带启动时间和可修服务台的M/M/1/N工作休假排队系统

分析带有启动时间、服务台可故障的M/M/1/N单重工作休假排队系统.在该系统中,服务台在休假期间不是完全停止工作,而是处于低速服务状态.假定服务台允许出现故障且当出现故障时,服务台停止为顾客服务且立即进行修理.服务台的失效时间和修理时间均服从指数分布,且工作休假期和正规忙期具有不同的取值;同时,从关闭期到正规忙期有服从指数分布的启动时间.建立此工作休假排队系统的有限状态拟生灭过程(QBD),使用矩阵几何方法得到QBD的各稳态概率相互依赖的率阵,从而求得稳态概率向量.通过有限状态QBD的最小生成元和稳态概率向量得到系统的基本阵和协方差矩阵,求解出系统方差、系统稳态可用度、系统吞吐率、系统稳态队长、系统稳态故障频度等系统性能.数值分析体现了所提出方法的有效性和实用性,通过敏感性分析将各参数对系统性能的影响进行了初探,为此模型的实际应用提供了很好的理论依据.     

带工作休假和工作故障的M/M/1/N排队系统性能分析

本文在可修M/M/1/N排队系统中引入了启动时间、工作休假和工作故障策略.在该系统中,服务台在休假期间不是完全停止工作,而是处于低速服务状态.设定服务台在任何时候均可发生故障,当故障发生时立刻进行维修.且当服务台在正规忙期出现故障时,服务台仍以较低的服务速率为顾客服务.服务台的寿命时间和修理时间均服从指数分布,且在不同的时期有不同的取值.同时,从关闭期到正规忙期有服从指数分布的启动时间.本文建立此模型的有限状态拟生灭过程(QBD),使用矩阵几何方法得到系统的稳态概率向量,并应用基本阵和协方差矩阵理论,计算出系统稳态可用度、系统方差、系统吞吐率、系统稳态队长及各系统稳态概率等系统性能指标.同时,通过数值实验对各系统参数对系统性能的影响进行了初探.文中的敏感性分析体现了这种方法的有效性和可用性.实验表明,文中提出的模型,可有效改善仅带有工作休假或工作故障策略排队模型的系统性能.     

考虑缓冲区故障的多产品生产系统的性能分析

对带有生产准备时间和缓冲区故障且生产时间服从任意分布的多产品生产系统进行分析,通过构建系统状态向量,建立其离散时间马尔可夫链模型.根据多产品生产系统的工作过程对系统状态向量分4种情况进行讨论,计算出系统的状态转移矩阵;在计算系统稳态向量的基础上获得系统生产率的计算流程.根据所建立的模型,对参数对称且可生产两种产品的多产品生产系统进行详细求解,给出其系统生产率的计算过程,通过Matlab进行数学实验,分析总结出缓冲区的无故障率、产品到达率、生产准备时间、服务率及其变异系数对系统生产率的影响.     

再访GI/M/1排队

通过构造两个向量马氏过程重新探讨了GI/M/1排队,某些新结果如忙期和闲期的 联合分布被得到了.这一方法容易推广到服务时间为无限位相型分布的GI/SPH/1排队.     

可修排队系统GI/G(M/G)/1的可靠性分析

利用更新过程理论和向量马氏过程方法全面考察了可修排队系统GI/G(M/G)/1的结 构,得到了所有感兴趣的指标,并证明了服务台的可靠性指标只与系统的忙期、闲期和忙期循 环时间有关.     

