Analyzing GI/E_r/1 queues

In this paper we study a single-server system with Erlang-r distributed service times and arbitrarily distributed interarrival times. It is shown that the waiting-time distribution can be expressed as a finite sum of exponentials, the exponents of which are the roots of an equation. Under certain conditions for the interarrival-time distribution, this equation can be transformed to r contraction equations, the roots of which can be easily found by successive substitutions. The conditions are satisfied for several practically relevant arrival processes. The resulting numerical procedures are easy to implement and efficient and appear to be remarkably stable, even for extreme high values of r and for values of the traffic load close to 1. Numerical results are presented

Organizing Multidisciplinary Care for Children with Neuromuscular Diseases

The Academic Medical Center (AMC) in Amsterdam, The Netherlands, recently opened the `Children's Muscle Center Amsterdam' (CMCA). The CMCA diagnoses and treats children with neuromuscular diseases. These patients require care from a variety of clinicians. Through the establishment of the CMCA, children and their parents will generally visit the hospital only once a year, while previously they visited on average six times a year. This is a major improvement, because the hospital visits are both physically and psychologically demanding for the patients. This article describes how quantitative modelling supports the design and operations of the CMCA. First, an integer linear program is presented that selects which patients to invite for a treatment day and schedules the required combination of consultations, examinations and treatments on one day. Second, the integer linear program is used as input to a simulation to study to estimate the capacity of the CMCA, expressed in the distribution of the number patients that can be seen on one diagnosis day. Finally, a queueing model is formulated to predict the access time distributions based upon the simulation outcomes under various demand scenarios

Modelling activities in a Critical Care Unit

The Critical Care Unit (CCU) is the sector of the hospital where, as the name suggests, critically ill patients receive treatment. The main aim of this research is to identify and apply suitable Operational Research techniques to model patient flow in the CCU at the University Hospital of Wales, Cardiff. The Operational Research techniques employed in this thesis include queueing theory and simulation. These methods have been utilised previously in the field of healthcare with much success. The thesis begins by considering two aspects of queueing theory, namely batch service queueing theory and batch arrival queueing theory. The latter of these is utilised to model patient flow within the CCU. Although queueing theory may be used as a good approximation to activities in the Unit, it does not incorporate all aspects of real-life. Thus discrete-event simulation is suggested as an alternative approach. Two types of statistical analysis, CART and Regression, are applied to both length of stay and mortality variables. The results from these statistical tests are compiled and investigated in more depth. Finally, a discrete event simulation model is built in Visual Basic for Applications, for Microsoft Excel. This simulation model incorporates many of the complexities of a CCU, such as patient priority and cancellation of scheduled patients if all beds on the Unit are occupied. The model is then used to test various "what-if type" scenarios, including the possibility of funding additional beds, the concept of ring-fencing of beds for different levels of care, and the likely effect of reducing the impact of bed-blocking

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