It is a goal universally acknowledged that a healthcare system should treat its patients –
and especially those in need of critical care – in a timely manner. However, this is
often not achieved in practice, particularly in state-run public healthcare systems that
suffer from high patient demand and limited resources. In particular, Accident and
Emergency (A&E) departments in England have been placed under increasing pressure,
with attendances rising year on year, and a national government target whereby 98% of
patients should spend 4 hours or less in an A&E department from arrival to admission,
transfer or discharge.
This thesis presents techniques and tools to characterise and forecast patient arrivals,
to model patient flow and to assess the response-time impact of different resource
allocations, patient treatment schemes and workload scenarios.
Having obtained ethical approval to access five years of pseudonymised patient timing
data from a large case study A&E department, we present a number of time series
models that characterise and forecast daily A&E patient arrivals. Patient arrivals are
classified as one of two arrival streams (walk-in and ambulance) by mode of arrival.
Using power spectrum analysis, we find the two arrival streams exhibit different statistical
properties and hence require separate time series models. We find that structural
time series models best characterise and forecast walk-in arrivals, but that time series
analysis may not be appropriate for ambulance arrivals; this prompts us to investigate
characterisation by a non-homogeneous Poisson process.
Next we present a hierarchical multiclass queueing network model of patient flow in
our case study A&E department. We investigate via a discrete-event simulation the
impact of class and time-based priority treatment of patients, and compare the resulting
service-time densities and moments with actual data. Then, by performing bottleneck
analysis and investigating various workload and resource scenarios, we pinpoint the
resources that have the greatest impact on mean service times.
Finally we describe an approximate generating function analysis technique which efficiently
approximates the first two moments of customer response time in class-dependent
priority queueing networks with population constraints. This technique is applied to
the model of A&E and the results compared with those from simulation. We find good
agreement for mean service times especially when minors patients are given priority
