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Unformatted text preview: 2 . Repair times for either machine are exponential with rate μ. a. Define a continuoustime Markov chain to analyze this problem. Define the state space and specify the generator matrix Q. b. If machine 1 works for an average of 5 hours, machine 2 for 4 hours, and a repair takes an average of 1 hour, solve for the equilibrium distribution and find the proportion of time neither machine is working. 3. A barbershop with a single barber has room for at most two customers. Potential customers arrive at a Poisson rate of 3 per hour, and the service times are independent exponential random variables with mean 15 minutes. a. Find the average number of customers in the shop. b. Find the proportion of potential customers that enter the shop. c. If the barber could cut his mean service time down to 10 minutes, how much of an increase in business (in customers per hour) would he see?...
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This note was uploaded on 01/16/2011 for the course STAT 333 taught by Professor Chisholm during the Spring '08 term at Waterloo.
 Spring '08
 Chisholm

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