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PS10 - 06 May 2009 IE 304 OPERATIONS RESEARCH III...

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06 May 2009 IE 304 OPERATIONS RESEARCH III: STOCHASTIC MODELS PS # 10 Question 1) A barbershop, operated by two barbers, has room for at most 3 customers. Potential customers arrive at a Poisson rate of 4 per hour and each barber works at an exponential rate of 3 services per hour. Set up the problem as a continuous time Markov Chain. Is it a birth and death process? What is: (a) The average number of customers in the shop? (b) The proportion of potential customers that enter the shop? (c) If there were three barbers in the barbershop, how much more business would be done? Question 2) Consider a network of three stations. Customers arrive at stations 1, 2, 3 in accordance with Poisson processes having respectively rate 5, 10, 15. The service times at the three stations are exponential with respective rates 10, 50, 100. A customer completing service at station 1 is equally likely to (i) go to station 2, (ii)go to station 3, or (iii) leave the system. A customer departing service at station 2 always goes to station 3. A departure from service at station 3 is equally likely to either go to station 2 or
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