Performance evaluation of an appointment-based medical service system with no-shows and emergency arrivals

Abstract

In an appointment-based service system, patients usually experience two types of delays: appointment delay (virtual wait) and service delay (physical wait). Managers want to give patients more opportunities to make appointments and also want to increase the number of patients served. For this purpose, schedulers allow as many patients as possible to make appointments to wait virtually. Meanwhile, more patients are permitted to wait physically in the waiting room. Do these methods work? We define a discrete time tandem queueing system to analyse the performance measures (patients’ opportunities to make appointments, number of patients served, two waiting times, and utilization of the medical resources) in such a system. These performance measures are obtained by combining an absorbing Markov Chain and two embedded Markov Chains. The parameter sensitivity analysis suggests that increasing the number of patients waiting in the appointment queue and service queue cannot increase their opportunities to make appointments and to be served. Increasing the number of patients is detrimental to the service system. The comparative analysis is carried out to determine the proper model parameters for different management targets. A proper time between consecutive appointments can improve the utilization of medical resources, control patient flow, and increase patients’ access to services.