Quality Control Chart for the Mean using Double Ranked Set Sampling

In this paper, an attempt is made to develop Quality Control Charts for monitoring the process mean based on Double Ranked Set Sampling (DRSS) rather than the traditional Simple Random Sampling (SRS). Considering a normal population and several shift values, the performance of the Average Run Length (ARL) of these new charts was compared with the control charts based on Ranked Set Sampling (RSS) and SRS with the same number of observations. It is shown that the new charts do a better job of detecting changes in process mean compared with SRS and RSS.     

Bayesian Inference and Prediction in an M/G/1 with Optional Second Service

In this article, we exploit the Bayesian inference and prediction for an M/G/1 queuing model with optional second re-service. In this model, a service unit attends customers arriving following a Poisson process and demanding service according to a general distribution and some of customers need to re-service with probability “p”. First, we introduce a mixture of truncated Normal distributions on interval (? ∞, 0) to approximate the service and re-service time densities. Then, given observations of the system, we propose a Bayesian procedure based on birth-death MCMC methodology to estimate some performance measures. Finally, we apply the theories in practice by providing a numerical example based on real data which have been obtained from a hospital.     

Estimation of Measures in M/M/1 Queue

Maximum likelihood and uniform minimum variance unbiased estimators of steady-state probability distribution of system size, probability of at least ? customers in the system in steady state, and certain steady-state measures of effectiveness in the M/M/1 queue are obtained/derived based on observations on X, the number of customer arrivals during a service time. The estimators are compared using Asympotic Expected Deficiency (AED) criterion leading to recommendation of uniform minimum variance unbiased estimators over maximum likelihood estimators for some measures.     

Valid estimation of odds ratio using two types of moving extreme ranked set sampling

The paper provides estimation of the odds ratio between two independent groups using two types of Moving Extreme Ranked Set Sampling (MERSS). Theoretical properties of the suggested estimator are derived and compared with its counterpart estimator using simple random sampling (SRS). It is found that the estimator based on MERSS is always valid and has some advantages over that based on SRS. Real data from a level I Trauma center are used to illustrate the procedures developed in this paper.     

Generalized Systematic Sampling

In this paper, we introduce a new systematic sampling design, called a Generalized Systematic Sampling (GSS), for estimation of finite population mean. The proposed design is found to be better than Simple Random Sampling (SRS) and the generalization of the several existing systematic sampling schemes such as, Linear Systematic Sampling (LSS), Diagonal Systematic Sampling (DSS), and Generalized Diagonal Systematic Sampling (GDSS). All of these designs become special cases of the proposed design.     

期权定价的蒙特卡罗模拟方差缩减技术研究

蒙特卡罗模拟的方差缩减技术作为模拟效率改进的重要途径,在金融衍生证券的定价分析中得到了广泛的应用和发展,特别是在控制变量、对偶变量、分层抽样、拉丁超立方抽样、矩匹配和重要性抽样技术方面。从方差缩减的效率来看,所有的蒙特卡罗模拟方差缩减技术都能显著地提高期权定价的模拟效率,其中基于最优漂移率的重要性抽样技术与沿着最优分层抽样方向进行的分层抽样技术的组合,要比普通的蒙特卡罗模拟具有极其明显的效率提高效果。     

Estimation of the mean of the exponential distribution using moving extremes ranked set sampling

Moving Extremes Ranked Set Sampling (MERSS) is a useful modification of Ranked Set Sampling (RSS). Unlike RSS, MERSS allows for an increase of set size without introducing too much ranking error. The method is considered parametrically under exponential distribution. Maximum likelihood estimator (MLE), and a modified MLE are considered and their properties are studied. The method is studied under both perfect and imperfect ranking (with error in ranking). It appears that these estimators can be real competitors to the MLE using the usual simple random sampling (SRS).     

Relative efficiency of a parameter for a M/G/1 queueing system based on reduced and full likelihood functions

The present paper derives the relative efficiency of a parameter for the M/G/1 queueing system based on reduced and full likelihood functions. Monte Carlo simulations were carried out to study the finite sample properties for estimating the parameters of a M/G/1 queueing system. The simulation runs were conducted using various traftic intensities with increaseing sample sizes. The simulation results indicate that the loss in efficiency is quite small due to the use of a reduced likelihood function approach for estimating the parameter instead of the full likelihood, even for a moderate sample size of 50     

Shift Techniques and Canonical Factorizations in the Solution of M/G/1-Type Markov Chains

ABSTRACT

By using properties of canonical factorizations, we prove that under very mild assumptions, the shifted cyclic reduction method (SCR) can be applied for solving QBD problems with no breakdown and that it always converges. For general M/G/1 type Markov chains we prove that SCR always converges if no breakdown is encountered. Numerical experiments showing the acceleration provided by SCR versus cyclic reduction are presented.     

