Least absolute value regression: a special case of piecewise linear minimization

The Barrodale and Roberts algorithm for least absolute value (LAV) regression and the algorithm proposed by Bartels and Conn both have the advantage that they are often able to skip across points at which the conventional simplex-method algorithms for LAV regression would be required to carry out an (expensive) pivot operation.

We indicate here that this advantage holds in the Bartels-Conn approach for a wider class of problems: the minimization of piecewise linear functions. We show how LAV regression, restricted LAV regression, general linear programming and least maximum absolute value regression can all be easily expressed as piecewise linear minimization problems.     

Hypothesis Testing and Confidence Regions for the Mean Sojourn Time of an M/M/1 Queueing System

This article discusses testing hypotheses and confidence regions with correct levels for the mean sojourn time of an M/M/1 queueing system. The uniformly most powerful unbiased tests for three usual hypothesis testing problems are obtained and the corresponding p values are provided. Based on the duality between hypothesis tests and confidence sets, the uniformly most accurate confidence bounds are derived. A confidence interval with correct level is proposed.     

Estimation of Traffic Intensity Based on Queue Length in a Single M/M/1 Queue

In this article, maximum likelihood estimator (MLE) as well as Bayes estimator of traffic intensity (ρ) in an M/M/1/∞ queueing model in equilibrium based on number of customers present in the queue at successive departure epochs have been worked out. Estimates of some functions of ρ which provide measures of effectiveness of the queue have also been derived. A comprehensive simulation study starting with the transition probability matrix has been carried out in the last section.     

Estimation in a bivariate integer-valued autoregressive process

ABSTRACT

A bivariate integer-valued autoregressive time series model is presented. The model structure is based on binomial thinning. The unconditional and conditional first and second moments are considered. Correlation structure of marginal processes is shown to be analogous to the ARMA(2, 1) model. Some estimation methods such as the Yule–Walker and conditional least squares are considered and the asymptotic distributions of the obtained estimators are derived. Comparison between bivariate model with binomial thinning and bivariate model with negative binomial thinning is given.     

β-Invariant Measures for Transition Matrices of GI/M/1 Type

In this paper, we study transition matrices of GI/M/1 type by using the approach proposed in Li and Zhao.[13] Li, Q.L. and Zhao, Y.Q. 2002. “A constructive method for finding β-invariant measures for transition matrices of M/G/1 type”. In Matrix-Analytic Methods Theory and Applications 237–263. New Jersey: World Scientific. [Crossref] , [Google Scholar] We obtain conditions on the α-classification of states for the transition matrix of GI/M/1 type. Unlike for matrices of M/G/1 type where association of the matrix multiplication can be easily justified, for matrices of GI/M/ type, we first construct formal expressions for the β-invariant measure based on a representation of factorization of the transition matrix, and then show that it is a β-invariant measure directly. We also prove some spectral properties for the matrix of GI/M/1 type, which are not only used in constructing a formal expression for the β-invariant measure, but also of their own interest. We point out that the spectral analysis required for studying matrices of GI/M/1 type is much more sophisticated than that for matrices of M/G/1 type. Finally, we discuss connections of expressions for the β-invariant measure provided in this paper and in the literature.     

BMAP/G/1 Queue Under D-Policy: Queue Length Analysis

ABSTRACT

We study the queue length distribution of a queueing system with BMAP arrivals under D-policy. The idle server begins to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We derive the vector generating functions of the queue lengths both at a departure and at an arbitrary point of time. Mean queue lengths are derived and a numerical example is presented.     

WISCHE: A DSS for water irrigation scheduling

In this paper we present the models and the algorithms which are being used in a decision support system (DSS) to determine water irrigation scheduling. The DSS provides dynamic scheduling of the daily irrigation for a given land area by taking into account the irrigation network topology, the water volume technical conditions and the logistical operations. The system has been validated by the Agriculture Community of Elche (Spain) and annexed to their Supervisory Control and Data Acquisition system (SCADA). We present two heuristic approaches to solve the mixed 0–1 separable nonlinear program for irrigation scheduling implemented with free software.     

形式级数对称理论在高维可积模型中的应用

本文首先总结了文献[1─4]提出的形式级数对称理论在高维可积模型的研究中所取得的科研成果，然后，将其推广应用到（2 1）维的离散型Toda方程，得到了二族四个广义截断对称。     

分配格上秩－1阵的特征及Schein秩的一个不变性

讨论了分配格Ｌ上的秩－１矩阵分解为向量叉积的特点，然后得到对Ｌ上的任一矩阵Ａ，只要，则在Ａ中插入或去掉元素都是λ的行（或列）所得矩阵与Ａ有相同的Ｓｃｈｅｉｎ秩．