COMPARATIVE ANALYSIS ON QUEUING THEORY MODELS GENERATED AMONG PATIENTS ON EMERGENCY AT UNIVERSITY TEACHING HOSPITAL AND ADEOYO HOSPITAL IBADAN

This study presents a comparative analysis of queuing models applied to emergency units of the University College Hospital (UCH) and Adeoyo Maternity Teaching Hospital, both located in Ibadan, Nigeria. The research aimed to evaluate patient flow, service efficiency, and waiting times using queuing theory as a framework for performance improvement. Data were collected through direct observation and hospital records over a three-week period. The study employed both single-server (M/M/1) and multi-server (M/M/c) queuing models under the First-Come-First-Served (FCFS) discipline, with analyses conducted using R statistical software. Results revealed that UCH recorded a higher traffic intensity (1.685) compared to Adeoyo Hospital (1.525), indicating a greater patient load and congestion at UCH. The optimal configuration for UCH was found to be the M/M/3 model, where service utilization averaged 56.2%, effectively balancing staff efficiency and patient waiting time. Conversely, Adeoyo achieved optimal performance under an M/M/2 system with a service utilization rate of 75.2%, ensuring efficient resource use without underutilization. The average patient inter-arrival time across both hospitals was 2.395 minutes, while mean service duration was 8.7 minutes. Findings suggest that both hospitals operate effectively under the FCFS discipline but could further improve efficiency through dynamic resource allocation and priority-based patient triage. The study concludes that queuing theory provides a valuable tool for healthcare administrators to optimize service delivery, reduce patient waiting times, and enhance overall satisfaction in emergency departments. Keywords: Queuing Theory, Emergency Unit, Healthcare Efficiency, Patient Flow, Service Utilization, Hospital Management