2004mt1

2004mt1 - Operations Research II University of California...

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Operations Research II University of California, Berkeley Spring 2004 Midterm 1 3 questions (45 points) + 1 bonus question (10 points). Any score of 45 or above will be regarded as a perfect score. 1. [10 points] A doctor has scheduled 2 appointments, one at 1pm and the other at 1:30pm. The lengths of time that appointments last are independent exponential random variables with mean 30. Assuming that both patients are on time, find the expected amount of time the 1:30 appointment spends at the doctor’s office. 2. [10 points]. Customers arrive at a two-server service station according to a Poisson process with rate λ . Whenever a new customer arrives, any customer that is in the system immedi- ately departs. A new arrival enters service first with server 1 and then with server 2. If the service times at the servers are independent exponentials with respective rates μ 1 and μ 2 , what proportion of entering customers completes their service with server 2?
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