Stationary distributions for a class of Markov-modulated tandem fluid queues

ABSTRACT

We consider a model consisting of two fluid queues driven by the same background continuous-time Markov chain, such that the rates of change of the fluid in the second queue depend on whether the first queue is empty or not: when the first queue is nonempty, the content of the second queue increases, and when the first queue is empty, the content of the second queue decreases.

We analyze the stationary distribution of this tandem model using operator-analytic methods. The various densities (or Laplace–Stieltjes transforms thereof) and probability masses involved in this stationary distribution are expressed in terms of the stationary distribution of some embedded process. To find the latter from the (known) transition kernel, we propose a numerical procedure based on discretization and truncation. For some examples we show the method works well, although its performance is clearly affected by the quality of these approximations, both in terms of accuracy and run time.     

Internalizing and Externalizing Symptoms and Marital Relationship Functioning: The Mediating Role of Demand–Withdraw Communication Processes

Marital outcomes are associated with internalizing and externalizing symptoms; however, the processes by which these domains are associated with marital outcomes are not well understood. This study examined how demand–withdraw (DW) couple communication accounts for the association between symptoms of mental illness and marital distress. A mediational model was tested in a sample of 100 newlywed couples to determine: (a) whether internalizing and externalizing symptoms influenced own and partner's level of DW communication, and (b) whether this communication pattern was associated with relationship outcomes, including lower marital satisfaction and presence of conflict. Results suggested that DW communication had significant effects on both partner's marital outcomes and mediated the association between externalizing symptoms (for husbands) and marital distress.     

Weaving Ropes with the Desert Fathers: (Re)Inventing Rhetorical Theory as Silence and Listening

Not until the past decade have communication scholars begun to depict silence as rhetoric (Bennett, 2006; Clair, 1998; Glenn, 2004; Kalamaris, 1994). Building upon recent theoretical development and definition of silence as rhetoric within a theoretical and didactic framework, this paper illustrates silence and listening as rhetoric in its origination with the monastic community of the Desert Fathers, while acknowledging it as a basic contemplative and ascetic practice in many ancient religions. Development of this concept was expressed by the following questions: How does the Desert Fathers’s concept of silence and listening contribute to a modern understanding of rhetorical communication theory? How does their concept of silence and listening conflict with modern presentations of contemporary evangelical worship? The work’s contributions include insight into the ancient Desert community’s use of silence and listening as rhetoric since it takes a theoretical approach to silence and symbols as rhetoric, theology, and protest (Glenn, 2004). It follows the desert community’s way and purpose of rhetorical memory and listening, while proposing practical and theoretical implications for higher learning, spirituality, and critical studies.     

Childhood Obesity: An Overview

This article reviews recent research evidence, largely from systematic reviews, on a number of aspects of childhood obesity: its definition and prevalence; consequences; causes and prevention. The basis of the body mass index (BMI) as a means of defining obesity in children and adolescents is discussed: a high BMI for age constitutes obesity. In recent years the prevalence of obesity has increased dramatically across most of the world, and in the UK obesity prevalence is high and continuing to increase. Despite a widespread perception that obesity in childhood or adolescence is a cosmetic issue, the research evidence shows that it does matter to physical and psychological health and that there are adverse health risks for both the obese child and the adult who was obese as a child. Few interventions aimed at preventing or treating childhood obesity have been successful. There is an urgent need for more research on better strategies that will enable children and adolescents to make long‐term changes to their dietary and physical activity behaviour in order to prevent obesity.     

Development and validation of a Biodata Inventory as an alternative method to measurement of the five factor model of personality

The present study was designed to test the effectiveness of using a biographical inventory as an alternative to a traditional personality inventory in measuring the five factor model of personality. A combination of empirical and rational strategies were incorporated in the development and scoring of the biodata items. All (N = 383) participants completed the newly developed Biodata Inventory and the NEO-Five Factor Inventory. Confirmatory factor analysis was performed to examine the goodness of fit of the five factor structure from the respondents’ data. All participants completed a letter cancellation task, reported grade point averages, and SAT scores. Predictive validity was assessed for both instruments’ scores. Results indicate that the five factor model fit the data from the biodata and personality inventories. Predictive validities of both inventories’ scores were consistent with many other research results. The relationship of the Conscientiousness biodata scores to grade point average and task completion performance were statistically significant.     

Training for collaboration: collaborative practice skills for mental health professionals

The purpose of the study was to identify skills that mental health practitioners need for successful collaborative practice in medical settings. Known experts in the field of collaborative health care completed a survey designed to elicit their suggestions about what is needed for successful collaborative care practice. Through qualitative analysis, a set of 56 skills was developed. These skills are organized into three general categories of competency: (a) skills for working in a medical setting; (b) skills for working with patients; and (c) skills for collaborating with healthcare providers.     

Wage Discrimination and Female Occupational Intensity

The analysis presented in this paper attempts to shed some light, in the context of the Italian labour market, on wage based gender discrimination effects and on the potential impact of gender occupational distribution on wage determination. The results obtained provide some useful insights for Equal Pay legislation and on the efficacy of Comparable Worth (CW) type policies. The wage equation estimates are broadly in line with results obtained elsewhere in the literature. A discrimination effect of nearly 17|X% results when an exclusively male occupational structure is considered. The gender wage gap showed to decrease as female intensity increases. In terms of the framework used, two competing interpretations have been proposed and their implications discussed. The implication of different policy measures which, in recent years, generated much discussion among scholars and in political arenas have been considered, namely: CW and Affirmative Action (AA) policies. Future research should consider a structural model of discrimination so as to discriminate between competing models and policy options.     

Estimating Moments of Subjectively Assessed Distributions*

Moment‐matching discrete distributions were developed by Miller and Rice (1983) as a method to translate continuous probability distributions into discrete distributions for use in decision and risk analysis. Using gaussian quadrature, they showed that an n‐point discrete distribution can be constructed that exactly matches the first 2n ‐ 1 moments of the underlying distribution. These moment‐matching discrete distributions offer several theoretical advantages over the typical discrete approximations as shown in Smith (1993), but they also pose practical problems. In particular, how does the analyst estimate the moments given only the subjective assessments of the continuous probability distribution? Smith suggests that the moments can be estimated by fitting a distribution to the assessments. This research note shows that the quality of the moment estimates cannot be judged solely by how close the fitted distribution is to the true distribution. Examples are used to show that the relative errors in higher order moment estimates can be greater than 100%, even though the cumulative distribution function is estimated within a Kolmogorov‐Smirnov distance less than 1%.