An Explicit Solution for a Series and Parallel Queue with Retrial, Losses, and Bernoulli Schedule

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• 作者：Shi-Zhong Zhou ; Li-Wei Liu ; Jian-Jun Li
• 关键词：Series and parallel queue ; Retrial ; Bernoulli schedule ; Explicit solution ; Hypergeometric function
• 刊名：Journal of the Operations Research Society of China
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：4
• 期：1
• 页码：121-129
• 全文大小：409 KB
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• 作者单位：Shi-Zhong Zhou (1)
  Li-Wei Liu (1)
  Jian-Jun Li (1)
  
  1. Department of Statistics and Financial Mathematics, School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China
  
• 刊物主题：Operations Research, Management Science;
• 出版者：Springer Berlin Heidelberg
• ISSN：2194-6698

文摘

This paper deals with the series and parallel queueing system in which there are two servers whose service time follow two exponential distributions. Each arriving customer either enters into the tandem service with probability or joins the service of the single server with complementary probability. We assume that the customers of arriving at the first server who find the first server is busy join an orbit and retry to enter the server after some time and of arriving at the second server who find the second server is busy are lost. For this model, we obtain the explicit expressions of the joint stationary distribution between the number of customers in the orbit and the states of the servers.