On the transition from heavy traffic to heavy tails for the M/G/1 queue: The regularly varying case

Two of the most popular approximations for the distribution of the steady-state waiting time, $W_{\infty}$, of the M/G/1 queue are the so-called heavy-traffic approximation and heavy-tailed asymptotic, respectively. If the traffic intensity, $\rho$, is close to 1 and the processing times have finite variance, the heavy-traffic approximation states that the distribution of $W_{\infty}$ is roughly exponential at scale $O((1-\rho)^{-1})$, while the heavy tailed asymptotic describes power law decay in the tail of the distribution of $W_{\infty}$ for a fixed traffic intensity. In this paper, we assume a regularly varying processing time distribution and obtain a sharp threshold in terms of the tail value, or equivalently in terms of $(1-\rho)$, that describes the point at which the tail behavior transitions from the heavy-traffic regime to the heavy-tailed asymptotic. We also provide new approximations that are either uniform in the traffic intensity, or uniform on the positive axis, that avoid the need to use different expressions on the two regions defined by the threshold.Comment: Published in at http://dx.doi.org/10.1214/10-AAP707 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Plasma Renin Activity in Children with Protein Energy Malnutrition (Kwashiorkor)

Plasma renin activity was measured by bio-assay in 100 children with kwashiorkor and in 20 healthy children, and also by radio-immunoassay in another 26 children with kwashiorkor and in another 20 healthy children. Both methods showed that (compared with healthy children) renin activity was significantly increased in children with kwashiorkor; and also that the activity was significantly higher in the patients who subsequently died in hospital, than in those who survived. Increased renin activity probably contributes to the retention of water characteristic of protein energy malnutrition.S. Afr. Med. J., 48, 499 (1974

Hubungan Keadaan Gizi Dengan Beberapa Aspek Intellegensia

Hubungan keadaan gizi dengan beberapa aspek intelligensi. (The relation of nutritional status on some aspects of intelligence). Presented at the Second National Pediatric Congress. Bandung, 1971. Data obtained in this empirical study agree very well with the theoretical assumption that nutritional status influences the functions of intelligence. The lower the degree of nutritional status, the greater it affects the functions of intelligence. The study showed clearly that undernutrition influences verbal abilities and abstraction. Undernutrition influences also attention and concentration which in turn decrease the mental effectiveness of the subjects; and performance tasks, but which ability is influenced was not clearly shown. It might be due to the environment which was not stimulating for the development of this ability. The effects of undernutrition on perception were also not clearly shown in this study. This study indicated that in the study of nutritional status one should not neglect the influence of the environment. In order that intelligence be able to function at an optimum, any improve­ment of nutritional status should be accompanied by improve­ment in socio-economic, psychological and educational conditions

Early risk factors for adolescent antisocial behaviour: an Australian longitudinal study

Objective: This investigation utilizes data from an Australian longitudinal study to identify early risk factors for adolescent antisocial behaviour. Method: Analyses are based on data from the Mater University Study of Pregnancy, an on-going longitudinal investigation of women’s and children’s health and development involving over 8000 participants. Five types of risk factors (child characteristics, perinatal factors, maternal/familial characteristics, maternal pre- and post-natal substance use and parenting practices) were included in analyses and were based on maternal reports, child assessments and medical records. Adolescent antisocial behaviour was measured when children were 14 years old, using the delinquency subscale of the Child Behaviour Checklist. Results: Based on a series of logistic regression models, significant risk factors for adolescent antisocial behaviour included children’s prior problem behaviour (i.e. aggression and attention/restlessness problems at age 5 years) and marital instability, which doubled or tripled the odds of antisocial behaviour. Perinatal factors, maternal substance use, and parenting practices were relatively poor predictors of antisocial behaviour. Conclusions: Few studies have assessed early predictors of antisocial behaviour in Australia and the current results can be used to inform prevention programs that target risk factors likely to lead to problem outcomes for Australian youth

Body composition in protein-calorie malnutrition

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