Our favorite ambulatory care pharmacist, Dr. Hoylman, has several patients that

Question

Our favorite ambulatory care pharmacist, Dr. Hoylman, has several patients that may call in to discuss their medication. Each call lasts an exponentially distributed length of time with a mean of 5 minutes. The time between calls is also exponentially distributed with a mean of 10 minutes. Currently, she has one pharmacy student take the calls.

a) Use Kendall’s notation to describe what type of queue this is.

b) What is the average waiting time when a patient calls?

c) What is the utilization of the pharmacy student?

Explanation / Answer

a) Given the characteristics, it is a M/M/1 queue with following characteristiccs

Arrival rate, = 1/interarrival time = 1/10 per minute = (1/10)*60 = 6 per hour

Service rate, = 1/service time = 1/5 = (1/5)*60 = 12 per hour

b) Average waiting time, Wq = /(*(-)) = 6/(12*(12-6)) = 0.0833 hour = 5 minutes

c) Utilization of the student = = / = 6/12 = 0.50

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