title: Five easy equations for patient flow through an emergency department.
abstract: BACKGROUND
  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.
  
  
  METHODS
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  The M/M/1 almost perfectly fits our. Thus modeling and simulations have contributed to the management process.
  
  
  BACKGROUND
  not relevant.
  
  
  BACKGROUND
  not relevant.
authors.affiliation: The Danish National Centre for Social Research, Sagasvej 18, Frederiksberg C, Denmark. thomas.lilll.madsen@gmail.com
authors.forename: Thomas Lill
authors.initials: TL
authors.lastname: Madsen
authors.forename: Allan
authors.initials: A
authors.lastname: Kofoed-Enevoldsen
mesh_terms: D003441:Crowding; D003718:Denmark; D004636:Emergency Service, Hospital / Q000458:organization & administration / Q000706:statistics & numerical data*; D006760:Hospitalization / Q000706:statistics & numerical data*; D006801:Humans; D007902:Length of Stay / Q000706:statistics & numerical data; D010361:Patients / Q000706:statistics & numerical data*; D013997:Time Factors