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

Abstract

We study how to manage returning customers in an appointment-based slotted-service queue with the goal of maximizing service volume. Returning customers prefer to be served by the same server that they visited in their previous visit. Applications of this model include a whole host of medical clinics, and lawyers, Councillors, tutors, and government officials who deal with the public. We consider a simple strategy that a service provider may use to reduce balking among returning customers — designate some returning customers as high-priority customers. These customers are placed at the head of the queue when they call for a follow-up appointment. In an appointment-based system, this policy can be implemented by booking a high-priority returning customer's appointment right before she leaves the service facility. We focus on a need-based policy in which the decision to prioritize some customers depends on their return probability. We analyze two systems, one in which the size of the waiting room is limited, and another in which it is not. We show that with limited waiting-room, a service system should not prioritize some returning customers in order to maximize the throughput rate. However, it is always optimal to prioritize some customers in the system with no limit on the waiting room. In those systems, we prove that the throughput rate is a quasi-concave function of the threshold under the assumption that returning customers see time averages (RTA). These findings will allow service systems to determine optimal operating policies that are both easy to implement and provably optimal.