Simplified Model of an Emergency Room. Let’s assume you want to model the cycle

Question

Simplified Model of an Emergency Room. Let’s assume you want to model the cycle times and bottlenecks in a hospital’s ER room. In this ER, all patients first go to the Triage station. From the Triage station, 40% of the patients are sent home. Those that are not sent home, the patients go to one of three departments in the ER, in equal amounts: Cardiac, Infections, or Broken Bones and Lacerations (BBL). From those three departments, 20% are sent home after treatment and 80% are sent to the ER Observation Department with other ER doctors take care of the patient. You’ve already decided to model each step in the process as a GGm queue. And, let’s assume you know the processing time for the station, the variability of that processing time, the variability of arrivals and departures from the queue. If on average 25 patients arrive per hour, what is the arrival rate to each of the following stations: a. Triage b. Cardiac c. Infections d. BBL e. ER Observation

Explanation / Answer

a) Arrival rate at Triage station = 25 patients per hour

Patients sent home = 25*40% = 10

Remaining patients go to the three departments in equal amounts = (25-10)/3 = 5 patients per hour

b) Arrival rate at Cardiac = 5 patients per hour

c) Arrival rate at Infections = 5 patients per hour

d) Arrival rate at BBL = 5 patients per hour

Patients sent home after treatment = 15*20% = 3

e) Arrival rate at ER Observation = 15-3 = 12 patients per hour

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