延迟D-策略Geo/G/1排队系统的队长分布及容量的优化设计

考虑延迟D-策略离散时间Geo/G/1排队系统, 使用全概率分解技术, 从任意初始状态出发, 研究了队长的瞬态和稳态性质, 推导出了在任意时刻n⁺ 瞬态队长分布的z-变换的递推表达式和稳态队长分布的递推表达式, 并获得稳态队长的随机分解结果, 同时得到了系统在三种任意时刻(n^-, n, n⁺)处稳态队长分布的重要关系. 最后, 通过数值实例, 讨论了稳态队长分布对系统参数的敏感性, 并阐述了获得便于计算的稳态队长分布的表达式在系统容量优化设计中的重要应用价值.     

延迟N-策略Geo/G/1排队系统的队长分布及数值计算

考虑延迟N-策略离散时间Geo/G/1排队系统,使用全概率分解技术,从任意初始状态出发,研究了队长的瞬态和稳态性质,导出了在任意时刻n瞬态队长分布的z-变换的递推表达式和稳态队长分布的递推表达式,以及稳态队长的随机分解.最后,通过数值实例, 讨论了稳态队长分布对系统参数的敏感性,并阐述了获得便于计算的稳态队长分布的表达式在系统容量设计中有重要的价值.     

延迟N-策略M/G/1排队系统队长的瞬态和稳态分布

研究延迟N-策略M/G/1排队系统,讨论了队长的瞬态和稳态性质.通过引进"服务员忙期"和使用全概率分解技术,导出了在任意时刻t瞬态队长分布的L变换的递推表达式和稳态队长分布的递推表达式,以及平稳队长的随机分解.     

延迟多重休假MX/G/1排队系统的队长分布

考虑延迟多重休假的M^x／G／1排队，在假定延迟时间、休假时间和服务时间都是一般概率分布函数下，研究了队长的瞬态和稳态性质、通过引进“服务员忙期”，导出了在任意时刻t瞬态队长分布的L变换的递推表达式和稳态队长分布的递推表达式，以及平稳队长的随机分解．     

基于多重休假的min(N,V)-策略M/G/1排队系统的队长分布

运用全概率分解技术和拉普拉斯变换工具，研究了基于服务员多重休假的min（N，V）-策略M/G/1排队系统，其中N是预设的休假终止的门限值.讨论了从任意初始状态出发队长的瞬态分布，获得了队长瞬态分布的拉普拉斯变换的递推表达式和稳态队长分布的递推表达式，同时求出了附加队长分布的显示表达式.进一步讨论了当休假时间V分别服从负指数分布和定长分布P{V=T}=1，以及当N=1，N→∞，P{V=0}=1与P{V=∞}=1时的特殊情形.最后，通过数值实例阐述了获得便于计算的稳态队长分布的表达式在系统容量设计中的重要价值.     

基于多重休假的min(N,V)-策略M/G/1排队系统的队长分布

运用全概率分解技术和拉普拉斯变换工具,研究了基于服务员多重休假的min(N,V)-策略M/G/1排队系统,其中N是预设的休假终止的门限值.讨论了从任意初始状态出发队长的瞬态分布,获得了队长瞬态分布的拉普拉斯变换的递推表达式和稳态队长分布的递推表达式,同时求出了附加队长分布的显示表达式.进一步讨论了当休假时间V分别服从负指数分布和定长分布P{V=T}=1,以及当N=1,N→∞,P{V=0}=1与P{V=∞}=1时的特殊情形.最后,通过数值实例阐述了获得便于计算的稳态队长分布的表达式在系统容量设计中的重要价值.     

离散时间有限缓冲空间GI / Geom / 1 / N 工作休假排队系统稳态概率算法及性能分析

综合使用离散补充变量方法和嵌入Markov链技术研究了离散时间有限缓冲空间工作休假GI/Geom/1/N排队系统.首先运用离散补充变量方法给出一个重要等式,从而获得系统在稳态情形下任意时刻队长分布和顾客到达前夕队长分布的迭代关系.然后,再利用嵌入Markov链技术通过求解不变概率测度方程获得顾客到达前夕队长分布的数值解.而后将顾客到达前夕队长分布代入迭代公式求得稳态情形下任意时刻的队长分布.最后给出几个特殊情形下的数值计算实例,并讨论了系统参数对几个主要性能指标的影响.     

