A Data-Driven Model of an Appointment-Generated Arrival Process at an Outpatient Clinic

Abstract

We develop a high-fidelity simulation model of the patient arrival process to an endocrinology clinic by carefully examining appointment and arrival data from that clinic. The data include the time that the appointment was originally made as well as the time that the patient actually arrived, as well as if the patient did not arrive at all, in addition to the scheduled appointment time. We take a data-based approach, specifying the schedule for each day by its value at the end of the previous day. This data-based approach shows that the schedule for a given day evolves randomly over time. Indeed, in addition to three recognized sources of variability-(i) no-shows, (ii) extra unscheduled arrivals, and (iii) deviations in the actual arrival times from the scheduled times-we find that the primary source of variability in the arrival process is variability in the daily schedule itself. Even though service systems with arrivals by appointment can differ in many ways, we think that our data-based approach to modeling the clinic arrival process can be a guideline or template for constructing high-fidelity simulation models for other arrival processes generated by appointments.

Using Robust Queueing to Expose the Impact of Dependence in Single-Server Queues

“…Such negative dependence occurs when there is a specified number of arrivals in a long time interval, as in the queues with arrivals by appointment, where there are i.i.d. deviations about deterministic appointment times; e.g., see Kim et al (2017).…”

Robust heavy-traffic approximations for service systems facing overdispersed demand

“…Several conclusions are drawn from these tables. Observe that the heavy-traffic approximations based on the Gaussian random walk, (24) and (25), capture the right order of magnitude for both EQ n and Var Q n . However, the values are off, in particular for small s n and relatively low ρ n := E[A n ]/s n .…”

“…Namely, a growing number of empirical studies show that the variance of demand typically deviates from the mean significantly. Recent work [24, 26] reports variance being strictly less than the mean in health care settings employing appointment booking systems. This reduction of variability can be accredited to the goal of the booking system to create a more predictable arrival pattern.…”

A robust queueing network analyzer based on indices of dispersion

“…There is extensive literature on the applications of queueing network models to service systems. For example, see Sauer and Chandy (1981) for a review of applications in computer networks, see Banerjee et al (2015), Freund et al (2017) and Ozkan and Ward (2017) for examples in ride‐sharing economies and see Chan et al (2016), Creemers and Lambrecht (2011), Dai and Shi (2019), Kim et al (2018) and Zacharias and Armony (2016) for healthcare‐related applications.…”