Application of Queuing Theory to Appointment Scheduling in Specialist Hospitals in Kano State

This study applies queueing theory to the design and evaluation of appointment scheduling systems in specialist hospitals in Kano State, North West Nigeria, addressing the persistent problem of excessive patient waiting times that reduce healthcare utilisation and patient satisfaction at referral facilities. Specialist hospitals in Kano, including Aminu Kano Teaching Hospital, operate under conditions of severely constrained specialist capacity relative to patient demand, making mathematically informed scheduling design an urgent management priority. Patient arrival data, appointment booking records, consultation duration observations, and clinic session schedules are collected from the general surgery, internal medicine, and ophthalmology outpatient clinics at two specialist hospitals over an eight-week observation period. The D/M/1, M/D/1, and M/G/1 queueing models are fitted to the observed arrival and service time distributions, and performance measures including mean waiting time, queue length, and server idle time are derived. Simulation using Arena discrete event simulation software is employed to evaluate the performance of alternative scheduling protocols, including fixed-interval scheduling, variable-interval scheduling, and no-show-adjusted overbooking algorithms. Results indicate that a variable-interval overbooking schedule calibrated to the empirically observed no-show rate of 22 percent reduces mean patient waiting time by 31 percent while maintaining specialist utilisation above 85 percent. The study provides a practical mathematical framework for hospital operations managers and health administration professionals. Keywords: queueing theory, appointment scheduling, specialist hospitals, discrete event simulation, Kano State