Early Reservation for Follow-up Appointments in a Slotted-Service Queue

Shall Follow-up Appointments Be Booked in Advance? Appointment systems are ubiquitous, especially in healthcare. By looking into a large data set with over 1.6 million appointments, we observe that many doctors booked a follow-up appointment at the end of their meeting with their patients. This strategy ensures that the patients would follow up but at the risk that the patient may not show up and the appointment ends being wasted. We develop a slotted-service queue model to study if and when such a strategy should be used in three representative appointment systems, respectively. In an open access system, it is optimal to never use this strategy. In a traditional appointment system that allows patients to book in advance, it is optimal to apply this strategy to some patients. While in a hybrid system with both walk-in patients and patients with appointments, whether to use this strategy depends on the load balancing between the two patient queues.