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Students arrive one at a time, completely at random, to an advice clinic at a rate of 10 per hour. Students take on average 5 minutes of advice but there is wide variation in the time they need; this variation may be well modeled by the exponential distribution.
a. Assume there is only one advisor serving in the clinic. Find the following expected measures of performance for this system: the expected time in the clinic, the expected time in the queue for advice, the expected number of students in the clinic, and the expected number of students waiting for advice.
b. Again assuming one advisor, what is the probability that there are more than ten students in the clinic at a random point in time? What is the probability that the time spent in the clinic exceeds 30 minutes?
c. Now suppose that a second advisor is hired. Repeat your answer for a. What are the advisors’ utilizations? Would you recommend this second advisor is hired?
d. What are some ways that the advice clinic could improve students’ experiences in the advice clinic without hiring more staff?
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