可修排队系统M~X／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ＭＸ／Ｇ（／Ｈ）／１．记号（Ｍ／Ｈ）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，我们得到了它的明态解．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     

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.     

一类可修非周期Fork-Join排队网络分析

研究一类排队空间有限且服务台可修的非周期Fork-Join排队网络,给出求解稳态 概率的直接法和等效法,并计算一些排队指标和可修指标(如稳态队长、服务台的可用度和服 务台的失效概率),最后通过仿真验证其正确性.     

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.     

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.     

一类排队系统模型的计算机模拟

排队系统是离散事件系统最典型的问题之一，本文讨论了服务时间与队长有关的排队系统模拟，在单服务台及串联，并联多服务台情形下，建立了六个模拟模型，并给出模拟模型的计算实例。     

多顾客流排队系统模型的计算机模拟

排队系统是离散事件系统最典型的问题之一。本文讨论了多随机顾客流的排队系统模拟，在单服务台，串联及并联多服务台情形下建立六个模拟模型，这一类模型在网络，多用户系统等方面的性能和设计都有较广泛的应用。     

排队规则为后进先出且系统容量有限的一类排队系统模型的计算机模拟

本文讨论了排队规则为后进先出，系统容量有限且服务时间与队长有关的一类排队系统机模型的计算机模拟，由于系统容量有限，当队长超过某一值时，到达系统的顾客将直接离开，不能进入系统接受任何服务，这将造成系统的某些损失，因此本文也讨论了影响系统信誉的损失率，在排队规则为后进先出和单服务台，串联及并联多服务台情形下建立六个模拟模型，这类模型在计算机系统，物资管理系统及情报系统中都有较广泛的使用，本文最后给出模     

多顾客流排队系统模型的计算机模拟

排队系统是离散事件系统最典型的问题之一。本文讨论了多随机顾客流的排队系统模拟，在单服务台、串联及并联多服务台情形下建立六个模拟模型，这一类模型在网络、多用户系统等方面的性能分析和设计都有较广泛的应用。本文最后给出模拟模型的计算实例。     

带启动时间和工作故障的M/M/1/N排队系统性能分析

在M/M/1/N可修排队系统中引入了工作故障和启动时间.服务台在忙期允许出现故障,且在故障期间不是完全停止服务而是以较低的服务速率为顾客服务.同时,从关闭期到正规忙期有服从指数分布的启动时间.通过分析此模型的二维连续时间Markov过程,求解出系统平稳方程,建立此系统的有限状态拟生灭过程(QBD).根据系统参数,求解出水平相依的子率阵,从而得到系统稳态概率向量的矩阵几何表示形式.在系统稳态概率向量的基础上,求解出系统吞吐率、系统稳态可用度、系统稳态队长及系统处于各个状态的概率等性能指标的解析表达式.文中的敏感性分析体现了这种方法的有效性和可用性,同时,对系统各性能受系统参数的影响进行了探索.实验表明,文中提出模型的稳定性较好,且更贴近实际服务过程,因此这种模型将被广泛应用于各种实际服务中.     

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.     

Control Policies of an M/G/1 Queueing System with a Removable and Non-reliable Server

This paper considers a single non-reliable server in the ordinary M/G/1 queueing system whose arrivals form a Poisson process and service times are generally distributed. We also study a single removable and non-reliable server in the controllable M/G/1 queueing systems operating under the N policy, the T policy and the Min( N , T ) policy. It is assumed that the server breaks down according to a Poisson process and the repair time has a general distribution. In three control policies, we show that the probability that the server is busy in the steady-state is equal to the traffic intensity. It is shown that the optimal N policy and the optimal Min( N , T ) policy are always superior to the optimal T policy. Sensitivity analysis is also investigated.     

Discrete-time queues with generally distributed service times and renewal-type server interruptions

In this contribution, we investigate a discrete-time single-server queue subjected to server interruptions. Server interruptions are modeled as an on/off process with geometrically distributed on-periods and generally distributed off-periods. As message lengths can exceed one time-slot, different operation modes are considered, depending on whether service of an interrupted message continues, partially restarts or completely restarts after an interruption. For all alternatives, we establish expressions for the steady-state probability generating functions (pgf) of the buffer contents at message departure times and random slot boundaries, of the unfinished work at random slot boundaries, the message delay, and the lengths of the idle and busy periods. From these results, closed-form expressions for various performance measures, such as mean and variance of the buffer occupancy and message delay, can be established. As an application, we show that this model is able to assess performance of a multi-class priority scheduling system. We then illustrate our approach with some numerical examples.     

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.     

Analysis of the discrete-time Geo/G/1 working vacation queue and its application to network scheduling

In this paper we present an exact steady-state analysis of a discrete-time Geo/G/1 queueing system with working vacations, where the server can keep on working, but at a slower speed during the vacation period. The transition probability matrix describing this queuing model can be seen as an M/G/1-type matrix form. This allows us to derive the probability generating function (PGF) of the stationary queue length at the departure epochs by the M/G/1-type matrix analytic approach. To understand the stationary queue length better, by applying the stochastic decomposition theory of the standard M/G/1 queue with general vacations, another equivalent expression for the PGF is derived. We also show the different cases of the customer waiting to obtain the PGF of the waiting time, and the normal busy period and busy cycle analysis is provided. Finally, we discuss various performance measures and numerical results, and an application to network scheduling in the wavelength division-multiplexed (WDM) system illustrates the benefit of this model in real problems.     

Optimal control of the M/G/1 queue with repeated vacations of theserver

An M/G/1 queue where the server may take repeated vacations is considered. Whenever a busy period terminates, the server takes a vacation of random duration. At the end of each vacation, the server may either take a new vacation or resume service; if the queue is found empty, the server always takes a new vacation. The cost structure includes a holding cost per unit of time and per customer in the system and a cost each time the server is turned on. One discounted cost criterion and two average cost criteria are investigated. It is shown that the vacation policy that minimizes the discounted cost criterion over all policies (randomized, history dependent, etc.) converges to a threshold policy as the discount factor goes to zero. This result relies on a nonstandard use of the value iteration algorithm of dynamic programming and is used to prove that both average cost problems are minimized by a threshold policy