M/G/1/MLPS compared with M/G/1/PS within service time distribution class IMRL

Multilevel processor-sharing (MLPS) disciplines were originally introduced by Kleinrock (in computer applications 1976) but they were forgotten for years. However, due to an application related to the service differentiation between short and long TCP flows in the Internet, they have recently gained new interest. In this paper we show that, if the service time distribution belongs to class IMRL, the mean delay in the M/G/1 queue is reduced when replacing the PS discipline with any MLPS discipline for which the internal disciplines belong to {FB, PS}. This is a generalization of our earlier result where we restricted ourselves to the service time distribution class DHR, which is a subset of class IMRL.     

Analysis of the M x /G/1 Queue with a Random Setup Time

Abstract

We consider an M ^x /G/1 queueing system with a random setup time, where the service of the first unit at the commencement of each busy period is preceded by a random setup time, on completion of which service starts. For this model, the queue size distributions at a random point of time as well as at a departure epoch and some important performance measures are known [see Choudhury, G. An M ^x /G/1 queueing system with setup period and a vacation period. Queueing Sys. 2000, 36, 23–38]. In this paper, we derive the busy period distribution and the distribution of unfinished work at a random point of time. Further, we obtain the queue size distribution at a departure epoch as a simple alternative approach to Choudhury4 Choudhury, G. 2000. An M^x/G/1 queueing system with setup period and a vacation period. Queueing Syst., 36: 23–38. [CROSSREF][Crossref], [Web of Science ®] , [Google Scholar]. Finally, we present a transform free method to obtain the mean waiting time of this model.     

Sojourn time asymptotics in the M/G/1 processor sharing queue

We show for the M/G/1 processor sharing queue that the service time distribution is regularly varying of index -ν, ν non-integer, iff the sojourn time distribution is regularly varying of index -ν. This result is derived from a new expression for the Laplace–Stieltjes transform of the sojourn time distribution. That expression also leads to other new properties for the sojourn time distribution. We show how the moments of the sojourn time can be calculated recursively and prove that the kth moment of the sojourn time is finite iff the kth moment of the service time is finite. In addition, we give a short proof of a heavy traffic theorem for the sojourn time distribution, prove a heavy traffic theorem for the moments of the sojourn time, and study the properties of the heavy traffic limiting sojourn time distribution when the service time distribution is regularly varying. Explicit formulas and multiterm expansions are provided for the case that the service time has a Pareto distribution. This revised version was published online in June 2006 with corrections to the Cover Date.     

A note on comparing response times in the M/GI/1/FB and M/GI/1/PS queues

We compare the overall mean response time (a.k.a. sojourn time) of the processor sharing (PS) and feedback (FB) queues under an M/GI/1 system. We show that FB outperforms PS under service distributions having decreasing failure rates; whereas PS outperforms FB under service distributions having increasing failure rates.     

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.     

An Arrival Time Approach to M/G/1-type Queues with Generalized Vacations

We propose a simple way, called the arrival time approach, of finding the queue length distributions for M/G/1-type queues with generalized server vacations. The proposed approach serves as a useful alternative to understanding complicated queueing processes such as priority queues with server vacations and MAP/G/1 queues with server vacations.     

C0-半群理论在动态M／C／1排队系统中的应用

考察了动态M／G／1排队系统问题．利用泛函分析中的C0-半群理论给出了系统非负解的存在唯一性．     

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.     

M/G/1排队论系统的渐近稳定性

通过M/G/1算子的谱分析得到了M/G/1排队论系统的渐近稳定性.首先,将系统方程转化为某一合适Banach空间上的抽象Cauchy闻题,从而引入M/G/1算子.其次,分析了M/G/1算子的谱分布,得到了0是M/G/1算子的简单本征值且M/G/1算子的谱分布在左半平面的结果.最后,利用谱分析结果和算子半群理论得到了M/...     

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。     

Tail asymptotics for M/G/1 type queueing processes with subexponential increments

Bivariate regenerative Markov modulated queueing processes {I _n ,L _n } are described. {I _n } is the phase process, and {L _n } is the level process. Increments in the level process have subexponential distributions. A general boundary behavior at the level 0 is allowed. The asymptotic tail of the cycle maximum, , during a regenerative cycle, , and the asymptotic tail of the stationary random variable L _∞, respectively, of the level process are given and shown to be subexponential with L _∞ having the heavier tail. This revised version was published online in June 2006 with corrections to the Cover Date.     

具有可利用服务员的M/G/1排队模型

本文考虑了具有可利用服务员的M／G／1有有限容量的排队模型．当工作量超过k(k是常数或者随机变量),可利用服务员参与工作,一直到工作量少于或等于k．可利用服务员的速率依赖于目前工作量．应用Level-crossing方法,获得了工作量的平稳分布．应用Kolmogorov向后微分方程方法,构造更新方程以获得忙期的Laplace变换．     

具有随机N—策略的M／G／1排队系统

本文讨论具有随机N-策略的M/G/1排队系统,采用向量Markov过程方法得到该系统有关的排队指标。上述结果可以看作是普通的和N-策略的M/G/1排队系统的推广。     

A Markov-modulated M/G/1 queue I: Stationary distribution

We consider an M/G/1 queueing system in which the arrival rate and service time density are functions of a two-state stochastic process. We describe the system by the total unfinished work present and allow the arrival and service rate processes to depend on the current value of the unfinished work. We employ singular perturbation methods to compute asymptotic approximations to the stationary distribution of unfinished work and in particular, compute the stationary probability of an empty queue.This research was supported in part by NSF Grants DMS-84-06110, DMS-85-01535 and DMS-86-20267, and grants from the U.S. Israel Binational Science Foundation and the Israel Academy of Sciences.     

Age-based Markovian approximation of the G/M/1 queue

We extend the approach of Koole et al. (2012) [15] and Legros et al. (2018) [20] for the G/M/1 queue. The idea is to provide a Markovian approximation where a state represents the oldest customer's wait. This modeling is made possible by creating states with negative wait, representing an estimate of the time at which a new customer would arrive when the system is empty. We apply this method for performance evaluation and routing optimization. Finally, we further extend the model to the G/M/1+G queue.     

Higher moments of the waiting time distribution in M/G/1 retrial queues

This work analyzes the waiting time distribution in the M/G/1 retrial queue. The first two moments of the waiting time distribution are known from the literature. In this work we obtain all the moments of the waiting time distribution.     

The interdeparture-time distribution for each class in the ∑ i M i /G i /1 queue

A stationary queueing system is described in which a single server handles several competing Poisson arrival streams on a first-come first-served basis. Each class has its own generally distributed service time characteristics. The principal result is the Laplace-Stieltjes transform, for each class, of the interdeparture time distribution function. Examples are given and applications are discussed.     

A NEW APPROACH FOR THE STUDY OF THE M X /G/1 QUEUE USING RENEWAL ARGUMENTS

The M ^X /G/1 queueing system as well as several of its variants have long ago been studied by considering the embedded discrete-time Markov chain at service completion epochs. Alternatively other approaches have been proposed such as the theory of regenerative processes, the supplementary variable method, properties of the busy period, etc. In this note we study the M ^X /G/1 queue via a simple new method that uses renewal arguments. This approach seems quite powerful and may become fruitful in the investigation of other queueing systems as well.     

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/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.