A Spectral Method for a Nonpreemptive Priority BMAP/G/1 QUEUE

Abstract

In this paper we consider a nonpreemptive priority queue with two priority classes of customers. Customers arrive according to a batch Markovian arrival process (BMAP). In order to calculate the boundary vectors we propose a spectral method based on zeros of the determinant of a matrix function and the corresponding eigenvectors. It is proved that there are M zeros in a set Ω, where M is the size of the state space of the underlying Markov process. The zeros are calculated by the Durand-Kerner method, and the stationary joint probability of the numbers of customers of classes 1 and 2 at departures is derived by the inversion of the two-dimensional Fourier transform. For a numerical example, the stationary probability is calculated.     

Workload Process,Waiting Times,and Sojourn Times in a Discrete Time MMAP[K]/SM[K]/1/FCFS Queue

Abstract

In this paper, we study the total workload process and waiting times in a queueing system with multiple types of customers and a first-come-first-served service discipline. An M/G/1 type Markov chain, which is closely related to the total workload in the queueing system, is constructed. A method is developed for computing the steady state distribution of that Markov chain. Using that steady state distribution, the distributions of total workload, batch waiting times, and waiting times of individual types of customers are obtained. Compared to the GI/M/1 and QBD approaches for waiting times and sojourn times in discrete time queues, the dimension of the matrix blocks involved in the M/G/1 approach can be significantly smaller.     

A consistent method of estimation for the parameters of the three-parameter inverse Gaussian distribution

In this paper, we propose a consistent method of estimation for the parameters of the three-parameter inverse Gaussian distribution. We then discuss some properties of these estimators and show by means of a Monte Carlo simulation study that the proposed estimators perform better than some other prominent estimators in terms of bias and root mean squared error. Finally, we present two real-life examples to illustrate the method of inference developed here.     

中国产业链供应链现代化水平的区域差异及收敛性研究

提升产业链供应链现代化水平是推动经济体系优化升级的重点任务。论文首先界定了产业链供应链现代化的内涵,并根据其内涵构建综合评价指标体系。然后,研究2011—2020年产业链供应链现代化水平的分布动态、区域差异与空间收敛性。结果表明：我国产业链供应链现代化水平在空间上呈现出“东高、中西低”的阶梯状空间分布特征;区域产业链供应链现代化水平差异主要来源于区域间差异,而区域间差异主要来源于东部-中部和东部-西部的地区差异;全国及各区域产业链供应链现代化水平在空间上无明显σ收敛特征,全国及各区域存在显著的绝对β收敛和条件β收敛,表明各区域朝着自身稳定状态发展。最后根据研究结果,提出关于产业链供应链现代化水平提升的对策建议。     

生产环节外包能否助力中国粮食安全？——来自粮食主产区的证据

在中国大力扶持和推进生产环节外包服务业发展的现实背景下,系统评估生产环节外包对中国粮食安全的影响具有重要的现实意义。聚焦粮食安全数量目标与环境目标两个维度,从农户是否参与外包、农户的外包横向参与度与农户的外包纵深参与度三个层面,理论剖析生产环节外包影响中国粮食安全的逻辑机理,并使用中国粮食主产区1211户农户的抽样调查数据和CMP方法进行实证检验。研究发现：①从三大主粮的总体估计来看,生产环节外包有助于中国粮食安全数量目标的实现,但不利于中国粮食安全环境目标的达成。在解决潜在的内生性问题后,这一结论依然成立;②从玉米、小麦和水稻的分样本估计来看,生产环节外包对中国粮食安全的多维影响在玉米和水稻生产中仍较为稳健,但对小麦的增产效果并不明显;从黑龙江、河南和湖南的分样本估计来看,生产环节外包对中国粮食安全的多维影响在三大粮食主产省均较为稳健。目前,从服务视角破解资源环境约束与农户行为约束暂未成为解决中国粮食安全环境问题的有效途径,仍需进一步推动生产环节外包服务市场的发育与完善,鼓励并引导外包供给主体的绿色生产导向。     

Exact confidence region for the parameters of the gamma distribution based on two independent samples

The gamma distribution has been discussed by many authors. This article proposes an exact confidence region for the parameters of a two-parameter gamma distribution. The result is based on the fact that the percentiles of the F-distribution, with equal degrees of freedom k, are monotonic in k.     

A generalized two-piece skew normal distribution and some of its properties

In this paper, we develop a generalized version of the two-piece skew normal distribution of Kim [On a class of two-piece skew-normal distributions, Statistics 39(6) (2005), pp. 537–553] and derive explicit expressions for its distribution function and characteristic function and discuss some of its important properties. Further estimation of the parameters of the generalized distribution is carried out.     

Reliability estimation in stress–strength models: an MCMC approach

In this paper, we consider the estimation of the stress–strength parameter R=P(Y<X) when X and Y are independent and both are modified Weibull distributions with the common two shape parameters but different scale parameters. The Markov Chain Monte Carlo sampling method is used for posterior inference of the reliability of the stress–strength model. The maximum-likelihood estimator of R and its asymptotic distribution are obtained. Based on the asymptotic distribution, the confidence interval of R can be obtained using the delta method. We also propose a bootstrap confidence interval of R. The Bayesian estimators with balanced loss function, using informative and non-informative priors, are derived. Different methods and the corresponding confidence intervals are compared using Monte Carlo simulations.     

Distance-based approach in univariate longitudinal data analysis

In this paper, we propose a methodology to analyze longitudinal data through distances between pairs of observations (or individuals) with regard to the explanatory variables used to fit continuous response variables. Restricted maximum-likelihood and generalized least squares are used to estimate the parameters in the model. We applied this new approach to study the effect of gender and exposure on the deviant behavior variable with respect to tolerance for a group of youths studied over a period of 5 years. Were performed simulations where we compared our distance-based method with classic longitudinal analysis with both AR(1) and compound symmetry correlation structures. We compared them under Akaike and Bayesian information criterions, and the relative efficiency of the generalized variance of the errors of each model. We found small gains in the proposed model fit with regard to the classical methodology, particularly in small samples, regardless of variance, correlation, autocorrelation structure and number of time measurements.