具有Bernoulli反馈且带有负顾客的PH/M/1排队系统

在PH/M/1排队模型中,引入了负顾客和Bernoulli反馈,并讨论了服务台容量为有限和无限两类模型,其中,模型一为服务台容量为无限的PH/M/1排队模型,利用拟生灭过程和矩阵几何解法得到了系统的转移速率矩阵,给出了系统正常返的充要条件,并得到了系统的稳态队长、忙期长度的拉普拉斯变换,以及系统的其它相关性能指标.模型二为服务台容量为有限的PH/M/1/N排队模型,同样使用拟生灭过程给出了马尔科夫过程的转移速率矩阵,并利用矩阵分析法进行求解,得到了该系统的稳态解和其它相关指标.     

可修排队系统GI/PH(M/PH)/1

在通常的排队系统中,考虑服务台在服务过程中可能失效和可修理,称之为可修排队系统(RQS).对此类排队系统的研究,继[1]之后,有[4]～[7]等.本文研究更一般的可修排队系统 GI/PH(M/PH)/1     

相依修理的可修排队系统 MAP/PH(M/PH)/2

系统地研究了两个不同并行服务台的可修排队系统MAP/PH(M/PH)/2,其中两个不同的服务台拥有一个修理工.若其中一台处于修理状态,则另一台失效后就处于待修状态.利用拟生灭过程理论,我们首先讨论了两个服务台的广义服务时间的相依性,然后给出了系统的稳态可用度和稳态故障度,最后得到了系统首次失效前的时间分布及其均值.     

离散时间排队MAP/PH/3

本文研究具有马尔可夫到达过程的离散时间排队MAP/PH/3,系统中有三个服务台,每个服务台对顾客的服务时间均服从位相型分布。运用矩阵几何解的理论,我们给出了系统平稳的充要条件和系统的稳态队长分布。同时我们也给出了到达顾客所见队长分布和平均等待时间。     

PH/M/c可修排队系统

研究了一个修理工和c个服务台的可修排队系统.假设顾客的到达过程为PH更新过程,服务台在忙时与闲时具有不同的故障率.顾客的服务时间、服务台的寿命以及服务台的修理时间均服从指数分布.通过建立系统的拟生灭过程,得到了系统稳态分布存在的充要条件.利用矩阵几何解方法,给出了系统的稳态队长.在此基础上,得到了系统的某些排队论和可靠性指标.     

离散时间服务台可修的排队系统MAP／PH（PH／PH）／1

本文研究离散时间可修排队系统,其中顾客的输入过程为离散马尔可夫到达过程（MAP）,服务台的寿命,服务台的顾客的服务时间和修理时间均为离散位相型（PH）变量,首先我们考虑广义服务过程,证明它是离散MAP,然后运用阵阵几何解理论,我们给出了系统的稳态队长分布和稳态等待时间分布,同时给出了系统的稳态可用度这一可靠性指标。     

PH-启动时间的 GI/M/1排队

本文研究启动时间服从相型分布的 GI/M/1随机服务系统.使用嵌入 Markov链和矩阵几何解方法,得到系统稳态下队长和等待时间的分布和随机分解.我们证明了,由启动时间引起的附加顾客数及附加延迟,分别是离散的和连续的 PH 变量,并给出其不可约表示.     

GI／PH／1休假排队系统队长的随机分解

对空竭服务、多重休假规则的GI/PH/1排队系统的稳态行为给出了详尽分析。在休假时间服从负指数分布情况下,讨论了到达点嵌入Markov链的结构、平衡条件和稳态队长。证明稳态队长可分解成两个独立随机变量之和。     

服务台可修的Geometric/G/1离散时间排队

本文讨论服务台可修的离散时间Geometric／G/1排队，平行于连续时间可修M／G／1模型，给出了系统的各种稳态指标．     

两个修理工的M/M/2可修排队系统

该文研究两个修理工的M/M/2可修排队系统, 系统有两个相同的服务台, 服务台忙时与闲时故障率不同. 文中给出系统的稳态状态概率, 系统的稳态可用度及系统的稳态平均队长, 并给出系统稳态概率存在的条件.     

