SHOW ALL WORK The Pediatric ED is currently organized so that all patients regis
ID: 394439 • Letter: S
Question
SHOW ALL WORK
The Pediatric ED is currently organized so that all patients register through an initial check-in process. At his or her turn, each patient is seen by a doctor and then exits the process, either with a prescription or with admission to the hospital. Currently, 55 people per hour arrive at the ED, 10% of whom are admitted to the hospital. On average 7 people are waiting to be registered and 34 are registered and waiting to see a doctor. The registration process takes, 4 minutes per patient. Among patients who receive prescriptions average time spent with a doctor is 10 minutes. Among those admitted to the hospital, average time is 30 minutes. Assume that the process is stable, meaning that average inflow rate equals average outflow rate and answer questions 1, 2, and 3.
1. On average, how long does a patient spend in the ED?
2. On average, how many patients are being examined by Doctors?
3. On average how many patients are there in the ED?
Explanation / Answer
Data provided:
No. of people arriving in ED / hour = 55
No. of people admitted to hospital / hour = 10% of people arrived in ED ~= 6
No. of people waiting to be registered = 7
No. of people registered but waiting to see the doctor = 34
Registration process = 4 mins/patient
No. of patients registered /hour = 60/4 = 15
Avg time with doctor for patient getting prescription = 10 mins
No. of patients given prescription meeting doctor/ hour = 60/10 = 6
Avg time with doctor for patient admitted to hospital = 30 mins
No. of patients admitted meeting doctor / hour = 60/30 = 2
Average inflow = Average outflow = 55/hour
1. on an average the patient with prescription and patient admitted to hospital take different time assuming there is no waiting time
For patient with prescription = 4 min for regsitration and 10 min for prescription
For patient admitted = 4 min for regsitration and 30 min with doctor
No. of patient admitted every hour = 6 and no. of patient given prescription every hour = 55-6 =49
So the average time a patient spends in ED = (time for prescription patient +time for admitted patient )/total no. of patients in an hour = (49*14 + 6 *34)/55 = 16.2 mins
assuming no waiting time , average time patient spends in ED = 16.2 mins
Assuming max waiting time in regsitration , average time patient spends in ED = 6*4 + 16.2 =40.2 mins ( 7th person waiting will have to wait for 4min registration of all 6 people ahead)
Assuming max waiting time to see doctor , average time patient spends in ED = 33*10 +16.2 = 5.7 hours (here all 33 patients are waiting for a prescription)
2. On an average 10% patient have to be admitted every hour so 49 patients have to be given prescription and 6 patients have to be admitted.
Time taken by doctor to examine all this 55 patients= 49*10 + 6 *30=670 mins
in 670 mins, 55 patients are examined
In 1 hour, on an average no. of patients examined by the doctor are = 55*60 /670 = 6
3. On an average , no. of patients in the ED are = no. of patients arrived + no. of patients waiting for regsitration + no. of patients waiting for doctor + patient examined ( assuming only 1 doctor)
= 55+ 7 + 34 +1 = 97
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