mahomed
Received: 4 October 2016 / Revised: 2 January 2017 / Accepted: 24 January 2017 / Published: 2 February 2017
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Abstract

This paper considers an M/G/1 retrial G-queue with general retrial times, in which the server is subject to working breakdowns and repairs. If the system is not empty during a normal service period, the arrival of a negative customer can cause the server breakdown, and the failed server still works at a lower service rate rather than stopping the service completely. Applying the embedded Markov chain, we obtain the necessary and sufficient condition for the stability of the system. Using the supplementary variable method, we deal with the generating functions of the number of customers in the orbit. Various system performance measures are also developed. Finally, some numerical examples and a cost optimization analysis are presented. View Full-Text
Keywords: M/G/1 queue; retrial; working breakdown; supplementary variable method M/G/1 queue; retrial; working breakdown; supplementary variable method
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Li, T.; Zhang, L. An M/G/1 Retrial G-Queue with General Retrial Times and Working Breakdowns. Math. Comput. Appl. 2017, 22, 15.

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