服务台可修的M／SM（PH／SM）／1排队系统

本文研究服务台可修的Ｍ／ＳＭ（ＰＨ／ＳＭ）／１排队系统的随机结构和性态．先证明这个可修排队系统在平稳状态下可转化为一个等价的通常排队模型，然后给出服务台的所有稳态可靠性指标及其相关的结果．     

Analysis of a finite MAP/G/1 queue with group services

The finite capacity queues, GI/PH/1/N and PH/G/1/N, in which customers are served in groups of varying sizes were recently introduced and studied in detail by the author. In this paper we consider a finite capacity queue in which arrivals are governed by a particular Markov renewal process, called a Markovian arrival process (MAP). With general service times and with the same type of service rule, we study this finite capacity queueing model in detail by obtaining explicit expressions for (a) the steady-state queue length densities at arrivals, at departures and at arbitrary time points, (b) the probability distributions of the busy period and the idle period of the server and (c) the Laplace-Stieltjes transform of the stationary waiting time distribution of an admitted customer at points of arrivals. Efficient algorithmic procedures for computing the steady-state queue length densities and other system performance measures when services are of phase type are discussed. An illustrative numerical example is presented.     

The GI/M/1 queue with phase-type working vacations and vacation interruption

Consider a GI/M/1 queue with phase-type working vacations and vacation interruption where the vacation time follows a phase-type distribution. The server takes the original work at the lower rate during the vacation period. And, the server can come back to the normal working level at a service completion instant if there are customers at this instant, and not accomplish a complete vacation. From the PH renewal process theory, we obtain the transition probability matrix. Using the matrix-analytic method, we obtain the steady-state distributions for the queue length at arrival epochs, and waiting time of an arbitrary customer. Meanwhile, we obtain the stochastic decomposition structures of the queue length and waiting time. Two numerical examples are presented lastly.     

The GI/M/1 queue with exponential vacations

In this paper, we give a detailed analysis of the GI/M/1 queue with exhaustive service and multiple exponential vacation. We express the transition matrix of the imbedded Markov chain as a block-Jacobi form and give a matrix-geometric solution. The probability distribution of the queue length at arrival epochs is derived and is shown to decompose into the distribution of the sum of two independent random variables. In addition, we discuss the limiting behavior of the continuous time queue length processes and obtain the probability distributions for the waiting time and the busy period.     

Sojourn Times in the <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">PH</Emphasis>/1 Processor Sharing Queue

We give in this paper an algorithm to compute the sojourn time distribution in the processor sharing, single server queue with Poisson arrivals and phase type distributed service times. In a first step, we establish the differential system governing the conditional sojourn times probability distributions in this queue, given the number of customers in the different phases of the PH distribution at the arrival instant of a customer. This differential system is then solved by using a uniformization procedure and an exponential of matrix. The proposed algorithm precisely consists of computing this exponential with a controlled accuracy. This algorithm is then used in practical cases to investigate the impact of the variability of service times on sojourn times and the validity of the so-called reduced service rate (RSR) approximation, when service times in the different phases are highly dissymmetrical. For two-stage PH distributions, we give conjectures on the limiting behavior in terms of an M/M/1 PS queue and provide numerical illustrative examples.This revised version was published online in June 2005 with corrected coverdate     

Simple Approximations for the GI/G/c Queue—I: The Steady-State Probabilities

Viewing the GI/G/c queue as a service system alternating between two basic states—that of a loaded (non-empty) GI/G/1 queue and that of a GI/G/∞ queue (dependent, respectively, on whether all servers in the GI/G/c queue are busy or otherwise)—approximations for the components of the mixture distribution of the steady-state probabilities are derived. The M/G/c queue is separately treated. Two imposed prerequisites, that only minimal prior information about the queue will be required and that no numeric method be needed other than a root-finding algorithm, are strictly adhered to. The accuracy attained is generally satisfactory, while remarkable algebraic simplicity is preserved.     

On the Queue Length Distribution for the GI/G/1/K/VM Queue

Abstract

We present a transform-free distribution of the steady-state queue length for the GI/G/1/K queueing system with multiple vacations under exhaustive FIFO service discipline. The method we use is a modified supplementary variable technique and the result we obtain is expressed in terms of conditional expectations of the remaining service time, the remaining interarrival time, and the remaining vacation, conditional on the queue length at the embedded points. The case K → ∞ is also considered.     

服务台可修的GI／M（M／PH）／1排队系统

本文首次讨论一个到达间隔为一般分布的可修排队系统。假定服务时间、忙期服务台寿命都服从指疏分布，修复时间是ＰＨ变量。首先证明该系统可转化为一个经典的ＧＩ／￣ＰＨ／１排队模型，然后给出系统在稳态下的各种排队论指标和可靠性指标。