具有Bernoulli反馈和Min(N,D)-策略控制的Geo~(λ_1,λ_2)/G/1离散时间可修排队的可靠性分析

考虑具有Bernoulli反馈,可变到达率以及Min(Ⅳ,D)-策略控制的Geo/G/1离散时间可修排队系统的可靠性指标.服务台在服务过程中可能发生故障,顾客的到达率依赖于服务员的状态.使用更新理论,全概率分解技术和概率母函数方法,首先讨论了服务员在任意时刻n~+处于忙的瞬态概率和稳态概率.其次,分析了一些可靠性指标,如服务台的瞬态和稳态不可用度、时间段(0~+,n~+]内服务台的平均故障次数和稳态故障频度.所得结果揭示了可靠性指标的随机分解性质.利用本文的结论直接给出了一些特殊离散时间可修排队系统的可靠性指标.最后,通过数值实例分析了系统参数对可靠性指标的影响.     

串联在可修服务台损失制排队系统分析

本文分析了一咱新的可修排队系统，该系统有两个可修单元组成，在服务时间内，顾客无须等待且很快离开，我们称这种情况为损失顾客，利用向量马尔科夫过程方法，我们获得一系列可靠性指桔，以及其他一些结果。     

服务台可修的N-策略单重休假M/G/1排队系统的可靠性分析

本文研究服务台可修的N-策略单重休假M/G/1排队系统,假定服务台的寿命有负指数分布和修理时间有任意分布,通过使用全概率分解技术和拉普拉斯变换,讨论了服务台的首次失效时间分布、不可用度和故障频度等可靠性指标,获得了服务台的一系列可靠性结果.     

具有Min(N,D)-策略控制的M/G/1可修排队系统及最优控制策略

考虑基于Min(N,D)-策略控制的M/G/1可修排队系统,其中服务台在服务员忙期中可能发生故障.使用全概率分解技术和拉普拉斯变换工具,讨论了系统的排队指标,同时重点讨论了服务台的一些可靠性指标,即服务台首次失效前的寿命分布、不可用度和(0,t]时间内的平均失效次数.最后,通过建立系统的费用模型,用数值计算实例讨论了最优控制策略(N~*,D~*).     

带负顾客,反馈,服务台可修的M/G/1重试排队系统

对负顾客的研究可以从不同的角度,不同的方法,不同的机制来进行.本文提出了带负顾客,反馈,服务台可修的M/G/1重试排队系统.其中负顾客的机制是带走正在接受服务的正顾客和使得服务器处于修理状态.在假定重试区域中只有队首的顾客允许重试的情况下,重试时间具有一般分布时,得到了系统稳态的充分必要条件.求得了系统稳态时队长和重试区域中队长分布及一些排队指标和可靠性指标.     

具有Bernoulli休假的M/G/1重试可修的排队系统

本文研究了具有Bernoulli休假、一般重试的服务台可修的M/G/1排队系统,求得系统稳态解存在的充分必要条件.利用补充变量法求得系统的排队指标和可靠性指标.     

具有优先权的Lu-Kumar排队网络的扩散逼近

对Lu-Kumar排队网络来说,标准的额定负荷条件,即每个工作站的工作强度ρ<1,并不足以保证该排队网络的稳定性,特别是在具有优先权的服务规则下.论文在讨论了Lu-Kumar排队网络稳定性相关结果的基础上,研究了Lu-Kumar排队网络在具有优先权的服务规则下的扩散逼近.证明了当每个工作站的额定负荷ρ→1时,Lu-Kumar排队网络对具有优先权的服务规则的所有优先级别来说,扩散逼近定理均成立.     

服务台可修的GI/PH/1排队系统

本文讨论服务台可修的GI/PH/1排队,其中服务台寿命和修复时间也是PH变量。首先证明系统在稳态下可转化为一个等价的经典GI/PH/1模型,然后给出系统的各种稳态指标。此外,对修复后重新服务和累积服务两种不同模型,我们给出了统一的处理。     

具有N策略和负顾客的反馈抢占型的M/G/1重试可修排队系统

本文研究了具有N策略和负顾客的反馈抢占型的M/G/1重试可修排队系统.所有顾客(包括正顾客和负顾客)的到达都是泊松过程,服务器是可修的.利用吸收分布,求出了系统存在稳态的充分必要条件.利用补充变量法,求出了系统稳态时系统和重试区域中队长分布的概率母函数,以及其他一些重要的排队指标.     

