ex-8 - Spring 2011 OR3510/5510 Problem Set 8 When this is...

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Spring 2011 OR3510/5510 Problem Set 8 When this is due–return to the usual routine: Due April 4. We return to the Monday to Monday cycle. Reading: We have finished the Poisson process and variants in Chapter 5 and are now concen- trating on continuous time Markov chains in Chapter 6. (1) Two machines are maintained by a single repairman. Machine i functions for an exponential time with rate μ i before breaking down, i = 1 , 2 . The repair times (for either machine) are exponential with rate μ . Can we analyze this as a birth and death process? If so, what are the parameters? If not, how can we analyze it? (Hint: Make the state space correspond to (# machines running, state of the repairman–idle, working on 1 or working on 2). (2) There are N individuals in a population, some of whom have a certain infection that spreads as follows. Contacts between two members of this population occur in accordance with a Poisson process having rate λ . When a contact occurs, it is equally likely to involve any
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This note was uploaded on 09/17/2011 for the course ORIE 3510 taught by Professor Resnik during the Spring '09 term at Cornell.

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