具有N-策略和延迟单重休假且休假不中断的M/G/1排队系统  

M/G/1 Queueing System with N-Policy and Delayed Single Vacation Without Interruption

作　　者：何亚兴 唐应辉 HE Yaxing;TANG Yinghui(School of Mathematical Sciences,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

出　　处：《应用数学》2021年第1期130-145,共16页Mathematica Applicata

基　　金：国家自然科学基金(71571127)。

摘　　要：本文考虑具有N-策略和延迟单重休假且休假不中断的M/G/1排队系统.运用更新过程理论,全概率分解技术和Laplace变换工具,从任意初始状态出发,研究了队长的瞬态和稳态性质,获得了瞬态队长分布的Laplace变换的表达式和稳态队长分布的递推表达式.同时求出了稳态队长分布的概率母函数和附加队长分布的显示表达式.进一步讨论了当延迟时间Y=0,或Y→∞,或休假时间V=0时的特殊情形.最后,在建立费用结构模型下,由更新报酬过程理论获得了系统长期运行单位时间内所产生的成本期望费用的显示表达式,并通过数值实例讨论了使得系统在长期单位时间内的期望费用最小的最优控制策略N*.This paper considers the M/G/1 queueing system with N-policy and delayed single vacation without interruption.By the renewal process theory,the total probability decomposition technique and the Laplace transform tool,we study the transient and equilibrium properties of the queue length from any initial states.Both the recursion expressions of the Laplace transformation of the transient queuelength distribution and the recursion expressions of the steady queue-length distribution are obtained.Meanwhile,we present the probability generating function of the steady queue-length distribution and the explicit expression of the additional queue-length distribution.Furthermore,some special cases,such as Y=0,or Y→∞,or vacation time V=0,are also discussed.Finally,by the renewal reward theorem the explicit expression of the long-run expected cost per unit is derived under a given cost structure.Through numerical calculation,the optimal control policy N~* which minimizes the long-run expected cost per unit time is determined.

关 键 词：N-策略 延迟休假 休假不中断 队长分布 最优控制策略 

分 类 号：O213.2[理学—概率论与数理统计]