Modelling critical care unit activities through queueing theory

Critical Care Units (CCUs) are one of the most complex and expensive of all medical resources and hospital managers are challenged to meet the demand for critical care services with adequate capacity. The pressure on critical care beds is continuously increasing as new medical equipment provides the opportunity to save more patients lives. It is therefore crucial that beds are managed well and used efficiently. This thesis describes two major projects, the first undertaken in conjunction with the CCU at the University Hospital of Wales in Cardiff (UHW); and the second with two CCUs from the Aneurin Bevan Health Board. In the first project data has been analysed to determine the flow of patients through the Unit. Admissions to CCUs were categorised under two headings: emergency, and elective. The length of stay in the CCU is heavily dependent on the admission category. In this thesis, both computer simulation and theoretical queueing models have been considered, which show how improvements in bed management may be achieved by considering these two categories of patients separately. The vast majority of previous literature in this field is concerned only with steady-state conditions, whereas in reality the processes are time-dependent. This thesis goes some way to addressing this deficiency. The second project relates to work undertaken with managers from the Royal Gwent Hospital in Newport and at the Nevill Hall Hospital in Abergavenny. Data from both hospitals have been analysed to define arrival and service processes. A state-dependent theoretical queueing model has been considered which has been used to investigate the significance of combining the two units. The model has been also utilised to advise on the number of beds the new combined unit should have in order to satisfy targets quoted by the hospital managers. In the final part of the thesis, consideration has been given to the impact of collaboration, or lack thereof, between hospitals using a game theoretical approach. The effect of patient diversion has been studied. To formally investigate the impact of patients transfers, a Markov chain model of the two CCUs has been set-up, each admitting two arrival streams: namely, their own patients and transfers from other hospital. Four different models were considered and for each model the effect of targets, demand and capacity were studied. The efficiency of a system which degrades due to selfish behaviour of its agents has been measured in terms of Price of Anarchy

Measuring the price of anarchy in critical care unit interactions

Hospital throughput is often studied and optimised in isolation, ignoring the interactions between hospitals. In this paper, critical care unit (CCU) interaction is placed within a game theoretic framework. The methodology involves the use of a normal form game underpinned by a two-dimensional continuous Markov chain. A theorem is given that proves that a Nash Equilibrium exists in pure strategies for the games considered. In the United Kingdom, a variety of utilisation targets are often discussed: aiming to ensure that wards/hospitals operate at a given utilisation value. The effect of these target policies is investigated justifying their use to align the interests of individual hospitals and social welfare. In particular, we identify the lowest value of a utilisation target that aligns these

Bed management in a critical care unit

One of the main problems facing hospital managers is in coping with the variability in demand for the services that the hospital provides. This is particularly the case in the Critical Care Unit (CCU), where inability to provide adequate facilities on demand can lead to serious consequences. Admissions to CCUs may be categorized under two headings: unplanned (emergency) and planned (elective). The length of stay (LoS) in the CCU is heavily dependent on the admission category: unplanned admissions have a much longer LoS on average than elective patients. In this paper, we propose a mathematical model that shows how improvements in bed management may be achieved by distinguishing between these two categories of patients. The vast majority of previous literature in this field is concerned only with steady-state conditions, whereas in reality, activities in virtually all hospital environments are very much time dependent. This paper goes some way to addressing this problem

Mathematical modelling of patient flows to predict critical care capacity required following the merger of two district general hospitals into one

There is both medical and political drive to centralise secondary services in larger hospitals throughout the National Health Service. High-volume services in some areas of care have been shown to achieve better outcomes and efficiencies arising from economies of scale. We sought to produce a mathematical model using the historical critical care demand in two District General Hospitals to determine objectively the requisite critical care capacity in a newly built hospital. We also sought to determine how well the new single unit would be able to meet changes in demand. The intention is that the model should be generic and transferable for those looking to merge and rationalise services on to one site. One of the advantages of mathematical modelling is the ability to interrogate the model to investigate any number of different scenarios; some of these are presented