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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 longrun 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).
 Spring '10
 DURRETT
 The Land

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