基于M/M/n/n+r排队模型的云计算中心服务性能分析

针对需要精确地评估分析云数据中心服务性能以保证服务质量(QoS)和避免违反服务水平协议(SLA)的问题,提出了一个基于M/M/n/n+r排队系统云计算中心近似分析模型。通过求解该模型获得用户请求响应时间的分布函数以及其他重要的QoS性能指标,同时通过仿真实验验证和获得服务器数量、队列缓冲区大小与响应时间、请求阻塞概率以及请求立即服务概率之间的关系。实验结果表明,提高服务器服务速率比增加服务器数量更利于提高服务性能。     

具有优先权的M/G/1重试可修排队系统

在服务台忙的情况下, 到达服务台的顾客以概率 q 进入无限位置的优先队列而以概率 p 进入无限位置的重试轨道 (orbit), 并且按照先到先服务 (FCFS) 规则排队, 假定只有队首的顾客允许重试, 同时考虑服务台可修的因素, 证明了系统稳态解存在的充要条件. 利用补充变量法求得稳态时两个队列与系统的平均队长、顾客等待时间、服务台的各种状态概率以及可靠性指标.     

考虑维修优先权的多状态温贮备系统可靠性模型

针对工程应用中装备维修和保养两类活动具备不同优先级这一问题,考虑单一维修台可进行维修和保养两类工作,其中维修具有优先权.以多状态温贮备系统为研究对象,采用可近似拟合任意分布的Phase-type(PH)分布构建一种描述能力更强的系统可靠性模型,得出系统稳态可用度、系统故障率、平均故障间隔时间等一系列可靠性指标的解析表达式.最后利用算例验证PH分布的适用性,演示系统可靠性函数随时间的变化趋势,并讨论维修台工作速率对系统故障率、稳态可用度、维修台忙期稳态概率和平均故障间隔时间的影响.算例结果表明,所提模型具有较广泛的应用价值.     

基于M/M/c排队模型的云计算中心能耗管理策略

由于云计算中心在降低能耗的同时还需要保证服务质量（QoS）,针对用户访问云计算中心的排队机制,给出一种云计算任务排队模型,在此基础上提出一种基于M/M/c排队过程的云计算中心能耗管理算法,通过求解该模型获得了平均等待时间、阻塞概率等性能指标进而建立系统的能耗模型。同时用参量ERP（Energy-Response time Product）作为排队网络的反馈量,引入反馈策略及服务器休眠预留机制,动态调整云计算中心服务器服务数。仿真结果表明,与其他策略进行比较该策略能够在保证QoS值的情况下,有效降低系统的能耗,避免了服务器资源浪费。     

大型M/P/C/C排队系统仿真研究

理论上推测Erlang B 公式对服务时问为任意分布的M/G/C/C系统的呼叫损失概率是有效的但缺乏严格证明.据此,对服务时间呈 Pareto 分布的M/P/C/C排队系统的仿真问题进行了研究,特别是对排队系统中服务装置数目很大的情况进行了研究.采用一种名为红黑树的数据结构较好地解决了超长序列、超大C值所造成的计算时间问题,并采用基于事件驱动的时间调度法进行排队仿真,结果与 Erlang-B 公式相符.表明Erlang B公式对M/P/C/C系统的呼叫损失概率是有效的.为采用仿真方法对自相似流下的网络性能进行深入研究打下了基础.     

Cost-minimization analysis of a working vacation queue with N-policy and server breakdowns

This paper investigates the N-policy M/M/1 queueing system with working vacation and server breakdowns. As soon as the system becomes empty, the server begins a working vacation. The server works at a lower service rate rather than completely stopping service during a vacation period. The server may break down with different breakdown rates during the idle, working vacation, and normal busy periods. It is assumed that service times, vacation times, and repair times are all exponentially distributed. We analyze this queueing model as a quasi-birth–death process. Furthermore, the equilibrium condition of the system is derived for the steady state. Using the matrix-geometric method, we find the matrix-form expressions for the stationary probability distribution of the number of customers in the system and system performance measures. The expected cost function per unit time is constructed to determine the optimal values of the system decision variables, including the threshold N and mean service rates. We employ the particle swarm optimization algorithm to solve the optimization problem. Finally, numerical results are provided, and an application example is given to demonstrate the applicability of the queueing model.     

