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midterm2Sln_2010

# midterm2Sln_2010 - Operations Research II IEOR161...

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Operations Research II, IEOR161 University of California, Berkeley Midterm II, 2010 1. [15+15+10] Consider a queueing system consisting of 2 servers. Customers arrive according to a Poisson process with rate λ = 4 (per hour). An arriving customer requests server 1 with probability p = 0 . 3 and with probability 1 - p = 0 . 7 requests server 2. Service times of both servers are exponential with rate μ = 3. Each server works on one customer at a time and new customers wait in line for service if their server is busy. (a) Suppose there is one customer at each service desk. What is the expected time for both of these customers to be cleared? (b) Suppose that server 1 is busy. What is the probability that the customer being served by server 1 is cleared from the system before another customer for server 1 arrives? (c) Suppose both servers start idle. After 10 hours, we are told that 15 customers went to server 2 of which 5 still remain in the system. What is the expected number of customers for server 1 to arrive during this (10 hour) period?

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midterm2Sln_2010 - Operations Research II IEOR161...

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