Where: F3.20 (KdVI)
An intensive care unit (ICU) is a crucial and limited resource in a hospital which is affected by uncertainty and
variability, and often operates close to capacity. Queueing theory has been used to model the bed occupancy in ICUs for the last 21 years, with a particular focus on using M/M/· and M/P H/· queueing models. These queueing models assume that the arrival process (patient arrivals) is a Poisson process, the service times (length of stay) follow an exponential or Phase-Type distribution, and most crucially that the arrival process and service times are independent of each other. However, Varney et al. showed that there is some dependence structure between the arrival process and the service times in an ICU. Without independence between the arrival process and service times, standard queueing models become invalid.
We aim to provide a more principled approach to modelling bed occupancy in ICUs using quasi-birth-and-death processes (QBDs). By allowing the phases of the arrival process and the service times to interact with each other, QBDs provide the flexibility to model a queueing system with dependence between the arrival process and the service times. In this talk, we describe the approaches we have taken to develop model-fitting procedures for QBD models, with a particular focus on fitting suitable QBD models to data from an intensive care unit.
Sarah James, University of Adelaide, Australia, firstname.lastname@example.org
Nigel Bean, University of Adelaide, Australia, email@example.com
Jono Tuke, University of Adelaide, Australia, firstname.lastname@example.org