On Estimation in M/G/c/c Queues

We derive the minimum variance unbiased estimator (MVUE) and the maximum likelihood estimator (MLE) of the stationary probability function (pf) of the number of customers in a collection of independent M / G / c / c subsystems. It is assumed that the offered load and number of servers in each subsystem are unknown. We assume that observations of the total number of customers in the system are utilized because it may be impractical or impossible to observe individual server occupancies. Both estimators depend on the R distribution (the distribution of the sum of independent right truncated Poisson random variables) and R numbers.     

移动环境下医院信息服务系统的设计与实现

信息移动化是企业数据应用重要发展方向.J2ME主要为无线应用提供技术解决方案,而J2EE主要针对性能较高的服务端应用,不能直接移植到移动应用中去.针对移动环境特征,文章给出了J2ME/J2EE集成框架,结合MVC模式,设计出了移动应用系统体系结构.对移动数据传输技术进行了探讨,提出了基于XML的数据传输方案.最后,结合医院实际需求,设计并实现了一个医院移动信息服务系统.     

基于PME重尾分布服务时间的M/G/1模型排队性能研究

通信网络的业务源普遍存在着白相似性（或称为长相关性）,传统的假定业务到达间隔服从负指数分布的Poisson模型或其改进形式已不再适用．但在利用M／G／1模型对白相似业务源进行排队分析时,由于重尾分布服务时间的LST变换无闭合形式,进行排队性能分析非常困难．该文通过引入一类混合指数分布证明此类分布服从Pareto重尾分布,并得到相应的LST变换闭合形式及服务时间渐进级数,同时将形状参数y=3／2时的服务时间及其LST变换推广到更一般的情形,从而较为有效地解决了重尾分布的信源排队等待时间分析问题．     

非强占有限优先权M/G/1排队系统

针对部分数据帧有完全优先权发送的计算机网络数据服务系统存在的网络拥塞风险问题,提出了一种非强占有限优先权M/G/1排队系统模型的方法。该系统模型引入控制完全优先权的参数n,使得数据帧的完全优先权变成有限优先权,考虑了不同优先级队伍之间的公平性,降低了计算机网络数据服务系统拥塞的风险,使得网络系统在有限优先权下有较好的稳定性。在模型研究中,运用全概率拆解方法获得各级队伍平均等待时间、平均逗留时间和平均队长的理论结果。对模型采用Matlab 2010a软件实验仿真,实验得到的各级队伍平均等待时间和理论平均等待时间的平均绝对误差为0.951%。实验中,有限优先权条件下各级顾客的平均等待时间比值显著小于完全优先权条件下各级顾客的平均等待时间比值。实验结果表明对非强占有限优先权M/G/1排队系统模型研究的理论结果是正确的,该模型具有更稳定的系统特性。     

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.     

The Geometry of M/D/1 Queues and Large Deviation

Since an M/D/1 queue is represented by a Markov chain, we can consider the set of all the M/D/1 queues as a subset of Markov chains. A geometric structure is induced from the geometric structure of the set of Markov chains, which forms an exponential family. In this paper, we show that in the large deviation of the tail probability of the queue length of an M/D/1, the rate function and a twisted Markov chain, etc., are represented in terms of the geometry. Moreover, in the importance sampling (IS) simulation for the M/D/1 queue, we elucidate the geometric relation between the underlying distribution and a simulation distribution, and evaluate the variance of an IS estimate by geometric quantities.     

Analysis of a finite-capacity M/G/1 queue with a resume level

In order to model the buffer pool behavior in a data communication component, an M/G/1/K queue where input is shut down when the queue size (number of messages) attains K until it decreases to a specified level is analyzed. By use of semi-Markov process approach, the queue length distribution at an arbitrary time is found, and the resultant performance measures (utilization, loss probability, and mean response time) are computed.     

Randomized control of T-policy for an M/G/1 system

We study an M/G/1 queueing system with a server that can be switched on and off. The server can take a vacation time T after the system becomes empty. In this paper, we investigate a randomized policy to control a server with which, when the system is empty, the server can be switched off with probability p and take a vacation or left on with probability (1 − p) and continue to serve the arriving customers. For this system, we consider the operating cost and the holding cost where the operating cost consists of the system running and switching costs (start up and shut down costs). We describe the structure and characteristics of this policy and solve a constrained problem to minimize the average operating cost per unit time under the constraint for the holding cost per unit time.     

Analysis of waiting time of M/G/1/K system with vacations under random scheduling and LCFS

This paper considers an M/G/1/K queueing system with multiple vacations under random scheduling and LCFS disciplines. As for M/G/1/K vacation models, Lee obtained the results of the joint distribution of the number of messages in the system and the remaining service or vacation time for a message. Using these expressions, we derive LSTs of the waiting time distribution under the two service disciplines. We show the calculation method for the first and the second moments of the waiting time under two service disciplines. Furthermore, we illustrate some numerical results of the mean waiting times and the coefficient of variations of the waiting time under FCFS, random scheduling and LCFS.     

