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山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (06): 1-6.doi: 10.6040/j.issn.1671-9352.0.2014.328

• 论文 •    下一篇

一个不同到达率及负顾客的离散工作休假排队

刘再明, 于森林   

  1. 中南大学数学与统计学院, 湖南 长沙 410083
  • 收稿日期:2014-07-10 修回日期:2015-01-06 出版日期:2015-06-20 发布日期:2015-07-31
  • 作者简介:刘再明(1961-),男,博士,教授,研究方向为马氏过程、排队论研究.E-mail:math_lzm@csu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11271373)

A discrete time working vacations queuing system with different arrival rates and negative customers

LIU Zai-ming, YU Sen-lin   

  1. School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China
  • Received:2014-07-10 Revised:2015-01-06 Online:2015-06-20 Published:2015-07-31

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摘要： 提出并研究了带负顾客的Geo/Geo/1多重工作休假排队模型,其中正顾客在工作休假期和正常忙期的到达率不同。通过拟生灭链矩阵分析的的方法,求出了这个排队系统的转移概率矩阵、队长平稳分布、队长均值、随机分解、忙期分析。最后建立了费用函数,为系统的优化设计提供参考,并给出两个数值实例分析了参数对队长的影响。

关键词: 负顾客, 矩阵几何解, 不同到达率, 工作休假

Abstract: A multiple working vacations Geo/Geo/1 queuing system with negative customers was proposed and studied in this paper. For this model, the positive customers have different arrival rates in the normal busy period and working vacation period. The quantities including the transition probability matrix of the queuing system, the equilibrium distribution of the queue length, the mean number of customers, the stochastic decomposition and the busy period analysis were obtained by using the matrix-analytical method of quasi birth-death chains. The cost function and two numerical examples were given to provide a basis for optimal design and illustrate the impact of parameters on the queue length.

Key words: matrix-geometric solution, different arrival rates, working vacations, negative customers

中图分类号: 

  • O226
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