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Unformatted text preview: 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 to (i) go to station 2, (ii)go to station 3, or (iii) leave the system....
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This note was uploaded on 07/30/2009 for the course INDUSTRIAL 304 taught by Professor Temeldursun during the Spring '09 term at Boğaziçi University.
- Spring '09
- Operations Research