Appointment-driven queueing systems with non-punctual customers

Information Systems and Operations Management 

Intervenant: Oualid Jouini (Central Supelec)

Salle Bernard Ramanantsoa 

Abstract

We consider a healthcare queueing system where a finite number of patients arrive over time to receive service. Arrivals are driven by appointments, with a scheduled appointment time associated with each patient. However, patients are not necessarily punctual and may arrive either earlier or later than their scheduled appointment times or may not show up at all. Arrival times relative to scheduled appointments are random. Patients are not homogeneous in their punctuality and show-up behavior. We develop both exact and approximate approaches for characterizing the distribution of the number of patients seen by each arrival. We show how this can be used to obtain the distribution of waiting time for each patient. We prove that the approximation provides an upper bound for the expected waiting time when non-punctuality is uniformly distributed. We also examine the impact of non-punctuality on system performance. In particular, we prove that non-punctuality deteriorates waiting time performance regardless of the distribution of non-punctuality. In addition, we illustrate how our approach can be used to support individualized appointment scheduling.