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Five easy equations for patient flow through an emergency department.

Authors
  • Madsen, Thomas Lill1
  • Kofoed-Enevoldsen, Allan
  • 1 The Danish National Centre for Social Research, Sagasvej 18, Frederiksberg C, Denmark. [email protected] , (Denmark)
Type
Published Article
Journal
Danish medical bulletin
Publication Date
Oct 01, 2011
Volume
58
Issue
10
Identifiers
PMID: 21975152
Source
Medline
Language
English
License
Unknown

Abstract

Queue models are effective tools for framing management decisions and Danish hospitals could benefit from awareness of such models. Currently, as emergency departments (ED) are under reorganization, we deem it timely to empirically investigate the applicability of the standard "M/M/1" queue model in order to document its relevance. We compared actual versus theoretical distributions of hourly patient flow from 27,000 patient cases seen at Frederiksberg Hospital's ED. Formulating equations for arrivals and capacity, we wrote and tested a five equation simulation model. The Poisson distribution fitted arrivals with an hour-of-the-day specific parameter. Treatment times exceeding 15 minutes were well-described by an exponential distribution. The ED can be modelled as a black box with an hourly capacity that can be estimated either as admissions per hour when the ED operates full hilt Poisson distribution or from the linear dependency of waiting times on queue number. The results show that our ED capacity is surprisingly constant despite variations in staffing. These findings led to the formulation of a model giving a compact framework for assessing the behaviour of the ED under different assumptions about opening hours, capacity and workload. The M/M/1 almost perfectly fits our. Thus modeling and simulations have contributed to the management process. not relevant. not relevant.

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