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运筹学学报 ›› 2013, Vol. 17 ›› Issue (3): 93-100.

• 运筹学 • 上一篇    下一篇

带有Bernoulli控制策略的M/M/1多重休假排队模型

张宏波1,2,*   

  1. 1. 中南大学数学与统计学院, 长沙 410075 2. 河南教育学院数学系, 郑州 450046
  • 出版日期:2013-09-15 发布日期:2013-09-15
  • 通讯作者: 张宏波, 中南大学数学博士后流动站在站博士后 E-mail:Email: zhanghb-168@163.com
  • 基金资助:

    国家自然科学基金 (No. 61174160), 中南大学博士后基金 (No. 125011)

The M/M/1 queue with controlled multiple vacations under Bernoulli policy

ZHANG Hongbo1,2,*   

  1. 1. School of Mathematics, Central South University, Changsha 410075, China 2. Department of Mathematics, Henan Institute of Education, Zhengzhou 450046, China
  • Online:2013-09-15 Published:2013-09-15

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863

被引次数

2

摘要： 研究具有Bernoulli控制策略的M/M/1多重休假排队模型: 当系统为空时, 服务台依一定的概率或进入闲期, 或进入普通休假状态, 或进入工作休假状态. 对该模型, 应用拟生灭(QBD)过程和矩阵几何解的方法, 得到了过程平稳队长的具体形式, 在此基础上, 还得到了平稳队长和平稳逗留时间的随机分解结果以及附加队长分布和附加延迟的LST的具体形式. 结果表明, 经典的M/M/1排队, M/M/1多重休假排队, M/M/1多重工作休假排队都是该模型的特殊情形.

关键词: M/M/1排队, 休假, 工作休假, 矩阵几何解, 随机分解

Abstract: In this paper, we study an M/M/1 queue with multiple vacation policy under the assumption that the decisions whether or not to take a new vacation and take what kind of vacation depend on certain probability, when the server becomes empty. For the queue model, by the quasi-birth-and-death (QBD) process and matrix geometric method, we derive the analytic expression of the stationary queue length, and demonstrate stochastic decomposition structures of the stationary queue length and sojourn time. Moreover, we also obtain the additional queue length and the additional delay. The results show that the classical M/M/1 queue, the M/M/1 queue with vacation or with working vacation are special cases of our model.

Key words: M/M/1 queue, vacation, working vacation, matrix-geometric solution, stochastic decomposition

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