Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

Learning to align organizational design and data

The relationship between organizational learning and organizational design is explored. In particular, we examine the information processing aspects of organizational learning as they apply to a two-valued decision making task and the relation of such aspects to organizational structure. Our primary contribution is to extend Carley's (1992) model of this process. The original model assumes that all data input into the decision making processes are of equal importance or weight in determining the correct overall organizational decision. The extension described here allows for the more natural situation of non-uniform weights of evidence. Further extensions to the model are also discussed. Such organizational learning performance measures provide an interesting framework for analyzing the recent trend towards flatter organizational structures. This research suggests that flatter structures are not always better, but rather that data environment, ultimate performance goals, and relative need for speed in learning can be used to form a contingency model for choosing organizational structure.     

Optimality of a Threshold Policy in theM/M/ queue with repeated vacations

Consider anM/M/1 queueing system with server vacations where the server is turned off as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding cost ofh per unit of time and per customer in the system and a fixed cost of each time the server is turned on. We show that there exists a threshold policy that minimizes the long-run average cost criterion. The approach we use was first proposed in Blanc et al. (1990) and enables us to determine explicitly the optimal threshold and the optimal long-run average cost in terms of the model parameters.     

Degrees of unsolvability of first order decision problems for finitely presented groups

We show that for any arithmetical -degree there is a first order decision problem such that has -degree for the free 2-step nilpotent group of rank 2. This implies a conjecture of Sacerdote.

     

Estimation of Multinomial Probabilities under a Model Constraint

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.     

Evaluation of the limit of performance of an analytical method based on a statistical calculation of its critical concentrations according to ISO standard 11843: Application to routine control of banned veterinary drug residues in food according to European Decision 657/2002/EC

Traceability of the measurement of analytical parameters capable of evaluating the performance of methods is an important concept for the assessment of quality for the routine control, especially for residue monitoring of non-authorized medicinal substances in food from animal origin. The European Decision no. 657/2002/EC recommends to calculate two statistical limits, CCα and CCβ, which allow to evaluate the critical concentrations above which the method reliably distinguish and quantify a substance taking into account the variability of the method and the statistical risk to take a wrong decision. The calculation, which can be derived from the ISO standard no. 11843 is applied on a routine basis. An example displays a very simple way for evaluating the performance of an LC-MSMS method which has been validated a few years ago and is qualified onto a Micromass Quattro LCZ tandem mass spectrometer to monitor and confirm the nitrofuran metabolite residues in food from animal origin. Community Reference Laboratory for Antimicrobial Veterinary Drug Residue Control in Food from Animal Origin     

New indices for analysing partial ranking diagrams

Interest is growing in decision making strategies and several techniques are now available. The assessment of priorities is a typical premise before final decisions are taken. Total and partial order ranking (POR) strategies, which from a mathematical point of view are based on elementary methods of discrete mathematics, appear as an attractive and simple tool to asses priorities. Despite the well-known total ranking strategies, which are scalar methods combining the different criteria values into a global index which always ranks elements in an ordered sequence, the partial order ranking is a vectorial approach which recognises that not all the elements can be directly compared with all the others. In fact when many criteria are considered, contradictions in the ranking are bound to exist and the higher the number of criteria, the higher the probability that contradictions in the ranking occur. The Hasse diagram technique (HDT) is a very useful tool to perform partial order ranking. The results of the partial order ranking are visualised in a diagram, called Hasse diagram. Incomparable elements are located at the same geometrical height and as high as possible in the diagram, thus incomparable elements are arranged in levels. The quality of a ranking procedure has to be evaluated by a deep analysis and by several indices, i.e. scalar functions that describe features of an ordered set and allow comparison among different rankings. For this purpose, new indices for ranking analysis are proposed here, compared with the ones found in literature and tested on theoretical examples and on real data.     

含一般模糊弹性约束的广义模糊变量线性规划

建立并讨论了一类含有一般模糊弹性约束的广义模糊变量线性规划问题.首先,简单介绍了结构元方法并对结构元加权排序中权函数表征决策者风险态度进行了深入分析.然后选取风险中性的决策者来定义序关系,应用Verdegay模糊线性规划方法将含一般模糊弹性约束的广义模糊变量线性规划转化经典的线性规划问题,简化了原问题的求解.最后通过数值算例进一步说明了该方法的有效性.     

Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making

A dual hesitant fuzzy set (DHFS) consists of two parts, that is, the membership hesitancy function and the nonmembership hesitancy function, supporting a more exemplary and flexible access to assign values for each element in the domain, and can handle two kinds of hesitancy in this situation. It can be considered as a powerful tool to express uncertain information in the process of group decision making. Therefore, we propose a correlation coefficient between DHFSs as a new extension of existing correlation coefficients for hesitant fuzzy sets and intuitionistic fuzzy sets and apply it to multiple attribute decision making under dual hesitant fuzzy environments. Through the weighted correlation coefficient between each alternative and the ideal alternative, the ranking order of all alternatives can be determined and the best alternative can be easily identified as well. Finally, a practical example of investment alternatives is given to demonstrate the practicality and effectiveness of the developed approach.     

The Occurrence of Pesticides in Groundwater—Results of Case-studies

Abstract

A comparative review of pesticide survey endosing 16 waterworks in the FRG tries to increase the understanding about interferences of pesticide utilization and pesticide occurrence in ground- and drinkingwater, which includes characterization of sampling points, subsurface situation, land use and pesticide application. Between 1986 and 1991, 5772 samples were measured and led to 219094 data about the occurrence of various pesticides. 5% of these analyses showed pesticide or metabolite concentrations above the particular detection limits. This result does not vary in large extent considering groups of different characterized sampling points like groundwater dominated or surface water sampling points. As the herbicide atrazine and its metabolite desethylatrazine as well as the herbicide simazine were detected most often in all samples independent whether considering groundwater und surface water samples, this fact confirms the FRG-application ban for atrazine as well as the application restriction for simazine.