Application of queueing theory in the bed allocation policy of a hospital intensive care unit

Masocha, Vusani
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An intensive care unit of a hospital receives critically ill patients at any given time. If no proper management of the flow of patients is done, a dire situation will be the order of day. This study has explored the problem of determining an optimal number of Intensive Care Unit (ICU) beds in such away that a certain level of service set is achieved. The purpose of the research has been to assess the patients flow in and out of the ICU in order to identify the best queueing system. This research work has found that patient inter-arrival times can be modelled using an exponential distribution although the lognormal distribution provides a better fit. Also the waiting times possibly follow an exponential distribution. On the basis of the Akaike Information Criterion and Bayes Information Criterion, it was found that the waiting times are best modelled using a Gamma distribution. The length of stay in the ICU by patients also can be modelled by an exponential distribution. The lognormal is however a better distribution at modelling the length of stay times. The two queueing models were compared. Another dimension explored in the analysis was to check for factors that impact on the length of stay of patients in an ICU. It was found that type of insurance and admission type (which is the nature of the illness) were the only two covariates that signficantly impacted on the length of stay. The research work winds up by giving recommendations, particularly on the need to replicate a similar study at an ICU in a health facility in South Africa
A research report submitted to the Faculty of Science, University of the Witwatersrand, in partial fulfillment of the requirements for the degree of Masters of Science (by Coursework and Research), 2021