A Constrained-Flow Lens for Emergency Department Crowding and Ambulance Ramping: Analogy, queues and evidence

Abstract

Objective: To present a conceptual research note that integrates a constrained-flow analogy, queueing relationships and emergency-care evidence to support investigation of emergency department (ED) crowding and ambulance ramping.

Design: Evidence-informed conceptual research note.

Setting: Australian public hospitals, with Queensland examples where definitions are jurisdiction-specific.

Main outcome measures: Candidate measures of demand, census, time, utilisation, variability, boarding, patient off-stretcher time and safety.

Results: Bernoulli’s principle is retained only as an intuitive analogy for restrictions and upstream accumulation. Little’s law provides the principal descriptive relationship between average number, effective flow and time; Kingman’s approximation explains how high utilisation magnifies variability. Established input-throughput-output models and Australian evidence locate ambulance ramping within whole-of-hospital access block. Intervention evidence is mixed and does not support universal prescriptions.

Conclusions: The framework may translate visible congestion into measurable hypotheses, but it is not a predictive hydraulic model. Construct validation, retrospective analysis, queueing analysis, simulation and prospective testing are required before operational use.