Queueing models for appointment-driven systems

Abstract

Many service systems are appointment-driven. In such systems, customers make an appointment and join an external queue (also referred to as the "waiting list"). At the appointed date, the customer arrives at the service facility, joins an internal queue and receives service during a service session. After service, the customer leaves the system. Important measures of interest include the size of the waiting list, the waiting time at the service facility and server overtime. These performance measures may support strategic decision making concerning server capacity (e.g. how often, when and for how long should a server be online). We develop a new model to assess these performance measures. The model is a combination of a vacation queueing system and an appointment system.

Appointment Capacity Planning in Specialty Clinics: A Queueing Approach

“…More similar to our research are the studies by Jiang et al (2012), Creemers and Lambrecht (2010), Kortbeek et al (2014), Green and Savin (2008), and Liu and Ziya (2014). Jiang et al (2012) propose an M/D/1 queue -with Poisson (M ) arrivals and deterministic (D) service times -with state-dependent balking as a suitable model for specialty clinics.…”

“…However, they do not consider no-shows and provide only partial characterization of the model. Considering cyclic appointment systems, Creemers and Lambrecht (2010) and Kortbeek et al (2014) develop two-time scale queueing models, representing the daily evolution of the appointment backlog as well as the minute by minute dynamics of the clinic sessions. Neither of these studies considers clinic appointment cancellations and rescheduling of no-shows.…”

“…The above contributions have been facilitated by using discrete-time (DT) models rather than continuous-time (CT) models used by Green and Savin (2008), Creemers and Lambrecht (2010) and Jiang et al (2012). Apart from simplifying the analysis to a great extent, DT models, we believe, provide a more realistic representation for the dynamics of the specialty clinics.…”

An advanced queueing model to analyze appointment-driven service systems

“…Of particular interest is the distribution of the number of customers in the queue at the start of a service session because it indicates the probability of having to serve a certain number of customers during a given service session. [4] link this information to an "appointment system" (for a review of appointment systems refer to [3] among others) and create an appointment-driven queueing system that allows the analysis of appointment-driven systems as a whole. More specifically, an appointmentdriven queueing system analyzes: (1) waiting list performance measures (by means of the CAS); (2) server performance (e.g.…”

“…CAS have been studied in [4]. In their work, [4] propose a CAS (which they refer to as an AMQ; an Appointment Making Queue) in which arrivals are allowed to take place at any moment in time. Moreover, they assume interarrival times to be exponentially distributed.…”