Infinite-server queueing models of demand in healthcare: A review of applications and ideas for further work

Abstract

Despite the apparently unrealistic assumption of infinite resources, infinite-server queueing models have played a central role in the development of queueing theory and its applications. Healthcare modelling applications have certainly benefited from these models, where arguably their greatest importance has been to provide the basis for the analysis of "offered load" in systems with single or multiple nodes with multiple servers and timevarying arrivals. In this paper, we provide a review of major healthcare applications to date, identifying and consolidating the underpinning theoretical results and commenting on the nature of the applications. We conclude by identifying potential further healthcare applications, their relationships to existing theory and methods, and the need for new theory and methods, including the use of infinite-server models alongside other modelling methodologies.

Modeling COVID-19 hospital admissions and occupancy in the Netherlands

“…In a general setting, Bertsimas, Pauphilet, Stevens, & Tandon (2020) focuses on predicting arrival counts in health care. For a more extensive exposition of these types of queues in health care, we refer the reader to Worthington, Utley, & Suen (2020) .…”

“…(2020) uses such an model to quantify how flattening the curve affects peak demand for hospital beds. The application of infinite-server models, also in discrete time, is also discussed in Worthington et al. (2020) .…”

Modeling COVID-19 hospital admissions and occupancy in the Netherlands

“…For the special case of (continuous) time-dependent Poisson arrivals, the M t /G/∞ has well been analyzed with tractable results [2,8,9]; [18] uses such an M t /G/∞ model to quantify how flattening the curve affects peak demand for hospital beds. The application of infinite-server models, also in discrete time, is also discussed in [28]. As our goal is to predict the demand for beds without capacity constraints, the infinite-server assumption is appropriate, albeit we use a discrete-time version.…”

“…However, the paper does not involve short-term predictions. For a more extensive exposition of these types of queues in health care, we refer the reader to [28].…”

Designing optimal allocations for cancer screening using queuing network models

“…Infinite server queuing models [ 27 ] can be used as a more tractable approximation of finite server queues: lower bounds on congestion in finite and possibly saturating resource models are found by considering their infinite resource counterparts. Applications include modeling the number of inpatients on a ward [ 28 ] or in a network of hospital wards [ 29 ], traffic of patients in a hospital [ 30 ], and an emergency department with a view to quantifying the probability that patients must be diverted to another hospital [ 31 ].…”