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.
 Spring '09
 RESNIK

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