Potentials Method for M/G/1/m Systems with Hysteretic Operating Strategies

A research technique is proposed to analyze M/G/1/m queueing systems with hysteretic strategies of random dropping of customers and control of service time. Formulas are obtained to find the Laplace transforms of the distribution of the number of customers in the system during busy period and the distribution function of busy period and to calculate the stationary characteristics. The relations for stationary characteristics are tested on examples by simulation models constructed with the use of GPSS World workbenches.     

Performance analysis of an M/G/1 queueing system under Bernoulli vacation schedules with server setup and close down periods

This paper is concerned with the analysis of a single server queueing system subject to Bernoulli vacation schedules with server setup and close down periods. An explicit expression for the probability generating function of the number of customers present in the system is obtained by using imbedded Markov chain technique. The steady state probabilities of no customer in the system at the end of vacation termination epoch and a service completion epoch are derived. The mean number of customers served during a service period and the mean number of customers in the system at an arbitrary epoch are investigated under steady state. Further, the Laplace-Stieltjes transform of the waiting time distribution and its corresponding mean are studied. Numerical results are provided to illustrate the effect of system parameters on the performance measures.     

An M/G/1 retrial G-queue with non-exhaustive random vacations and an unreliable server

This paper deals with an M/G/1 retrial queue with negative customers and non-exhaustive random vacations subject to the server breakdowns and repairs. Arrivals of both positive customers and negative customers are two independent Poisson processes. A breakdown at the busy server is represented by the arrival of a negative customer which causes the customer being in service to be lost. The server takes a vacation of random length after an exponential time when the server is up. We develop a new method to discuss the stable condition by finding absorb distribution and using the stable condition of a classical M/G/1 queue. By applying the supplementary variable method, we obtain the steady-state solutions for both queueing measures and reliability quantities. Moreover, we investigate the stochastic decomposition law. We also analyse the busy period of the system. Some special cases of interest are discussed and some known results have been derived. Finally, an application to cellular mobile networks is provided and the effects of various parameters on the system performance are analysed numerically.     

可修排队系统Mx/G (M/H)1的瞬态解

本文研究一个典型的批到达可修排队系统＾ｘ／（／）１．记号（／）表服务台寿命服从指数分布，而其修理时间为一连续型分布。利用向量马氏过程方法，我们得到了它的瞬态解。特别是发现了服务台的可靠性指标仅依赖于可修排队系统的空闲概率，或等价地仅依赖于它的忙期和忙循环。     

On Homogeneity and On Line=Off-Line Behavior in M/G/1 Queueing Systems

Operational analysis replaces certain classical queueing theory assumptions with the conditions of "homogeneous service times" and "on-line= off-line behavior." In this paper we explore the relationship between the operational and classical concepts for the sample paths of an M/G/1 queueing system. The primary results are that the sample paths can have these operational properties with nonzero probability if and only if the service time is exponential. We also state dual results for interarrival times in G/M/l. Additionally, we show that open, feedforward networks of single server queues can have product form solutions valid across a range of system arrival rates if and only if all of the service times are exponential. Finally, we consider the relationship between the operational quantities S(n) and the mean service time in M/G/1. This relationship is shown to depend on the form of the service time distribution. It follows that using operational analysis to predict the performance of an M/G/1 queueing system will be most successful when the service time is exponential. Simulation evidence is presented which supports this claim.     

Analysis of a G/M/K/O queueing loss system with heterogeneous servers and retrials

Consider a G/M/K/O queueing loss system with K heterogeneous servers, exponentially distributed service times, no waiting room, a stationary counting arrival process, and an ordered entry. The ordered entry rule implies that, if the servers are indexed from 1 to K, units first arrive at the first server, then at the second server, and finally at the Kth server. In this queueing system, units that find the servers busy are not lost. Those units re-try to receive service by merging with the incoming units to be reconsidered for service by one of the free servers. This queueing system is analysed in terms of approximating the flows of units inside the system by a two parameter method. An example is introduced and approximation results are compared with those from a simulation study.