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4.35. Customers arrive at a carnival ride at rate . The ride takes an exponential amount of time with rate µ, but when it is in use, the ride is subject to
breakdowns at rate ↵. When a breakdown occurs all of the people leave since
they know that the time to ﬁx a breakdown is exponentially distributed with
rate . (i) Formulate a Markov chain model with state space { 1, 0, 1, 2, . . .}
where 1 is broken and the states 0, 1, 2, . . . indicate the number of people
waiting or in service. (ii) Show that the chain has a stationary distribution of
the form ⇡ ( 1) = a, ⇡ (n) = b✓n for n 0.
4.36. Customers arrive at a twoserver station according to a Poisson process
with rate . Upon arriving they join a single queue to wait for the next available
server. Suppose that the service times of the two servers are exponential with
rates µa and µb and that a customer who arrives to ﬁnd the system empty
will go to each of the servers with probability 1/2. Formulate a Markov chain
model for this system with state space {0, a, b, 2, 3, . . .} where the s...
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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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