Ted Glickman, the administrator at D.C. General Hospital emergency room faces the problem of providing treatment forpatients who arrive at different rates during the day. There are 4 doctors available to treat patients when needed. If not needed, they can be assigned other responsibilities (such as doing lab tests, reports, X-ray diagnoses) or else rescheduled to work at other hours. It is important to provide quick and responsive treatment, and Ted feels that, on the average, patients should not have to sit in the waiting area for more than5minutes before being seen by a doctor. Patients are treated on a first-come, first-served basis and see the first available doctor after waiting in the queue. The arrival pattern for a typical day is as follows: TimeArrival Rate9A.M.−3P.M.8patients/hour3P.M.−8P.M.3patients/hour8P.M.−midnight13patients/hour Arrivals follow a Poisson distribution, and treatment times,12minutes on the average, follow the negative exponential pattern.a) How many doctors should be on duty during each period to maintain the level of patient care expected?

a) The required number of doctors 9 A.M to 3P.M λ=8 patients/hourμ=4 patients/hour The utilization…

Answered: Ted Glickman, the administrator at…

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Ted Glickman, the administrator at D.C. General Hospital emergency room faces the problem of providing treatment for

patients who arrive at different rates during the day. There are 4 doctors available to treat patients when needed. If not needed, they can be assigned other responsibilities (such as doing lab tests, reports, X-ray diagnoses) or else rescheduled to work at other hours.

It is important to provide quick and responsive treatment, and Ted feels that, on the average, patients should not have to sit in the waiting area for more than

minutes before being seen by a doctor. Patients are treated on a first-come, first-served basis and see the first available doctor after waiting in the queue. The arrival pattern for a typical day is as follows:

Time	Arrival Rate
9 A.M.−3 P.M.	8	patients/hour
3 P.M.−8 P.M.	3	patients/hour
8 P.M.−midnight	13	patients/hour

Arrivals follow a Poisson distribution, and treatment times,

minutes on the average, follow the negative exponential pattern.

a) How many doctors should be on duty during each period to maintain the level of patient care expected?

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