休假随机服务系统

本文拟对休假排队研究的现状和方法作一简要介绍。包括各种休假规则模型的描述,稳态指标的随机分解。以两个最重要的M/G/1休假系统为例,着重介绍导致随机分解结果的几种方法——嵌入Markov链(MC)法、直接概率法、水平交叉法和样本轨道比较法。最后,扼要列举一般GI/G/1休假排队及其他相关模型的主要结果。以期引起随机运筹、应用概率工作者及工程技术人员的注意和兴趣。 1.休假排队与休假规则 1.1 模型的背景不同领域中发生的许多实际问题可导致休假排队研究。在这里,我们列举几个诱发休假排队研究的典型问题:     

Statistical analysis of queueing systems

This paper provides an overview of the literature on statistical analysis of queueing systems. Topics discussed include: model identification, estimation, hypothesis testing and other related aspects. Not all of these statistical problems are covered in books on queueing theory or stochastic processes. The bibliography is not exhaustive, but comprehensive enough to provide sources from the literature.     

On the optimal control of a single-server queueing system: Further remarks

This comment is in response to a reply by Scott and Jefferson (Ref. 3) concerning the application of control theory to a queueing problem.     

Mean-value analysis for a class of Petri nets and batch-movement queueing networks with product-form equilibrium distributions

A number of recent papers have shown that there are classes of queueing networks, with batches of customers served and routed through the network, which have generalized product form equilibrium distributions. This extends to some Petri nets. In this paper, we indicate how a class of these is amenable to a mean-value analysis similar to that used for single-movement networks. To bring out the simplicity of the underlying ideas, we do this by working a simple example rather than presenting the development in its generality.     

Proof of Monotone Loss Rate of Fluid Priority-Queue with Finite Buffer

This paper studies a fluid queueing system that has a single server, a single finite buffer, and which applies a strict priority discipline to multiple arriving streams of different classes. The arriving streams are modeled by statistically independent, identically distributed random processes. A proof is presented for the highly intuitive result that, in such a queueing system, a higher priority class stream has a lower average fluid loss rate than a lower priority class stream. The proof exploits the fact that for a work-conserving queue, the fluid loss rate for a given class is invariant of what queueing discipline is applied to all arriving fluid of this particular class. AMS subject classification: 60K25, 68M20     

排队系统中的泰勒展开方法

综述了排队系统中的泰勒展开方法。它由Gong和Hu在1990s首次提出,并在最近几年里有了一些新的发展。首先,通过GI/GI/1队列的简单例子介绍其基本原理;其次,展示如何应用该方法分析相关性队列和离去过程;然后,阐述如何基于该方法发展排队网络近似的高阶矩方法;最后,讨论未来的几个可能研究方向。     

基于有限服务排队系统的未决赔款准备金分布

若保险赔付工作中赔付人员有限,根据服务人员有限的排队系统的性质,可以研究保险公司所需计提的未决赔款准备金的分布函数.当假设赔付服务工作人员为c个,使用M/M/c/∞和G/M/c/∞排队系统的性质可以得到未决赔款准备金分布函数和年末所需增加计提的未决赔款准备金的分布及其界值.当假设赔付服务工作人员仅一个,使用M/G/1/∞排队系统的性质可以得到此时未决赔款准备金的分布函数.并且在假设损失赔付额取正整数的条件下,得到年末保险公司所需增加计提的未决赔款准备金分布的递推公式.而且通过计算实例表明结论的实用性,及所得到的递推公式在以往难以准确求解未决赔款准备金分布时是十分有效的.     

On the optimal control of a single-server queueing system: Reply

This comment replies to a criticism due to Klein and Gruver (Ref. 1) of our earlier paper (Ref. 2) on the application of control theory to a queueing system. The criticism concerns the state-space diagram and the table which we inadvertently gave for the terminal-reward problem, albeit incorrectly labeled, rather than for the free-endpoint problem considered in our paper. We show that the solution given by Klein and Gruver is itself incorrect and nonoptimal.     

Queueing Models of Call Centers: An Introduction

This is a survey of some academic research on telephone call centers. The surveyed research has its origin in, or is related to, queueing theory. Indeed, the queueing-view of call centers is both natural and useful. Accordingly, queueing models have served as prevalent standard support tools for call center management. However, the modern call center is a complex socio-technical system. It thus enjoys central features that challenge existing queueing theory to its limits, and beyond.The present document is an abridged version of a survey that can be downloaded from www.cs.vu.nl/obp/callcenters and ie.technion.ac.il/serveng.     

常微分方程形式的M/M/1排队模型的一个注

讨论动态Ｍ／Ｍ／１排队模型，运用半群理论证明了该模型存在唯一的正解，并研究了相应算子的谱特征．     

A state‐dependent Markov‐modulated mechanism for generating events and stochastic models

In this paper, we introduce a versatile block‐structured state‐dependent event (BSDE) approach that provides a methodological tool to construct non‐homogeneous Markov‐modulated stochastic models. Alternatively, the BSDE approach can be used to construct even a part (e.g. the arrival process) of the model. To illustrate the usefulness of the BSDE approach, several arrival patterns as well as queueing and epidemic models are considered. In particular, we deal with a state‐dependent quasi‐birth‐and‐death process that gives a constructive generalization of the scalar birth‐and‐death process and the homogeneous quasi‐birth‐and‐death process. Copyright © 2009 John Wiley & Sons, Ltd.