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
Math. Comput. Appl. 2017, 22(1), 15; https://doi.org/10.3390/mca22010015
Received: 4 October 2016 / Revised: 2 January 2017 / Accepted: 24 January 2017 / Published: 2 February 2017
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.
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Keywords:
M/G/1 queue; retrial; working breakdown; supplementary variable method
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MDPI and ACS Style
Li, T.; Zhang, L. An M/G/1 Retrial G-Queue with General Retrial Times and Working Breakdowns. Math. Comput. Appl. 2017, 22, 15.
AMA Style
Li T, Zhang L. An M/G/1 Retrial G-Queue with General Retrial Times and Working Breakdowns. Mathematical and Computational Applications. 2017; 22(1):15.
Chicago/Turabian StyleLi, Tao; Zhang, Liyuan. 2017. "An M/G/1 Retrial G-Queue with General Retrial Times and Working Breakdowns" Math. Comput. Appl. 22, no. 1: 15.
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