Petri Nets Validation of Markovian Models of Emergency Department Arrivals

International audienceModeling of hospital’s Emergency Departments (ED) is vital for optimisation of health services offered to patients that shows up at an ED requiring treatments with different level of emergency. In this paper we present a modeling study whose contribution is twofold: first, based on a dataset relative to the ED of an Italian hospital, we derive different kinds of Markovian models capable to reproduce, at different extents, the statistical character of dataset arrivals; second, we validate the derived arrivals model by interfacing it with a Petri net model of the services an ED patient undergoes. The empirical assessment of a few key performance indicators allowed us to validate some of the derived arrival process model, thus confirming that they can be used for predicting the performance of an ED

Advanced capabilities for materials modelling with Quantum ESPRESSO

Quantum ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudo-potential and projector-augmented-wave approaches. Quantum ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement theirs ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software

A Markovian canonical form of second-order matrix-exponential processes

Besides the fact that - by definition - matrix-exponential processes (MEPs) are more general than Markovian arrival processes (MAPs), only very little is known about the precise relationship of these processes in matrix notation. For the first time, this paper proves the persistent conjecture that - in two dimensions - the respective sets, MAP(2) and MEP(2), are indeed identical with respect to the stationary behavior. Furthermore, this equivalence extends to acyclic MAPs, i.e., AMAP(2), so that AMAP(2)[reverse not equivalent]MAP(2)[reverse not equivalent]MEP(2). For higher orders, these equivalences do not hold. The second-order equivalence is established via a novel canonical form for the (correlated) processes. An explicit moment/correlation-matching procedure to construct the canonical form from the first three moments of the interarrival time distribution and the lag-1 correlation coefficient shows how these compact processes may conveniently serve as input models for arrival/service processes in applications.

Vähittäiskauppiaitten yhteiset liikeyritykset meillä ja muualla

In this article we define the classes of bilateral and multivariate bilateral matrix-exponential distributions. These distributions have support on the entire real space and have rational moment-generating functions. These distributions extend the class of bilateral phasetype distributions of [1] and the class of multivariate matrix-exponential distributions of [9]. We prove a characterization theorem stating that a random variable has a bilateral multivariate distribution if and only if all linear combinations of the coordinates have a univariate bilateral matrix-exponential distribution. As an application we demonstrate that certain multivariate disions, which are governed by the underlying Markov jump process generating a phasetype distribution, have a bilateral matrix-exponential distribution at the time of absorption, see also [4].</jats:p