Queuing Theory Application to Patient Waiting Time Reduction at the University of Calabar Teaching Hospital

Long patient waiting times remain a persistent challenge in Nigerian public hospitals, contributing to patient dissatisfaction and adverse health outcomes. This study applies queuing theory, specifically the M/M/1 and M/M/c models, to analyse patient flow at the outpatient department of the University of Calabar Teaching Hospital, located in Cross River State, South South Nigeria. Observational data were collected over eight weeks, covering patient arrival rates, service times, and the number of active service channels during morning and afternoon shifts. Performance measures including average queue length, mean waiting time, system utilization, and probability of idle servers were computed using queuing formulas and validated through simulation. Findings indicate that the current single-server configuration at the triage station generates average waiting times exceeding 45 minutes during peak hours, with server utilization rates above 90 percent, reflecting significant system congestion. The multi-server model demonstrates that adding two additional triage nurses reduces mean waiting time to under 12 minutes and brings utilization to a sustainable 65 percent. The study also recommends appointment scheduling as a complementary intervention. This research demonstrates the utility of operations research tools in solving real-world healthcare delivery problems in Nigeria and provides hospital administrators with evidence-based staffing recommendations. The methodology is replicable across similar tertiary health facilities in the South South zone. Keywords: queuing theory, patient waiting time, outpatient department, Calabar, healthcare operations