Simulation of Queueing Systems in Primary Healthcare Centres in Ogun State Using Mathematical Models

This study models and simulates queueing dynamics in primary healthcare centres in Ogun State, South West Nigeria, applying classical queueing theory to assess service efficiency and identify bottlenecks in patient flow. Long waiting times at public health facilities represent a persistent barrier to healthcare utilisation in Nigeria, and mathematical modelling offers a rigorous basis for evaluating service reconfiguration options without the cost and disruption of physical trials. Data on patient arrival rates, consultation durations, and service channel configurations are collected through direct observation and time-motion studies conducted over six weeks at three primary healthcare centres in Abeokuta South Local Government Area. The M/M/1 and M/M/c queueing models are applied to characterise single-server and multi-server scenarios, respectively, and the resulting theoretical performance measures including mean queue length, mean waiting time, and server utilisation are computed and compared against observed values. Discrete event simulation is subsequently employed to model more complex, non-stationary arrival patterns that depart from the Poisson assumption. Results indicate that the facilities operate at server utilisation rates exceeding 85 percent during peak morning hours, resulting in mean waiting times of approximately 47 minutes, substantially above acceptable benchmarks. Adding a second consultation room to the highest-volume facility is projected to reduce mean waiting time by 38 percent. Keywords: queueing theory, M/M/c model, healthcare simulation, primary healthcare, Ogun State