The Emergency Department

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View from the Waiting Room

Problem: Many patients have complained that they are waiting too long in the emergency department, in some cases more than 5 hours. A fish tank has been installed at the request of the local politician, but the complaints keep coming in. You are asked to investigate. Having just read the first section of this collection, you decide to try out your new system dynamics software and build a simple stock and flow model. You start with a view from the walk-in patient’s perspective. From this viewpoint, the first stock (box) you draw is the number of people in the waiting room.

There is an inflow of arrivals and an outflow of patients who are assessed and treated.

Importance of the hour of day pattern in ED

The arrival pattern of patients over a typical day is known and the pattern seems quite consistent, with the busiest time of day from 10am to 10pm and a quiet period from midnight to 4 am. ED staff measure time in minutes and hours, and the pattern of activity varies depending on the time of day and the time of shift changes. One key function of the ED is to produce after-hours services to the community when other healthcare facilities are closed or inactive. Therefore we may sure that all our ED models include at least daily arrival patterns by hour of day. Sometimes we also include day of week and month of year effects if relevant to the question we are trying to answer. Note we can replicate this daily pattern by using the Time mod 24 function, when the simulation run units are in hours. Here is a table from a converter showing the repeating arrival pattern.

Fig. 1 - Arrivals per hour Insightmaker Converter [Source]

Simplest One Stock Model

Fig. 2 - Simplest ED Stock Flow Model [Source]

The outflow of patients treated depends on the number of clinical staff rostered on (12) and the average treatment time, the time it takes to complete assessment and treatment for each patient, say 0.25 hrs (15 minutes).

The model equations are:

  • Patients_in_waiting_room(t) = Patients_in_waiting_room(t - dt) + (arrivals - treated) * dt
    • INIT Patients_in_waiting_room = 0
    • INFLOWS:
      • arrivals = arrivals_per_hour
      • treated = patients_per_hour
  • arrivals_per_hour = GRAPH(mod (time,24))

(0.00, 10.0), (2.00, 10.0), (4.00, 10.0), (6.00, 20.0), (8.00, 40.0), (10.0, 35.0), (12.0, 40.0), (14.0, 35.0), (16.0, 50.0), (18.0, 40.0), (20.0, 60.0), (22.0, 50.0), (24.0, 10.0)

  • Ave_Treatment_Time_hrs = 0.25
  • No_of_staff_on = 12
  • patients_per_hour = No_of_staff_on/Ave_Treatment_Time_hrs

The Behaviour over time output graph

From running the simulation, we display arrivals per hour and the number of patients in the waiting room over 48 hours on an output graph.

Fig. 3 - Simulation Run Output of Simplest ED Model [Source]

The run of 48 hours shows the waiting room is empty from three AM till after lunch, about 20 people waiting at 6pm and a peak of 70 people in the waiting room just before midnight and clearing around 2am. Note that the stock of people in the waiting room looks like the inflow pattern for some but not all of the time.

Virtual “what-if” Experiments

Change the number of staff on over the day in a time of day graph to more closely match the pattern of arrivals. Cut back the staff on the night shift. Note the peak takes longer to clear if less staff are on the night shift. When is the best time to start the night shift?

Addition of People who Did Not Wait

Extending the Theory of Did Not Waits

Patient Flow is NOT Workflow

Emergency Department Treatment Spaces

Emergency Department Patient Flow Concept Map

Emergency Department Performance

Emergency Department Medical Imaging Interaction

More Complex ED Models

Responses to Service Work Pressure


Questions & Comments to Geoff McDonnell
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