Bernoulli反馈排队的N策略Geom／G／1排队系统的队长分布

考虑具有Bernoulli反馈排队和N策略体假的离散时间Geom/G/1排队系统,采用一种直观、简洁的全概率分解方法以及U-变换技术,研究了该排队系统队长的瞬态性质,得到队长瞬态分布的U-变换形式的递推表达式;进一步导出队长稳态分布的递推表达以及平稳队长分布的随机分解;最后,计算出稳态队长分布,并且考察了其统计性质.     

带启动时间的N-策略M/G/1排队系统的队长

从任意初始状态出发, 直接研究了系统队长的瞬态分布和稳态分布.通过引进的“服务员忙期", 使用全概率分解技术和拉普拉斯变换,导出了在任意时刻t队长的瞬态分布的拉普拉斯变换的表达式,进一步获得了有重要应用价值的稳态分布的具体的递推式子,以及稳态队长的随机分解结果. 特别地,还直接获得了一些特殊排队系统的更实用的稳态队长分布的递推表达式.     

延迟启动-关闭型的N-策略M/G/1排队系统队长分布

研究服务台具有延迟启动和延迟关闭的N-策略M/G/1排队系统,利用全概率分解技术,导出了任意时刻t瞬态队长分布的Laplace变换的递推关系式,进一步得到稳态队长分布的递推式以及平稳队长分布的随机分解.最后进行了数值实验,并考察了稳态队长分布以及附加队长分布的统计性质.     

Queue Size Distribution of Geo/G/1 Queue Under the Min(N,D)-Policy

This paper considers a discrete-time Geo/G/1 queue under the Min(N,D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D,whichever occurs first(Min(N,D)-policy).By using renewal process theory and total probability decomposition technique,the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state,and obtain both the recursive expression of the z-transformation of the transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n~+.Meanwhile,the authors obtain the explicit expressions of the additional queue length distribution.Furthermore,the important relations between the steady state queue length distributions at different time epochs n~-,n and n~+ are also reported.Finally,the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution,and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.     

Recursive Solution of Queue Length Distribution for Geo/G/1 Queue with Delayed Min(N,D)-Policy

In this paper we consider a discrete-time Geo/G/1 queue with delayed Min(N, D)-policy.Using renewal process theory, total probability decomposition technique and z-transform, we study the transient and equilibrium properties of the queue length from an arbitrary initial state, and obtain both the recursive expressions of the transient state queue length distribution and the steady state queue length distribution at arbitrary time epoch n~+. Furthermore, we derive the important relations between equilibrium queue length distributions at different time epochs n~-, n and n~+. Finally, we give some numerical examples about capacity decision in queueing systems to demonstrate the application of the analytical results reported in this paper.     

Queue size distribution of Geo/G/1 queue under the Min(<Emphasis Type="Italic">N,D</Emphasis>)-policy

This paper considers a discrete-time Geo/G/1 queue under the Min(N,D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first (Min(N,D)-policy). By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of the transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n ⁺. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution. Furthermore, the important relations between the steady state queue length distributions at different time epochs n ^-, n and n ⁺ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.     

The Queue Length Distribution for M/G/1 Queue with Delay Single Server Vacation

1　IntroductionDuringrecentseveraldecadesmanyauthorsstudiedM/G/1queueswithdifferentservervacationregimes(seeRefs.[1～6]).Theynotonlystudiedthestochasticdecompositionpropertiesofthequeuelengthandwaitingtimewhenthesystemisinequilibrium,butalsostudiedthetransientandequilibriumdistributionsofthequeuelength.InRef.[6]theau-thorsstudiedM/G/1queuewithdelaymultipleservervacationsinwhichtheserverhasthreestates:vacation-preparation,vacationandbusyperiod.InthispaperwefirstdiscusstheM/G/1queuewithdelay…     

具有温储备失效的M/G/1可修排队系统

本文把“服务台在系统闲期中可能温储备失效”引入到M/G/1可修排队系统中,考虑了具有温储备失效特征的M/G/1可修排队系统.使用全概率分解技术和利用拉普拉斯变换工具,导出了在任意时刻t队长的瞬态分布的拉普拉斯变换的表达式,进一步获得了队长的稳态分布的递推式,同时,给出了稳态队长和稳态等待时间的随机分解结果. 最后通过数值计算实例讨论了平均附加队长随温储备失效参数和修复参数的变化情况.     

An M/G/1 Queueing System with Delay Server Vacations

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