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运筹学学报 ›› 2013, Vol. 17 ›› Issue (1): 29-37.

• 运筹学 • 上一篇    下一篇

批到达M/G/1重试排队的队长的尾渐近

王颖俐1,3，刘维奇1,2，李继红2   

  1. 1. 山西大学数学科学学院 2. 山西大学管理科学与工程研究所 3. 长治学院数学系
  • 出版日期:2013-03-15 发布日期:2013-03-15
  • 通讯作者: 刘维奇 E-mail:Liuwq@sxu.edu.cn
  • 基金资助:

    教育部人文社会科学研究项目(Nos. 07JA630027, 06JA630035)；山西省高校人文社科重点研究基地项目(No. 20083006)

Asymptotic analysis of the tails of queue length retrial queue with batch arrival

WANG Yingli1,3, LIU Weiqi1,2, LI Jihong2   

  1. 1. School of Mathematical Science, Shanxi University 2. Institute of Management Science and Engineering, Shanxi University 3.  The department of mathematics, Changzhi College
  • Online:2013-03-15 Published:2013-03-15

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摘要： 用随机分解法研究成批到达服务时间为次指数分布的重试排队中队长的尾行为，得到了该系统与其相应的标准排队系统队长尾分布的关系；对次指数尾，结果也能用于正则变化尾，进而得到正则变化尾渐近．

关键词: 重试排队, 尾渐近, 随机分解, 次指数, 正则变化

Abstract: In this paper, we study the tail behavior of the stationary queue length of an M/G/1 retrial queue which is batch arrived and have subexponential service time by using stochastic decomposition. Then we obtain the correlation between the stationary queue length tail distribution of an M/G/1 retrial queue with batch arrival and the  stationary queue length tail distribution in the corresponding standard M/G/1 queue with batch arrival. Our results for subexponential tails also can be applied to regularly varying tails. Therefore, we get the regularly varying tail asymptotics for the stationary queue length.

Key words: retrial queue, tail asymptotics, stochastic decomposition, subexponential, regular variation