G／G／1排队系统的渐近泊松离去过程

本文给出了Ｇ／Ｇ／１排队系统的离去过程的有限维分布弱收敛到泊松过程的有限维分布的条件,特别给出了生灭排队系统及Ｇ／Ｍ／１排队系统的离去过程的有限维分布弱收敛到泊松过程的有限维分布的简单条件．     

推广的M~x/G(M/G)/1(M/G)可修排队系统(I)── 一些排队指标

考虑M     

Markov-modulatedPH/G/1 queueing systems

We study a PH/G/1 queue in which the arrival process and the service times depend on the state of an underlying Markov chain J(t) on a countable state spaceE. We derive the busy period process, waiting time and idle time of this queueing system. We also study the Markov modulated E_K/G/1 queueing system as a special case.     

Matched queueing system MoPH/G/1

In this paper, we study the matched queueing system, MoPH/G/1, where the type-I input is a Poisson process, the type-II input is a PH renewal process, and the service times are i.i.d. random variables. A necessary and sufficient condition for the stationariness of the system is given. The expectations of the length of the non-idle period and the number of customers served in a non-idle period are obtained.This project is supported by the National Natural Science Foundation of China and partially by the Institute of Mathematics, Academia Sinica.     

ANALYSIS OF M/G/1 STOCHASTIC CLEARING SYSTEMS

In this paper, we consider M/G/1 queuing systems governed by a stochastic clearing mechanism, called “disaster,” which removes all workload in the system whenever it occurs to the system. The clearing mechanism of disasters can be applied to computer systems in the presence of a virus as a clearing operation of all stored messages present in the system. We present the system size distribution and the sojourn time distribution.     

The MacLaurin expansion for a G/G/1 queue with Markov-modulated arrivals and services

Consider a Markov-modulated G/G/1 queueing system in which the arrival and the service mechanisms are controlled by an underlying Markov chain. The classical approaches to the waiting time of this type of queueing system have severe computational difficulties. In this paper, we develop a numerical algorithm to calculate the moments of the waiting time based on Gong and Hu's idea. Our numerical results show that the algorithm is powerful. A matrix recursive equation for the moments of the waiting time is also given under certain conditions.     

M/G/1重试排队系统的渐近稳定性

用算子半群理论研究了带有重试排队的M/G/1系统.通过解算子方程和预解方程,证明了0是系统算子的本征值,且为虚轴上唯一的谱点.从而得出了当时间趋于无穷时系统时间依赖解收敛于稳态解的结论.     

Optimal Flow Control of a G/G/c Finite Capacity Queue

The optimal flow control of a G/G/c finite capacity queue is investigated by approximating the general (G-type) distributions by a maximum entropy model with known first two moments. The flow-control mechanism maximizing the throughput, under a bounded time-delay criterion, is shown to be of window type (bang-bang control). The optimal input rate and the maximum number of packets in the system (i.e. sliding window size) are derived in terms of the maximum input rate and the second moment of the interinput time, the maximum allowed average time delay, the first two moments of the service times and the number of servers. Moreover, the relationship between the maximum throughput and maximum time delay is determined. Numerical examples provide useful information on how critically the optimal throughput is affected by the distributional form of the input and service patterns and the finite capacity of the queue.     

A Maximum Entropy Analysis of the G/G/1 Queue at Equilibrium

The principle of maximum entropy is used to analyse a G/G/1 queue at equilibrium when the constraints involve only the first two moments of the interarrival-time and service-time distributions. Robust recursive relations for the queue-length distribution are determined, and a probability density function analogue is characterized. Furthermore, connections with classical queueing theory and operational analysis are established, and an overall approximation, based on the concept of ‘global’ maximum entropy, is introduced. Numerical examples provide useful information on how critically system behaviour is affected by the distributional form of the interarrival and service times, and favourable comparisons are made with diffusion and other approximations. Comments on the implication of the work to the analysis of more general queueing systems are included.     

多重休假GI／G／1排队系统的非统计平衡理论

文献[1]引入了一类具有广泛应用前景的随机过程-Markov骨架过程，文献[2]研究了GI/G/1排队系统，本文对其进行了拓展，研究了多重休假GI/G/1排队模型。求出了此模型的到达过程，等待时间及队长的概率分布。     

M/G/1/K queues withN-policy and setup times

A steady-state analysis is given for M/G/1/K queues with combinedN-policy and setup times before service periods. The queue length distributions and the mean waiting times are obtained for the exhaustive service system, the gated service system, the E-limited service system, and the G-limited service system. Numerical examples are also provided.     

A note on the C2/G/1 queue and the C2/G/1 loss system

In this note, we consider the steady-state probability of delay (PW) in the C₂/G/1 queue and the steady-state probability of loss (p_loss) in the C₂/G/1 loss system, in both of which the interarrival time has a two-phase Coxian distribution. We show that, for c_X ²<1, where c_X is the coefficient of variation of the interarrival time, both p_loss and PW are increasing in β(s), the Laplace–Stieltjes transform of the general service-time distribution. This generalises earlier results for the GE₂/G/1 queue and the GE₂/G/1 loss system. The practical significance of this is that, for c_X ²<1, p_loss in the C₂/G/1 loss system and PW in the C₂/G/1 queue are both increasing in the variability of the service time. This revised version was published online in June 2006 with corrections to the Cover Date.     

