Application of Queuing Theory to Patient Flow Management at University of Nigeria Teaching Hospital, Enugu

Long patient waiting times at public teaching hospitals in Nigeria represent a critical barrier to healthcare access and a leading driver of patient dissatisfaction. This study applies queuing theory, specifically the M/M/s multi-server queuing model, to analyse and optimise patient flow in the outpatient department of the University of Nigeria Teaching Hospital in Enugu, South East Nigeria. Observational data on patient arrival times, registration durations, consultation lengths, and queue lengths are collected over a six-week period across morning and afternoon sessions. Arrival rates and service rates are estimated by fitting exponential distributions to inter-arrival and service time data, with goodness-of-fit confirmed using Kolmogorov-Smirnov tests. Model performance metrics including average queue length, mean waiting time, server utilisation, and system throughput are computed for current configurations and proposed alternatives. Results indicate an average waiting time of 47 minutes in the current two-doctor configuration, with server utilisation exceeding 89 percent during peak morning hours. Simulation of a three-doctor model reduces mean waiting time to 19 minutes and server utilisation to 68 percent, achieving a more sustainable service balance. The marginal cost of the additional physician is projected to be recovered through improved patient throughput within eight months. Keywords: queuing theory, M/M/s model, patient flow, UNTH Enugu, outpatient department.