End-to-end queuing delay assessment in multi-service ip networks

Packet-based networks are more and more used to transport interactive streaming services like telephony and videophony. To guarantee a good quality for these services, the queuing delay and delay jitter introduced in the transport of voice or video flows over the packet-based network should be kept under control. Because data sources tend to increase their sending rate until (a part of) the network is congested, mixing real-time traffic and data traffic in one queue would lead to unacceptable high delays for real-time services. Therefore, voice and video packets need to get preferential treatment ( e.g. head-of-line priority) over data packets in the network nodes. Therefore, the queuing behavior of the voice and video packets can be studied more or less independently from the traffic generated by data services. Simple methods to assess the end-to-end delay are primordial. Since it is well known that an aggregate of voice (and CBR video) sources is accurately modeled by a Poisson arrival process and that delays in consecutive nodes are more or less statistically independent, this boils down to developing methods to calculate quantiles of the total queuing delay through a system of N statistically independent M/G/1 nodes. This paper develops four methods to calculate quantiles of the total queuing delay: a Gaussian method, a method based on the numerical inversion of the moment generating function of the total queuing delay developed by Abate and Whitt and two methods based on the assumption that the tail distribution of the individual queuing delay of one node is approximately exponential. The Gaussian method is the simplest, but only gives crude results. The method of Abate and Whitt is the most complex and breaks down for large quantiles. The methods based on the assumption of an exponential tail produce results that are more or less equally accurate as long as there is a node where the load is high enough.     

公交车辆在中途站点的排队论分析

公交站台停靠区的排队问题决定了公交车辆的通行能力。把公交中途站台与公交车辆模拟成一个单服务系统、公车到达率 ,两服务率 、 的负指数分布的排队M/M/1/N系统。根据排队论理论,实测计算了北京中关村海淀黄庄、人民大学站点公交车辆排队队长,站内逗留时间等参数。结论为：城市主干道关键站台改造为主、副双公交站台制式以及调整公交线路布设,优化各线路发车频率是花费成本低,畅通成效大的解决站点塞车排队的方法。     

An M/G/1 clearing queueing system with setup time and multiple vacations for an unreliable server

This paper studies an M/G/1 clearing queueing system with setup time and multiple vacations, in which all present customers in the system are served simultaneously and breakdowns may occur in busy or setup period. We investigate the stationary distribution of system size and the Laplace–Stieltjes transform of sojourn time. In addition, various performance measures are discussed, such as the mean system size at arbitrary time and the mean length of a vacation circle. Moreover, a cost analysis is carried out for this queueing system. Numerical results are presented to study the sensitivity of the system parameters on the expected cost function and system performances.     

银行服务窗口调度策略模型的统计分析

 用较少投入显著降低顾客排队等待时间的服务窗口调度策略对银行保持顾客有重要意义。根据采集的某银行顾客到达时间和服务时间数据,使用最佳平方逼近方法拟合出顾客到达间隔时间及服务时间曲线,经柯尔莫哥洛夫-斯米尔诺夫检验法验证数据符合M/M/n排队论模型分析条件。分别对普通顾客和VIP顾客进行了M/M/n建模分析,比较统计分析结果,确定服务窗口均衡调度策略是较优的调度策略,该调度模式可以在不追加硬件资源投入的前提下,缩短顾客排队等待时间,提高顾客满意度。     

A computational algorithm for the loss probability in the M/G/1+PH queue

This article develops a computational algorithm for the loss probability in the stationary M/G/1 queue with impatient customers whose impatience times follow a phase-type distribution (M/G/1+PH). The algorithm outputs the loss probability, along with an upper-bound of its numerical error due to truncation, and it is readily applicable to the M/D/1+PH, M/PH/1+PH, and M/Pareto/1+PH queues.     

Estimation of system reliability for exponential distributions based on L ranked set sampling

Abstract

In the case where strength and stress both follow exponential distributions, this paper considers the maximum likelihood estimator (MLE) of the system reliability based on L ranked set sampling (LRSS). The proposed MLE is shown to have existence, uniqueness and asymptotic normality, and its asymptotic variance is obtained by the Fisher information matrix of LRSS. The values of asymptotic relative efficiencies show that the proposed MLE is always more efficient than the MLE using simple random sampling (SRS). However, the MLE using LRSS cannot be written in closed form. Therefore, the modified MLE is proposed using the technique replaced some terms in the maximum likelihood equations by their expectations. The newly modified MLE using LRSS is shown to be superior to the MLE using SRS. Finally, the proposed method is applied to a real data set on metastatic renal carcinoma study.     

Estimation of the distribution function under hybrid ranked set sampling

Recently, a hybrid ranked set sampling (HRSS) scheme has been proposed in the literature. The HRSS scheme encompasses several existing ranked set sampling (RSS) schemes, and it is a cost-effective alternative to the classical RSS and double RSS schemes. In this paper, we propose an improved estimator for estimating the cumulative distribution function (CDF) using HRSS. It is shown, both theoretically and numerically, that the CDF estimator under HRSS scheme is unbiased and its variance is always less than the variance of the CDF estimator with simple random sampling (SRS). An unbiased estimator of the variance of CDF estimator using HRSS is also derived. Using Monte Carlo simulations, we also study the performances of the proposed and existing CDF estimators under both perfect and imperfect rankings. It turns out that the proposed CDF estimator is by far a superior alternative to the existing CDF estimators with SRS, RSS and L-RSS schemes. For a practical application, a real data set is considered on the bilirubin level of babies in neonatal intensive care.