Information theoretic approximations for M/G/1 and G/G/1 queuing systems

Summary This paper presents new results concerning the use of information theoretic inference techniques in system modeling and concerning the widespread applicability of certain simple queuing theory formulas. For the case when an M/G/1 queue provides a reasonable system model but when information about the service time probability density is limited to knowledge of a few moments, entropy maximization and cross-entropy minimization are used to derive information theoretic approximations for various performance distributions such as queue length, waiting time, residence time, busy period, etc. Some of these approximations are shown to reduce to exact M/M/1 results when G = M. For the case when a G/G/1 queue provides a reasonable system model, but when information about the arrival and service distributions is limited to the average arrival and service rates, it is shown that various well known M/M/1 formulas are information theoretic approximations. These results not only provide a new method for approximating the performance distributions, but they help to explain the widespread applicability of the M/M/1 formulas.     

Regulating an M/G/1 queue when customers know their demand

Customers do not necessarily join a queue at a socially optimal rate. Hence, queueing systems may call for regulation. For customers in an M/G/1 unobservable (not necessarily FCFS) queue and homogeneous with respect to waiting costs and service rewards, we show how queueing systems can be regulated by imposing an entry fee, a holding fee (based on time in the system), or a service fee (based on the required service time) when customers know their service requirements. We start with a unified approach and state the socially optimal fees. We show that customers are always worse off under a flat entry fee in comparison with holding and service fees. As for holding vs. service fees, the answer depends on the queueing regime and/or the service length itself. For example, under FCFS, service fees are preferred by all. Details are given on some common service regimes. We also review the case where customers know only the common distribution of service times, but not their actual requirements.     

码头装卸服务G／M／1排队模型及仿真研究

研究码头装卸仿真服务系统,M/M/1排队模型有严格的理论条件,在工程应用中对不满足理论条件的情况,模型分析结果的准确性会受到影响。为提高控制序列的准确性,提出了等间隔到达和随机到达的混合序列到达时间间隔概率分布,假定该混合到达顾客到达时间间隔相互独立同分布,采用G/M/1排队模型得出了排队服务系统的系统参数。编写MAT-LAB仿真程序,结合实例比较了G/M/1与M/M/1模型分析结果和仿真结果,表明比M/M/1模型能更准确地描述系统的各项参数,结果证明可为排队系统设计提供参考依据。     

On the optimal control of M/G/1 systems under the cycle criterion

This paper deals with some optimal control problems of M/G/1 queues which have commonly been analyzed under the asymptotic average criterion. This paper is focused on such controlled systems but with the cycle criterion. We assume linear cost structure involving running, switching, holding and serving costs. M/G/1 models with standard policies: N-policy and T-policy are analyzed in detail. Specifically, optimal design problems for the cycle criterion are established and compared with optimal models related to the asymptotic criterion.     

M/G/1 round robin discipline

This paper analyzes a round robin M/G/1 queuing discipline with quantum sizes that depend on the number of circuits a job has made. Tight bounds on the steady state mean response conditional on job size are found. Results show that the round robin discipline is relatively insensitive to changes in workload and follows the processor sharing response curves surprisingly closely, even for large quantum sizes. The analysis allows determination of a proper cutoff point, the point at which a job would be sent to a lower priority queue. Also derived is the Laplace-Stieltjes transform of the response of a job that arrives to find a given workload. The transient mean response is calculated for this case.     

On a singular feature of critical G/M/1 queues

In this paper, we consider a critically loaded G/M/1 queue and contrast its transient behaviour with the transient behaviour of stable (or unstable) G/M/1 queues. We show that the departure process from a critical G/M/1 queue converges weakly to a Poisson process. However, as opposed to the stable (or unstable) case, we show that the departure process of a critical GI/M/1 queue does not couple in finite time with a Poisson process (even though it converges weakly to one). Thus, as the traffic intensity (ratio of arrival to service rates), , ranges over (0, ∞), the point = 1 represents a singularity with regard to the convergence mode of the departure process.     

Performance Analysis of Discrete-Time Finite-Buffer Batch-Arrival GIX/Geom/1/N Queues

This paper presents the performance analysis of a discrete-time finite-buffer queue with batch input, general interarrival and geometric service times. It is assumed that a batch arriving with size larger than the available buffer is partially accepted and the rest is rejected. The queue is analyzed for early arrival system as well as for late-arrival system with delayed access using both the supplementary variable and imbedded Markov chain techniques. Besides obtaining state probabilities at various epochs and loss probability of a batch as well as of a customer, other performance measures have also been discussed. The waiting time analysis of an arbitrary customer of a batch is also carried out.     

谈谈网络环境下的信息服务(一)

谈谈网络环境下的信息服务一）文：胡小明一项传统的网上业务信息服务应当算是最传统的网上业务，它开展得最早。早在６０年代，人们就利用集中型主机带着一系列终端的网络来开展信息服务和电子函件服务。信息服务与电子函件服务开展得比较早的最重要原因还是因为这样的两...