The least number of doctors required during the 8 P.M.minusMidnightshift to meet

Question

The least number of doctors required during the 8 P.M.minusMidnightshift to meet the set waiting time goal is??????

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 5 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: Arrivals follow a Poisson distribution, and treatment times, 12 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? The least number of doctors required during the 9 A.M. - 3 P.M. shift to meet the set waiting time goal is .

Explanation / Answer

Solution:

a) For the lapse 9 a.m - 3 p.m:
= 6/60 = 0.1 patients/hr
= 4/12 = 0.333 pat/hr
p = / = 0.333/0.1 = 3.33 doctors

b) The least number of doctors required during the 8 P.M.minusMidnightshift to meet the set waiting time goal is
For the lapse 8 p.m:
= 13/60 = 0.217 patients/hr
= 4/12 = 0.333 pat/hr
p = / = 0.333/0.217 = 1.535 doctors

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