Approximate Queueing Network Analysis of Patient Treatment Times

Abstract

We develop an approximate generating function analysis (AGFA) technique which approximates the Laplace transform of the probability density function of customer response time in networks of queues with class-based priorities. From the approximated Laplace transform, we derive the first two moments of customer response time. This technique is applied to a model of a large hospital's Accident and Emergency department for which we obtain the mean and standard deviation of total patient service time. We experiment with different patient-handling priority schemes and compare the AGFA moments with the results from a discrete event simulation.

Operations research/management contributions to emergency department patient flow optimization: Review and research prospects

“…Au et al (2009) use a six-hour moving average to represent time-dependency in an M/M/s model for predicting overflow. Au-Yeung et al (2007) develop a queueing model with an approximate generating function analysis, designed to accommodate a larger state space than traditional models. This is modeled with a network of M/M/s queues where patients are identified by arrival and acuity.…”

Modeling and analysis of work flow and staffing level in a computed tomography division of University of Wisconsin Medical Foundation

“…Green et al [5] considers significant variation of patient arrival rates in the ED and provides staffing patterns based on a queueing model to reduce the number of patients who leave without being seen. In order to alleviate the state space explosion problem in queueing network, Au-Yeung et al [6] develops an approximate generating function analysis (AGFA) technique to approximate the mean and variance of response time in queueing network with blocking and priorities. Queueing models are also used in de Bruin et al [7] to investigate the bottlenecks in the emergency care chain of cardiac in-patient flow and provide insight of the relation between variation and system performance.…”

Modeling and analysis of care delivery services within patient rooms

“…(13) (14) (15) Therefore, the steady state probabilities can be obtained by solving the equation. Since we consider an irreducible Markov chain with finite number of states, there exists a unique steady state solution.…”