带有广义随机工作休假的Geom／Geom／1排队系统

J4 ›› 2011, Vol. 46 ›› Issue (6): 103-109.

带有广义随机工作休假的Geom／Geom／1排队系统

韦才敏,邹宗保

汕头大学数学系, 广东汕头 515063

收稿日期:2010-11-23 出版日期:2011-06-16 发布日期:2011-12-19
作者简介:韦才敏(1977- ),男,副教授,博士,主要研究方向为随机规划、排队论、随机模型理论与方法. Email: cmwei@stu.edu.cn
基金资助:
国家自然科学基金资助项目(71065001)

The Geom／Geom／1 queue system with generalized
random working vacation policy

WEI Caimin, ZOU Zongbao

Department of Mathematics, Shantou University, Shantou 515063, Guangdong, China

Received:2010-11-23 Online:2011-06-16 Published:2011-12-19

摘要/Abstract

摘要：

针对带有广义随机工作休假的Geom／Geom／1排队系统，通过采用拟生灭链和矩阵几何解法,得到了平稳状态下系统队长和顾客逗留时间的概率母函数与均值。另外,也得到了正规忙期、忙循环和假周期的概率母函数和均值。最后,给出了本模型的两个特例。

关键词: 离散时间排队;广义随机工作休假;矩阵几何解;逗留时间

Abstract:

A discretetime Geom／Geom／1 queue with generalized random working vacation policy is studied. By using the quasi birth and death chain and matrixgeometric solution approaches, the generating functions and the expectations of the steady state queue length and sojourn time are derived. In addition, the generating functions and the means of the regular busy period, busy cycle and vacation period are obtained. Finally, two special cases of the model are given.

Key words: discrete-time queue; generalized random working vacation; matrix-geometric solution; sojourn time

韦才敏,邹宗保. 带有广义随机工作休假的Geom／Geom／1排队系统[J]. J4, 2011, 46(6): 103-109.

WEI Caimin, ZOU Zongbao. The Geom／Geom／1 queue system with generalized
random working vacation policy[J]. J4, 2011, 46(6): 103-109.

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