Queues with Markovian Arrivals, Phase Type Services, Breakdowns, and Repairs

In service sectors, the server interruptions occur naturally and are studied using queueing models with interruptions. Such models have been studied extensively in the literature. The server interruptions may occur due to external events such as shocks and negative customers, or due to internal events which are dictated by a timer or a clock which when expired may result in an interruption. In this paper, we analyze models of MAP/PH/1-type with phase type breakdowns and phase type repairs analytically. The breakdowns are modeled using internal clocks. The study of such breakdowns in the context of MAP/PH/c-type models is carried out via simulation. Some illustrative examples are discussed

Postnatal epithelial growth of the small intestine in the rat occurs by both crypt fission and crypt hyperplasia

Studies of growth of the small intestine have largely concentrated on crypt hyperplasia rather than crypt fission. The aim of this study was to investigate quantitatively both crypt fission and crypt hyperplasia. DAxPVG/c rats were killed at 7, 11, 14, 17, 19, 21, 25, 55, and 72–73 days of life. Samples of jejunum at one third of the intestinal length were taken for morphometry (villous area, crypt area, percentage of bifid crypts, and crypt mitotic count) by microdissection. Growth factors and their receptors were assessed by oligonucleotide microarray. Crypt fission was 10.5%, 5.2%, and 1.5% at days 11, 25, and 72–73 of life, respectively. Crypt hyperplasia increased from day 21. No conventional growth factor was identified during crypt fission. We conclude that crypt fission contributes to growth of the small intestine prior to weaning and crypt hyperplasia to growth after weaning.Adrian G. Cummins, Ben J. Jones, and Fiona M. Thompso