北大中文核心期刊
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运筹学学报 ›› 2023, Vol. 27 ›› Issue (3): 109-120.doi: 10.15960/j.cnki.issn.1007-6093.2023.03.008

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具有插队行为的M/M/c/m+c排队系统等待时间分析

吴文青1,2,(), 柯淇淋3, 唐应辉3, 陈林4   

  1. 1. 中国民用航空飞行学院理学院, 四川德阳 618307
    2. 西南科技大学数理学院, 四川绵阳 621010
    3. 四川师范大学数学科学学院, 四川成都 610068
    4. 重庆交通大学数学与统计学院, 重庆 400067
  • 收稿日期:2020-12-11 出版日期:2023-09-15 发布日期:2023-09-14
  • 通讯作者: 吴文青 E-mail:wwqing0704@swust.edu.cn
  • 作者简介:吴文青, E-mail: wwqing0704@swust.edu.cn
  • 基金资助:
    国家自然科学基金(72001181);可视化计算与虚拟现实四川省重点实验室基金(SCVCVR2020.01VS)

Analysis of waiting time of customers in an M/M/c/m + c queueing system with customer interjections

Wenqing WU1,2,(), Qilin KE3, Yinghui TANG3, Lin CHEN4   

  1. 1. School of Science, Civil Aviation Flight University of China, Deyang 618307, Sichuan, China
    2. School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China
    3. School of Mathematical Sciences, Sichuan Normal University, Chengdu 610068, Sichuan, China
    4. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400067, China
  • Received:2020-12-11 Online:2023-09-15 Published:2023-09-14
  • Contact: Wenqing WU E-mail:wwqing0704@swust.edu.cn

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摘要：

本文研究具有插队行为和容量有限的多服务台排队系统中顾客的等待时间分布函数。将进入系统的顾客按照插队与否分为常规顾客和插队顾客，常规顾客进入系统后在等待队尾排队等待服务，插队顾客进入系统后总是尽可能地靠近队首插队接受服务。利用负指数分布和位相型分布的性质推导了处于等待队列位置$n$的顾客、常规顾客、插队顾客的等待时间分布函数的矩阵表达式，并在此基础上给出了等待时间分布函数随时间的变化情况。

关键词: $M/M/c/m+c$排队系统, 插队行为, 等待时间分布函数, 位相型分布

Abstract:

This paper studies waiting time distributions of customers in a multi-server queueing system with customer interjections and finite buffer. The customers who enter the system are divided into regular customers and interjection customers according to whether they interject the queue or not. After entering the system, the regular customers queue up at the end of the waiting line and wait for service, while the interjection customers queue up as close as possible to the head of the waiting line to receive service. By using the properties of negative exponential distribution and phase type distribution, the matrix expressions of waiting time distribution of customers in waiting queue position $n$, regular customers and interjection customers are derived. Further, the plots of waiting time distributions with time $t$ are given.

Key words: $M/M/c/m+c$ queueing system, customer interjection, the function of the waiting time distribution, phase type distribution

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