Waiting times in classical priority queues via elementary lattice path counting

In this paper we describe an elementary combinatorial approach for deriving the waiting and response time distributions in a few classical priority queueing models. By making use of lattice paths that are linked in a natural way to the stochastic processes analysed, the proposed method offers new insights and complements the results previously obtained by inverting the associated Laplace Transforms

Approximate Order-up-to Policies for Inventory Systems with Binomial Yield

This paper studies an inventory policy for a retailer who orders his products from a supplier whose deliveries only partially satisfy the quality require- ments. We model this situation by an infinite-horizon periodic-review model with binomial random yield and positive lead time. We propose an order- up-to policy based on approximating the inventory model with unreliable supplier by a model with a reliable supplier and suitably modified demand distribution. The performance of the order-up-to policy is verified by com- paring it with both the optimal policy and the safety stock policy proposed in Inderfurth & Vogelgesang (2013). Further, we extend our approximation to a dual-sourcing model with two suppliers: the first slow and unreliable, and the other fast and fully reliable. Compared to the dual-index order- up-to policy for the model with full information on the yield, the proposed approximation gives promising results

Does the quantitative assessment of coronary artery dimensions predict the physiologic significance of a coronary stenosis?

To study the relationship between the quantitatively assessed coronary artery dimensions and the regional coronary flow reserve as measured by digital subtraction cineangiography, we investigated 17 coronary arteries with a single discrete proximal stenosis and 12 normal coronary arteries before and after intracoronary administration of papaverine. Coronary flow reserve was found to be curvilinearly related to minimal luminal cross-sectional area (r = .92, SEE = 0.73) and to percentage area stenosis (r = .92, SEE = 0.74). Normal coronary arteries had a coronary flow reserve of 5.0 (+/- 0.8 [SD]), which differed significantly from the coronary flow reserve of the coronary arteries with obstructive disease, in which values ranging from 0.5 to 3.9 were found. Coronary arteries with a percentage area stenosis between 50% and 70% and a minimal luminal cross-sectional area between 2 and 4.5 mm2 differed significantly (p = .001), with respect to the coronary flow reserve, from coronary arteries with a percentage area stenosis in excess of 70% and a minimal luminal cross-sectional area less than 2 mm2. With the use of hemodynamic equations that describe the pressure loss over a stenosis, a theoretical pressure-flow relationship can be inferred that characterizes the severity of the stenosis. Based on this theoretical pressure-flow relationship, coronary arteries that have a limited coronary flow reserve and critical stenosis (distal coronary perfusion pressure below 40 mm Hg at coronary flow of 3 ml/sec) can be identified with high sensitivity (83%) and specificity (82%). Thus, in coronary artery disease the consequent reduction in coronary flow reserve can be predicted with reasonable accuracy by quantitative assessment of coronary artery dimensions