Queueing Systems with Appointment-Driven Arrivals, Non-Punctual Customers, and No-Shows

Abstract

We consider queueing systems where a finite number of customers arrive over time to a service system, consisting of either a single or multiple servers. The arrival of customers is driven by appointments, with a scheduled appointment time associated with each customer. However, customers are not necessarily punctual and may arrive either earlier or later than their scheduled appointment times. Customers may also not show up altogether. The arrival times of customers (relative to their scheduled appointments) and their service times are both stochastic. Customers are not homogeneous in their punctuality, show-up probabilities, and time between previous and subsequent appointments, which may vary from customer to customer. We develop an exact analytical approach to obtain various performance measures of interest and illustrate the usefulness of the approach by describing numerical results that examine the impact of not accounting for non-punctuality and no-shows. We also illustrate how our approach can be used to support individualized appointment scheduling, and show how such a scheduling scheme can significantly outperform schemes where all appointment times are equally spaced.