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运筹学学报 ›› 2018, Vol. 22 ›› Issue (4): 127-134.doi: 10.15960/j.cnki.issn.1007-6093.2018.04.012

• 运筹学 • 上一篇    下一篇

具有插队和止步行为的M/M/c 排队系统

吴文青1  何刚2  唐应辉3,*  余玅妙4   

  1. 1. 西南科技大学理学院, 四川绵阳 621010; 2. 西南科技大学计算机科学与技术学院, 四川绵阳 621010; 3. 四川师范大学数学科学学院, 成都 610066; 4. 四川理工学院理学院, 四川自贡 643000
  • 收稿日期:2017-11-15 出版日期:2018-12-15 发布日期:2018-12-15
  • 通讯作者: 唐应辉 E-mail: tangyh@sicnu.edu.cn
  • 基金资助:

    国家自然科学基金(No.71571127), 西南科技大学龙山学术人才科研支持计划"研究专项''(No.17LZXY20), 西南科技大学博士研究基金(No.15zx7141)

An M/M/c queue with customer interjections and balking

WU Wenqing1  HE Gang2  TANG Yinghui3,*  YU Miaomiao4   

  1. 1. School of Science, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China; 2. School of Computer Science and Technology, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China; 3. School of Mathematics Science, Sichuan Normal University, Chengdu 610066, China; 4. School of Science, Sichuan University of Science and Engineering, Zigong 643000, Sichuan, China
  • Received:2017-11-15 Online:2018-12-15 Published:2018-12-15

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摘要：

研究了具有插队和止步行为的M/M/c排队系统. 将到达顾客分为常规顾客和插队顾客, 常规顾客在队尾排队等待服务, 插队顾客总是尽可能的靠近队首插队等待服务. 插队行为由到达顾客的插队概率和队列中等待顾客对插队行为的容忍来描述. 利用负指数分布的性质、Laplace-Stieltjes变换和全概率公式, 给出了处于等待队列位置n的顾客、任意一个常规顾客和任意一个插队顾客的等待时间的表达式. 在此基础上, 讨论了系统相关指标随系统参数的变化情况.

关键词: M/M/c排队系统, 插队行为, 止步, 等待时间

Abstract:

This paper studies an M/M/c queueing system with customer interjections and balking. Arriving customers are divided into normal customers and interjecting customers, in which the normal customers join the queue at the end, and the interjecting customers try to cut in the queue and occupy a position as close to the head of the queue as possible. The behavior of the interjecting customers is described by the percentage of customers interjecting and the tolerance level of interjection by individual customer. By using the theory of the exponential distributions, the Laplace-Stieltjes transform and the formula of the total probability, we obtain the waiting time of a customer in position n, the waiting time of a normal customer, and the waiting time of an interjecting customer. Furthermore, we discuss the influence of system parameters on the system performance measures.

Key words: M/M/c queueing system, customer interjections, balking, waiting time