Analysis of M^X/M/1/n systems with impatient customers

Analysis of M^X/M/1/n systems with impatient customers

Abstract: Customer behavior upon arrival at a system plays a very important role in analyzing the performance and success of a service provider organization. In current busy days, organizations increasingly deal with impatient customers who often give up on ordering the service due the number of customers waiting in queue before them. The success of organizations depends on minimizing such customer losses, known in the queueing systems literature as customer balking, while maintaining a reasonable number of services per period of continuous occupancy of their server. Aiming to guide organizations in decision making to minimize the balking problem, in this work we analyze M^X/M/1/n systems with balking. These are queueing systems with finite capacity, n, in which customers arrive in batches according to a Poisson process and are served by a single server, in a first come first served discipline. The batch sizes are independent and identically distributed. The customer service times are independent and identically exponential distributed random variables and are independent of the arrival process. Specifically, relying on the Markovian structure of that systems, we derive the joint probability function of the number of customers served and the number of customers lost in periods of continuous system occupancy (busy-periods), as well as the respective marginal probability functions. This is accomplished by proposing efficient recursive procedures for the evaluation of the corresponding probability-generating functions. The sensitivity analysis of such systems measures is then performed.

Keywords: Queueing system; Batch arrival; Balking; Busy-period; Markov chain.

Induced nonparametric ROC surface regression

Induced nonparametric ROC surface regression

Abstract: The receiver operating characteristic (ROC) surface is a popular tool for evaluating the discriminatory ability of diagnostic tests measured on a continuous scale when there exist three ordered disease groups. Motivated by the impact that covariates may have on the diagnostic accuracy, and to safeguard against model misspecification, we develop a flexible model for conducting inference about the covariate-specific ROC surface and its functionals. Specifically, we postulate a location-scale regression model for the test outcomes in each of the three disease groups where the mean and variance functions are estimated through penalised-splines, while the distribution of the error term is estimated via a smoothed version of the empirical cumulative distribution function of the standardised residuals. Our simulation study shows that our approach successfully recovers the true covariate-specific volume under the surface and optimal pair of thresholds in a variety of scenarios. Our methods are motivated by and applied to data derived from an Alzheimer's disease study and we seek to assess the accuracy of several potential biomarkers to distinguish between individuals with normal cognition, mild cognitive impairment, and dementia and how this discriminatory ability may change with the age and gender

Transition models: extensions to grouped polytomous data

Transition models: extensions to grouped polytomous data

Abstract: Transition models are useful for analyzing categorical longitudinal data, particularly when the primary interest is in prediction. Thus, in this work the basic ideas of this model class and tests for stationarity are presented. Additionally, it is noted that the methods available for this model are directed to cases in which the responses are individual. However, in many areas, it is common to obtain grouped categorical responses, that is, there are different categories of response with the registration of the number of individuals in each one of them. As a motivation for the methodological extension, a study applied to agricultural sciences, involving Diaphorina citri, which is a pest and vector of bacteria that attacks citrus, is considered.

Keywords: stochastic process, transition probabilities, maximum likelihood, entomology.

Coalescent structure of Galton Watson processes in varying environment.

Coalescent structure of Galton Watson processes in varying environment.

Abstract: Consider a critical Galton Watson tree in varying environment. If the system survives until a large time N, then choose k particles uniformly from those alive. Consider the ancestral tree drawn out by these particles. We are going to discuss the shape of this ancestral tree. This is a joint work with Simon Harris (Auckland, NZ) and Juan Carlos Pardo (CIMAT, Mexico).

The role of statistical methods for Design of Experiments in the development of new civil engineering solutions

The role of statistical methods for Design of Experiments in the development of new civil engineering solutions

Abstract: The Design of Experiments (DoE) is a statistical tool particularly relevant in the study of new materials and new manufacturing processes. It allows us to save time and money and enables us analyse different options for combining constituents of the material under study, obtaining models and material optimisation. In this talk we briefly introduce different currently used DoE schemes and we focus on their use in some practical situations: (a) improvement of building materials manufacturing, including the introduction of new constituents and new manufacturing processes; (b) stabilization of soils. The models that explain the material response are conventional regression and Poisson regression models. Emphasis will be given to applications to real world problems.

Keywords: design of experiments, new materials engineering, regression.

Meta-analysis: when the whole is greater than the sum of the parts

Meta-analysis: when the whole is greater than the sum of the parts

Abstract: A systematic review is a research for (primary) studies on some topic of interest whose results are summarized. Meta-analysis is more than a systematic review. It consists in a statistical analysis of the summary findings of these primary studies. This branch of Statistics has become popular since the publication of some books about this subject in the 80s of the last century. In this talk, the fundamentals of any meta-analysis are covered, i.e., how to measure an effect size, as well as methods of combining the effect sizes reported by the different primary studies. Assumptions regarding the use of a fixed or random effects model are also discussed. The different steps that comprehend a meta-analysis are analysed: the definition of the research question, where and how to search for the studies, the selection criteria, the assessment of the quality and heterogeneity of the studies and the publication bias, the presentation of the results and the computation of a pooled estimate of the effect size. The use of subgroup analysis and meta-regression to explain the heterogeneity of the studies is also explored.

Keywords: Meta-analysis, systematic review, pooled estimate, subgroup analysis, meta-regression.