Specialty clinics provide specialized care for patients referred by primary care physicians, emergency departments, or other specialists. Urgent patients must often be seen on the referral day, whereas nonurgent referrals are typically booked an appointment for the future. To deliver a balanced performance, the clinics must know how much “appointment capacity” is needed for achieving a reasonably quick access for nonurgent patients. To help identify the capacity that leads to the desired performance, we model the dynamics of appointment backlog as novel discrete-time bulk service queues and develop numerical methods for efficient computation of corresponding performance metrics. Realistic features such as arbitrary referral and clinic appointment cancellation distributions, delay-dependent no-show behaviour, and rescheduling of no-shows are explicitly captured in our models. The accuracy of the models in predicting performance as well as their usefulness in appointment capacity planning is demonstrated using real data. We also show the application of our models in capacity planning in clinics where patient panel size, rather than appointment capacity, is the major decision variable.
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