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 than4minutes 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? The least number of doctors required during the 9A.M.−3P.M. shift to meet the set waiting time goal is▼ 4231.The least number of doctors required during the 3P.M.−8P.M. shift to meet the set waiting time goal is▼ 4321.The least number of doctors required during the 8P.M.−Midnightshift to meet the set waiting time goal is▼ 3124.b) What condition would exist if only one doctor were on duty between9 A.M.and3 P.M.? A.Sinceλ>μ,the line would back up indefinitely. B.Sinceλ<μ,the line would back up indefinitely. C.Sinceλ>μ,the average wait time would increase slightly. D.Sinceλ<μ,the average wait time would increase slightly.

Answered: a) How many doctors should be on duty…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 18P

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Question

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?

The least number of doctors required during the 9

A.M.−3

P.M. shift to meet the set waiting time goal is

▼

The least number of doctors required during the 3

P.M.−8

P.M. shift to meet the set waiting time goal is

▼

The least number of doctors required during the 8

P.M.−Midnight

shift to meet the set waiting time goal is

▼

b) What condition would exist if only one doctor were on duty between

9 A.M.

and

3 P.M.?

Since

λ>μ,

the line would back up indefinitely.

Since

λ<μ,

the line would back up indefinitely.

Since

λ>μ,

the average wait time would increase slightly.

Since

λ<μ,

the average wait time would increase slightly.

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