The pharmacist at Arnold Palmer Hospital, Wende Huehn-Brown, receives 6 requests

Question

The pharmacist at Arnold Palmer Hospital, Wende Huehn-Brown, receives 6 requests for prescriptions each hour, Poisson distributed. It takes her a mean time of 5 minutes to fill each, followinga negative exponential distribution. The waiting line table is provided below and also we know that Wa Click the icon to view the waiting line table. a) Using the table, the average number of prescriptions in the queueprescriptions (round your response to two decimal places). b) Using the given relationship, the average time a prescription spends in the queu minutes (round your response to two decimal places) c) Wende decides to hire a second pharmacist, Ajay Aggerwal, whom she went to school with and who operates at the same speed in filling prescriptions. Using the table, the average number of prescriptions in the queue- prescrptions round your response to two decimal places Using the given relationship, the average time a prescription spends in the queue after Wende has hired Ajay Agarwal-minutes (round your response to two decimal places).

Explanation / Answer

a)Arrival rate(lambda)= 6

service rate(mu)= 5minute i.e 60/5 per hour

= 12 /hr

Average number of prescritions in queue = lambda2/(mu(mu-lambda)

= 62/(12(12-6))

= 36/ (12*6)

= 0.50 person

b) Average time a perescription spends in the queue = L/lambda

= 0.5/6

= 0.083

i.e 0.083*60= 4.90 minutes.

c) Now the average number of prescriptions in the queue will be 0.33 ( from table we see that with 2 service channels and poission value 0.50)

d) Average time a perescription spends in the queue = L/lambda

= 0.33/6

= 0.055

i.e 0.055*60= 3.30 minutes.

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