This paper investigates an infinite buffer capacity fluid queueing model driven by a state-dependent birth-death process prone to catastrophes. We employ the Laplace-Stieltjes transform and the continued fraction techniques to determine explicit expressions for the joint probability of the number of customers in the background queueing model and the content of the buffer in the steady state. The importance of the proposed system is that, in numerous practical situation, the service facility possesses defence mechanisms versus long waiting lines. The servers may increase their rate of service under the pressure of a large backlog of work. Therefore, it is of interest to discuss queueing systems taking into regard the state dependent nature of the systems. For example, the congestion control mechanisms deny the formation of long queue in computer and communication systems by controlling the transmission rates of packets based on the queue length (of packets) at source or destination. Numerical illustrations are added to uphold the theoretical results.

This paper investigates an infinite buffer capacity fluid queueing model driven by a state-dependent birth-death process prone to catastrophes. We employ the Laplace-Stieltjes transform and the continued fraction techniques to determine explicit expressions for the joint probability of the number of customers in the background queueing model and the content of the buffer in the steady state. The importance of the proposed system is that, in numerous practical situation, the service facility possesses defence mechanisms versus long waiting lines. The servers may increase their rate of service under the pressure of a large backlog of work. Therefore, it is of interest to discuss queueing systems taking into regard the state dependent nature of the systems. For example, the congestion control mechanisms deny the formation of long queue in computer and communication systems by controlling the transmission rates of packets based on the queue length (of packets) at source or destination. Numerical illustrations are added to uphold the theoretical results.

Advances in treating infertile couples by assisted reproductive technologies (ART) over more than three decades have greatly improved the chances of better outcomes.While twinning and higher order multiple birth rates are still high in most countries, lower rates have sometimes been achieved by single-embryo transfer. Multiple pregnancy increases the risk of preterm birth (less than 37 weeks’ gestation), low birthweight, and perinatal deaths. It also results in a higher risk of newborn complications and cerebral palsy, and longer hospitalisation. Preterm birth is also more common in singleton pregnancies in which two or more gestational sacs are detected by ultrasound in early pregnancy.Compared to the perinatal death rate (stillbirths and neonatal deaths) in singleton IVF births, the risk is more than double in twins, five times higher in triplets, and ten times higher in other multiple births.Studies of birth defects in ART pregnancies need to take account of the underlying causes of infertility and changes in treatment regimes. Maternal factors such as age, obesity and diabetes should also be considered. The overall occurrence of major birth defects is slightly increased in ART pregnancies. However, some birth defects such as neural tube defects, oesophageal atresia and other gut malformations, urogenital malformations, and some rare malformation syndromes are more common after ART. The causes of these birth defects need further research.Reducing the risk of adverse outcomes in ART pregnancies is best achieved by transferring just one embryo in each treatment cycle and freezing the other embryos. Counselling about the greater risks associated with multiple pregnancies should be available for all couples. Prenatal diagnosis should also be discussed and offered when indicated for older women.Educational programs should encourage women and their partners to plan their pregnancies at younger ages and so avoid the necessity of ART in the later years of reproductive life. This will also assist couples to avoid the maternal and newborn risks associated with advanced maternal age.