C let pi j be the transition probability for the

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Unformatted text preview: 00 and a second one at 1:17 then she will not be able to get to sleep until at least 1:53, and it will be even later if there is another emergency before that time. (a) Compute the long-run fraction of time she spends sleeping, by formulating a renewal reward process in which the reward in the ith interval is the amount of time she gets to sleep in that interval. (b) The doctor alternates between sleeping for an amount of time si and being awake for an amount of time ui . Use the result from (a) to compute Eui . (c) Solve problem (b) by noting that the doctor trying to sleep is the same as chicken crossing the road in Exercise 2.33. 3.12. A worker has a number of machines to repair. Each time a repair is completed a new one is begun. Each repair independently takes an exponential amount of time with rate µ to complete. However, independent of this, mistakes occur according to a Poisson process with rate . Whenever a mistake occurs, the item is ruined and work is started on a new item....
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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