Probability Seminar Charles-Edouard Bréhier (Claude Bernard University Lyon 1)

Efficient sampling for the invariant distributions of SPDEs, 31st October, at 10:00A.M., F1.15 (KdVI)

Dear all,

After a longer summer break we are back with two SPIP talks in October.

Our first speaker is Sarah James from the University of Adelaide. Sarah is doing her PhD under the supervision of Professor Nigel Bean and is working on statistical methods for queueing systems. She is visiting for Monday and Tuesday (21.10-22.10) and will be happy to meet people from the community here.

*Title*: Modelling intensive care units using quasi-birth-and-death processes
*Time*: 14:00 on Tuesday October 22
*Location*: 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.

Information about SPIP talks can also be found on the website: . If you would like to give a talk yourself or making a proposal for a speaker, please contact the organizers, we are happy to hear from you!

Hope to see you!

Mariska Heemskerk
Sven Karbach