The M/G/1 queue with disasters and working breakdowns

In this paper, we analyze the M/G/1 queueing system with disasters and working breakdown services. The system consists of a main server and a substitute server, and disasters only occur while the main server is in operation. The occurrence of disasters forces all customers to leave the system and causes the main server to fail. At a failure instant, the main server is sent to the repair shop and the repair period immediately begins. During the repair period, the system is equipped with the substitute server which provides the working breakdown services to arriving customers. After introducing the concept of working breakdown services, we derive the system size distribution and the sojourn time distribution. We also obtain the results of the cycle analysis. In addition, numerical works are given to examine the relation between the sojourn time and the some system parameters.     

M/G/1排队系统的性能灵敏度分析

非Markov型排除系统经常被用来作为某些实际工程问题（如通讯网络）的研究模型,对于一般的M／G／1排队系统,本文通过研究其嵌入Markov链,讨论了系统的稳态性能灵敏度分析问题,并给出用嵌入Markov链的势能表示的稳态性能灵敏度公式,由于嵌入Markov链要比描述其系统状态的半Markov过程简单得多,故本文的结果对M／G／1排队系统的性能灵敏度仿真计算及系统的优化,都将带来极大的方便。     

Clearing Models for M/G/1 Queues

We consider M/G/1-type queueing systems with disasters, occurring at certain random times and causing an instantaneous removal of the entire residual workload from the system. After such a clearing, the system is assumed to be ready to start working again immediately. We consider clearings at deterministic equidistant times, at random times and at crossings of some prespecified level, and derive the stationary distribution of the workload process for these clearing times and some of their combinations.     

M x /G/1 Queue with Multiple Vacations

Abstract

In this article, we study a queueing system M ^x /G/1 with multiple vacations. The probability generating function (P.G.F.) of stationary queue length and its expectation expression are deduced by using an embedded Markov chain of the queueing process. The P.G.F. of stationary system busy period and the probability of system in service state and vacation state also are obtained by the same method. At last we deduce the LST and mean of stationary waiting time in the service order FCFS and LCFS, respectively.     

An M/G/1 queue with cyclic service times

In this paper we consider a single server queue with Poisson arrivals and general service distributions in which the service distributions are changed cyclically according to customer sequence number. This model extends a previous study that used cyclic exponential service times to the treatment of general service distributions. First, the stationary probability generating function and the average number of customers in the system are found. Then, a single vacation queueing system with aN-limited service policy, in which the server goes on vacation after servingN consecutive customers is analyzed as a particular case of our model. Also, to increase the flexibility of using theM/G/1 model with cyclic service times in optimization problems, an approximation approach is introduced in order to obtain the average number of customers in the system. Finally, using this approximation, the optimalN-limited service policy for a single vacation queueing system is obtained.On leave from the Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran 16844, Iran.     

A MAP/G/1 Queue with Negative Customers

In this paper, we consider a MAP/G/1 queue with MAP arrivals of negative customers, where there are two types of service times and two classes of removal rules: the RCA and RCH, as introduced in section 2. We provide an approach for analyzing the system. This approach is based on the classical supplementary variable method, combined with the matrix-analytic method and the censoring technique. By using this approach, we are able to relate the boundary conditions of the system of differential equations to a Markov chain of GI/G/1 type or a Markov renewal process of GI/G/1 type. This leads to a solution of the boundary equations, which is crucial for solving the system of differential equations. We also provide expressions for the distributions of stationary queue length and virtual sojourn time, and the Laplace transform of the busy period. Moreover, we provide an analysis for the asymptotics of the stationary queue length of the MAP/G/1 queues with and without negative customers.     

An M/G/1 queueing model with vacation times

This paper deals with an M/G/1 queueing system with finite capacity for the workload, where the workload at timet is defined as the total amount of work in the system at timet. When the server provides service he will continue servicing until the system becomes empty, after which he leaves the system for a stochastic period of time, which will be called a vacation. When the server, returning from a vacation, finds the system still empty, he leaves for another vacation, otherwise he immediately starts servicing again.Using an embedding approach several characteristics of this system are derived amongst which the joint stationary distribution of the workload and the stage of the server.

---

Zusammenfassung Diese Arbeit befaßt sich mit einem M/G/1 Wartesystem, das hinsichtlich der anstehenden Arbeit eine endliche Kapazität hat. Wenn der Bediener tätig ist, bleibt er es solange, bis das System leer ist. Danach ist er während einer stochastischen Pausenzeit nicht verfügbar. Ist am Ende einer Pausenzeit das System immer noch leer, so schließt sich eine weitere Pausenzeit an; ansonsten wird unverzüglich die Bedienung am Ende der Pausenzeit wieder aufgenommen.Unter Verwendung eines eingebetteten Prozesses werden mehrere Kenngrößen des Systems ermittelt, darunter z.B. die gemeinsame Verteilung von anstehender Arbeit und Zustand des Bedieners.

     

G/M/1 queues with delayed vacations

We considerG/M/1 queues with multiple vacation discipline, where at the end of every busy period the server stays idle in the system for a period of time called changeover time and then follows a vacation if there is no arrival during the changeover time. The vacation time has a hyperexponential distribution. By using the methods of the shift operator and supplementary variable, we explicitly obtain the queue length probabilities at arrival time points and arbitrary time points simultaneously.