摘要
本文研究一个有Bernoulli中断休假和随机启动时间的N-策略多重休假M/G/1排队模型,其中Bernoulli中断休假是指:如果在休假中有顾客到达,服务员以概率p(0≤p≤1)立即中断休假回到系统中并启动服务设施,以概率(1−p)不中断休假直到此次休假结束后才回到系统启动服务设施.当系统的启动完成后,若系统中顾客数大于等于事先设置的阈值N(≥1),则服务员开始为顾客服务直到系统再次变空.运用全概率分解技术和更新过程理论讨论了系统在时刻t队长的瞬态概率分布,得到了队长瞬态概率分布的拉普拉斯变换表达式.在瞬态分析的基础上,使用洛必达法则和一些代数运算推导出了队长稳态概率分布的递推表达式,以及其它一些排队指标,如队长稳态概率分布的母函数、平均队长和附加队长的概率分布等.最后,讨论了一些特殊情形.
This article studies a N-strategy and multiple-vacation M=G=1 queuing model with Bernoulli interruption vacation and random start-time,in which Bernoulli interruption vacation means that if a customer arrives during the vacation,the waiter interrupts the vacation with probability p(0p1)and immediately starts the service facility,otherwise,he/she does not interrupt the vacation with probability(1p)until the end of the vacation.After the system startup is completed,if the number of customers in the system is greater than or equal to the given threshold N,the server starts serving the customers until the system becomes empty again.We apply the total probability decomposition technology,the renewal process theory and the Laplace transform tool to discuss the transient queue-length distribution of the system at time t,and obtain the Laplace transform expressions of the transient queue-length distribution.On the basis of transient analysis,the recursive expressions of the steady queue-length distribution are derived by employing the L'Hospital’s rule.Also,some other queueing indicators,such as the probability generating function of the steady queue-length distribution,the average queue size and the probability distribution of the additional queue-length,are presented by using some algebraic operations.Finally,some special cases are discussed.
作者
李茜
唐应辉
余玅妙
魏瑛源
LI Xi;TANG Yinghui;YU Miaomiao;WEI Yingyuan(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610068,China;School of Mathematics Statistics,Hexi University,Zhangye 734000,China)
出处
《应用数学》
北大核心
2025年第1期276-293,共18页
Mathematica Applicata
基金
国家自然科学基金项目(71571127)
教育部人文社科研究规划基金项目(24YJA630121)
四川师范大学学科建设专项基金项目(XKZX2021-04)
河西学院校长基金创新团队项目(CXTD2022013)。
作者简介
通讯作者:唐应辉,男,汉族,四川人,二级教授,博士生导师,研究方向:排队论、系统可靠性与决策论及应用.
