The asymptotic variance rate of the output process of finite capacity birth-death queues

We analyze the output process of finite capacity birth-death Markovian queues. We develop a formula for the asymptotic variance rate of the form λ *+σvi where λ * is the rate of outputs and v i are functions of the birth and death rates. We show that if the birth rates are non-increasing and the death rates are non-decreasing (as is common in many queueing systems) then the values of v i are strictly negative and thus the limiting index of dispersion of counts of the output process is less than unity. In the M/M/1/K case, our formula evaluates to a closed form expression that shows the following phenomenon: When the system is balanced, i.e. the arrival and service rates are equal, σvi\λ* is minimal. The situation is similar for the M/M/c/K queue, the Erlang loss system and some PH/PH/1/K queues: In all these systems there is a pronounced decrease in the asymptotic variance rate when the system parameters are balanced

The past, present and future in scaffold-based tendon treatments

Tendon injuries represent a significant clinical burden on healthcare systems worldwide. As the human population ages and the life expectancy increases, tendon injuries will become more prevalent especially among young individuals with long life ahead of them. Advancements in engineering, chemistry and biology have made available an array of three-dimensional scaffold-based intervention strategies, natural or synthetic in origin. Further, functionalisation strategies, based on biophysical, biochemical and biological cues, offer control over cellular functions; localisation and sustained release of therapeutics/biologics; and the ability to positively interact with the host to promote repair and regeneration. Herein, we critically discuss current therapies and emerging technologies that aim to transform tendon treatments in the years to come. (C) 2014 Elsevier B.V. All rights reserved