在Min(N,V)-策略控制下带启动时间和多级适应性休假的M/G/1排队系统分析  

Analysis of M/G/1 Queueing System with Setup Time and Multiple Adaptive Vacations Under Min(N,V)-Policy Control

作　　者：秦西平 唐应辉 QIN Xi-ping;TANG Ying-hui(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610068,China;School of Fundamental Education,Sichuan Normal University,Chengdu 610068,China)

机构地区：[1]四川师范大学数学科学学院,四川成都610068 [2]四川师范大学基础教学学院,四川成都610068

出　　处：《数学的实践与认识》2021年第17期130-143,共14页Mathematics in Practice and Theory

基　　金：国家自然科学基金(51271127)。

摘　　要：考虑带启动时间与在Min(N,V)-策略控制下休假次数是随机的M/G/1排队系统,使用全概率分解方法分析了在任意初始状态下系统队长的瞬态分布和稳态分布,利用拉普拉斯变换推导出了队长瞬态分布关于时间t的拉普拉斯变换式子,而且应用洛必达法则得到了稳态队长分布的递推表达式和稳态队长的随机分解结果.This paper considers the M/G/1 queueing system with setup time and multiple adaptive vacations under Min(N,V)-policy control.Applying the method of the total probability decomposition,we investigate the transient queue-length distribution that the system begins from the beginning of the any initial state.Using the Laplace transformation,the expressions of the Laplace transformation of the transient queue-length distribution with respect to time t are obtained.Furthermore,the recursive formulas of the steady queue-length distribution are given by Employing L’ Hospital’ s rule.Also,the stochastic decomposition structure of the steady state queue-length are presented.

关 键 词：启动时间 多级适应性休假 Min(N V)-策略 队长分布 

分 类 号：O226[理学—运筹学与控制论]